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In KSP, there are many terms pertaining to orbiting and physics that often can be confusing. Consider this a cheat sheet to help you get started down the road to being a full fledged astronaut!
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In to KSP, there are many terms pertaining to orbiting and physics that often can be confusing to non-technicians. In addition, various other scientific terms and abbreviations are used to describe common terms.
  
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This sheet is designed as a concise lookup table of necessary terms to help you get started down the road to being a full fledged astronaut!
  
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== Mathematics ==
  
== Helpful Terms ==
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<div style="float:right;">[[File:cartesian.svg|thumb|upright|left|Cartesian coordinate system - Uses rectangular coordinates]][[File:polar.svg|thumb|upright|Polar (spherical) coordinate system - Uses only angles and one length]]</div>
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;Elliptical
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:Oval shaped, often in reference to your orbit.
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;Hyperbolic
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:Open smooth curve, often in reference to escape trajectories.
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;Normal vector
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:A vector perpendicular to a plane. (Usually the direction of the north pole if you are in an equatorial orbit.)
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;Scalar
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:A single value without a direction. Scalars are usually followed by a unit of measurement that tells what the scalar's dimension is. eg 3&nbsp;m/s, 3&nbsp;m,3&nbsp;s are scalar: they have units which denote speed, length/distance, and time respectively, but have no direction.
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;Vector
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:A set of a direction and a value. eg. heading (direction) and speed together give a velocity. How a vector is expressed depends on what the coordinate system is, and how many dimensions are taken into consideration. <35°, 12> is a two dimensional polar vector, where <14, 9, -20> is a three dimensional Cartesian vector. There are other coordinate systems but these are the most utilized.
  
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:<35°, 12> looks like an arrow which is 12 units long, starting from the origin (zero, angle does not matter because it is a point with no length) and ending at a point 35° from the base axis (typically the x-axis, positive angles progress counter-clockwise)
  
=== Mathematic & Geometric ===
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:<14, 9, -20> looks like an arrow starting from the origin (<0,0,0>) and ending at a point where the x coordinate is at 14, the y coordinate = 9 and the z coordinate = -20.  
* Scalar: A single value without a direction. Scalars are usually followed by a unit of measurement that tells what the scalar's dimension is. Ie. 3&nbsp;m/s is a speed, 3&nbsp;m is a length, 3&nbsp;s is a duration of time.
 
* Vector: A set of a direction and a value. Ie. heading and speed together give a velocity.
 
** Vectors can numerically only be expressed in the presence of a co-ordinate system. How a vector is expressed depends on how the co-ordinate system is set up.
 
** The following physical qualities are '''all''' vectors: velocity, acceleration, force,
 
** A 3D Co-ordinate systems needs:
 
*** A point of reference. This is your Origo.
 
*** 3&nbsp;base-vectors. These give your base unit of measurement along an axis and the direction of said axis.
 
*** A Mix of 3 scalars, that could be either angles or co-ordinates to express locations in your co-ordinate space.
 
**** Co-ordinate systems using only co-ordinates are Cartesian.[[File:cartesian.gif|thumb|120px|right|alt=Cartersian]]
 
**** Co-ordinate systems using only angles are Polar.[[File:polar.gif|120px|thumb|right|alt=Polar]]
 
* Normal vector: A vector perpendicular to a plane.
 
* Elliptical: Oval shaped, often in reference to your orbit.
 
  
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:The upside to using Cartesian coordinates is that you know exactly where the terminal position is, but it is more difficult to figure the length, however in polar coordinates it is trivial to find the length, the downside is its more difficult to know the position.
  
=== Orbital Terms ===
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:The following physical qualities are all vectors: '''velocity''', '''acceleration''', '''force'''
* Orbital Plane: The imaginary disk described by the path of an orbit around a body (usually used when dealing with inclinations).
 
* Orbit normal: A normal vector of the Orbital Plane. Produced by cross multiplying the ship's velocity and gravity. Since this follows the right hand rule, from a perspective where the ship is orbiting counter-clockwise it will point "up", while for a ship orbiting "clockwise" it will point down.
 
* Reference Plane: Any plane used as a reference for describing your current orbit.  For local orbits around a planet, this is often the equatorial plane.  When multiple bodies in a solar system are involved, the ecliptic plane can be used.  For intercepting another orbiting body, the orbital plane of the body to be intercepted is used.  An orbital plane can be fully described by giving the inclination and the longitude of the ascending node relative to a reference plane.
 
* Inclination: The angle between an orbital plane relative to a reference plane.
 
* Orbital Nodes: specific points-of-reference in any orbit such as Apoapsis, Periapsis, Crossing points with other orbits, etc.
 
** Periapsis: In an elliptical orbit, the point of the orbit closest to the planet.
 
** Apoapsis: In an elliptical orbit, the point of the orbit farthest from the planet.
 
*** Peri* and Apo*:  When speaking of orbits, oftentimes you replace the Apsis of Periapsis and Apoapsis with something signifying which planet you are speaking of (In this game, kee and kerb are both in common use.  i.e. Perikee/perikerb and Apokee/Apokerb when talking about orbiting the starting planet.
 
** Ascending Node: The point at which the orbit crosses the reference plane moving north.  Here, "north" means the direction of the orbit normal of the reference plane.
 
** Descending Node: The point at which the orbit crosses the reference plane moving south.
 
* Eccentricity: A Scalar of how non-circular an orbit is.
 
** ecc=0 => circular orbit.
 
** 0<ecc<1 => elliptical orbit.
 
** ecc=1 => parabolic orbit - this is an escape orbit.
 
** ecc>1 => hyperbolic orbit - this is an escape orbit.
 
* Semi-major axis: The major-axis is the long axis of an elipse, and the semi-major axis is half this. The semi-major axis is calculated in KSP from sma = 600km + (Aa + Ap) /2 - i.e. it's the average of the Apokee and Perikee computed relative to the center of the planet. All orbits with the same semi-major axis have the same period, regardless of their eccentricity.
 
* Sub-Orbital : Any trajectory that will lead an object (rocketload of kerbals) back to the ground.
 
* Prograde: The "Direct" direction of your orbital path. Since orbits are elliptical, it's actually the tangent of the orbit where the ship is.
 
* Retrograde: The reverse of Prograde, "backwards".
 
* Zenith: "Up" in ground-relative coordinates, i.e. the direction your rocket points at when at the launchpad, aka: "the highest point in the sky".
 
* Nadir: opposite direction of "Zenith".
 
  
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A 3D coordinate systems needs:
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* A point of reference. This is your origin.
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* 3&nbsp;base-vectors. These define your base unit of measurement along the axis and the direction of said axis.
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* A mix of 3 scalars, that could be either angles or co-ordinates to express locations in your co-ordinate space.
  
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== Orbital Terms ==
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[[File:Orbit.svg|thumb|upright=2.25|Visualization of the most common orbital parameters]]
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;<span id="ap">Apoapsis</span>
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;<span id="pe">Periapsis</span>
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;Apsis
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{{See also|Orbit|section=Apoapsis and periapsis}}
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:Every elliptical orbit has two apsides. The '''periapsis''' (<tt>q</tt>) is at the closest point to the body being orbited (the lowest point in the orbit) and the '''apoapsis''' (<tt>Q</tt>) is on the other side of the orbit and is the farthest from the body being orbited (the highest point in the orbit). The apsides are usually given from the body's surface while most formula require the distance from the center of the body so the radius usually needs to get added.
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;<span id="appe">Peri-* and Apo-*</span>
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:When speaking of orbits, oftentimes the words "periapsis" and "apoapsis" will be modified to specify which planet or moon the orbit is around. For example, -kee and -kerb are both commonly used to describe orbits around Kerbin, resulting Perikee/Perikerb and Apokee/Apokerb. (This is not to be confused with "Apogee" and "Perigee", which are used for Earth orbit.) The periapsis is the lowest point in your orbit while the apia-sis is the highest point in your orbit.
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;<span id="an">Ascending node</span>
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:The point ([[#on|orbital node]]) at which the orbit crosses the reference plane moving north.  Here, "north" means the direction of the orbit normal of the reference plane.
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;<span id="dn">Descending node</span>
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:The point ([[#on|orbital node]]) at which the orbit crosses the reference plane moving south.
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;<span id="ecc">Eccentricity</span>
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{{See also|Orbit|section=Eccentricity}}
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<math style="float:right;padding:0.5em;">\text{ecc} = 1 - \frac{2}{\frac{Ap}{Pe}+1}</math>
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:A scalar describing how non-circular an orbit is.
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:* ecc = 0 → circular orbit.
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:* 0 < ecc < 1 → elliptical orbit.
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:* ecc = 1 → parabolic orbit - this is an escape orbit.
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:* ecc > 1 → hyperbolic orbit - this is an escape orbit.
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;<span id="inc">Inclination</span>
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{{See also|Orbit|section=Inclination}}
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:The angle between an orbital plane relative to a reference plane (e.g. an orbit with 90° inclination to an equatorial reference plane would be called polar).
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;<span id="lo">Low orbit</span>
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: An orbit that is only just high enough to indefinitely avoid succumbing to hazards of the body being orbited, such as atmospheric drag. Low orbits are typically used as '''parking orbits''', where spacecraft will wait after ascent and before burning to a future destination, as it allows the exit burn to be performed in any direction, requires the least amount of fuel to reach from the body's surface, and generally allows for some downtime as the craft shuts down its engines and coasts safely while the next series of maneuvers is planned and scheduled. A low orbit for [[Kerbin]] is at least 70km but is generally considered to extend up to 100km.  Bodies with no atmosphere can theoretically allow an orbit at any height above the ground, but below 10km the risk of crashing into mountains or other elevated terrain becomes very high.  The [[time warp]] is restricted to lower values while in low orbits.
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;<span id="on">Orbital node</span> ''(astronomical definition)''
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:The point at which the orbit crosses the reference plane. At the ascending node the craft is moving in the direction of the orbit normal of the reference plane. Ususally the ascending direction is pointing north while the descending direction is pointing south.
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;<span id="node">Orbital nodes</span> ''(as in game)''
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:Specific points of reference in any orbit such as Apoapsis, Periapsis, intersect points with other orbits etc.
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;<span id="orbnorm">Orbit normal</span>
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:A normal vector of the Orbital Plane. Produced by cross multiplying the ship's velocity and gravity. Since this follows the right hand rule, from a perspective where the ship is orbiting counter-clockwise it will point "up", while for a ship orbiting "clockwise" it will point down. "Up" is also often labeled as "North" or "N+", and in tandem with that "Down" is labeled "Anti-Normal", "South" or "N-".
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;<span id="orbplane">Orbital plane</span>
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:The imaginary disk described by the path of an orbit around a body (commonly used when describing inclinations).
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;<span id="orbspeed">Orbital speed</span>
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:The orbital speed of an orbiting body, is the speed at which it orbits around the barycenter of the system, usually around a more massive body. It can be used to refer to either the mean orbital speed, i.e. the average speed as it completes an orbit, or the speed at a particular point in its orbit.
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;<span id="prograde">Prograde</span>
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:The direction in which a ship is traveling along its orbital path. Since orbits are elliptical, it is always tangent to the orbit at the point where the ship is.
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;<span id="retrograde">Retrograde</span>
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:The reverse of Prograde, backwards along the orbital path.
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;<span id="refplane">Reference plane</span>
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:Any plane used as a reference for describing your current orbit. For local orbits around a planet, this is often the equatorial plane. When multiple bodies in a solar system are involved, the ecliptic plane can be used.  For intercepting another orbiting body, the orbital plane of the body to be intercepted is used. An orbital plane can be fully described by giving the inclination and the longitude of the ascending node relative to a reference plane.
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;<span id="sma">Semi-major axis</span>
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<math class="float-right">\text{a} = \text{R} + \frac{Q+q}{2}</math>
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{{See also|Orbit|section=Semi-major axis}}
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:The major-axis is the long axis of an ellipse, and the semi-major axis (<tt>a</tt>) is half of this. It's the average of the apoapsis (<tt>Q</tt>) and periapsis (<tt>q</tt>) computed relative to the center of the body. As both are relative to the body's surface, the radius (<tt>R</tt>) must be added. All orbits with the same semi-major axis have the same period, regardless of their eccentricity.
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;<span id="sidereal period">Sidereal period</span>
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:The sidereal period is the temporal cycle that it takes an object to make a full orbit, relative to the stars. This is the orbital period in an inertial (non-rotating) frame of reference.
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;<span id="suborb">Sub-orbital</span>
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:Describes an orbit where the periapsis is below the surface of a planetary body. If a suborbital path is followed for too long the orbiter will collide with the body being orbited.
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;<span id="synodic period">Synodic period</span>
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:The synodic period is the temporal interval that it takes for an object to reappear at the same point in relation to two or more other objects, e.g. when the [[Mun|Mun]] relative to [[Kerbol]] as observed from [[Kerbin]] returns to the same illumination phase. The synodic period is the time that elapses between two successive conjunctions with the Kerbol–Kerbin line in the same linear order. The synodic period differs from the sidereal period due to Kerbin orbiting around Kerbol.
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;<span id="true anom">True Anomaly</span>
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:The polar angle (counterclockwise and in the orbital plane) measured from the periapsis to the spacecraft's position.
  
A quick picture to help with some of the explanation:
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== Ship Orientation ==
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The ship orientation is always relative to a specific object. The terms are usually defined relative to the cockpit.
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;Attitude
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The ship's orientation with respect to its direction of motion (prograde).
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;Zenith
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:Direction in space from the observer pointing away from the parent body (i.e. orbited planet). Opposite of nadir.
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;Nadir
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:Direction in space from the observer pointing towards the orbited body. Opposite of zenith.
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;Port
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:Left side of the ship. Opposite of starboard.
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;Starboard
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:Right side of the ship. Opposite of port.
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;Forward (Fore)
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:Front side/end of the ship which is usually towards the nose or prograde. Opposite of aft.
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;Aft
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:Back side/end of the ship which usually houses the primary rockets and faces retrograde. Opposite of forward.
  
[[File:Orbit.jpg]]
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== Space Maneuvers ==
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;Atmospheric braking
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{{Main article|Aerobraking}}
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:Lowering the periapsis so it is inside a planetary atmosphere. This will lead to the vessel being slowed by atmospheric drag. Can lead to atmospheric entry, but also is used to reduce the necessary burn time for significant orbit alterations.
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;Lithobraking
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{{See also||{{Wikipedia|Lithobraking}}}}
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:An attempted aerobrake using the ground instead of air. Usage of this term implies jokingly that the resulting crash-landing was not in the original plan. An adaptation of the term ''aerobraking'' where ''aero'' was replaced by the Greek word ''lithos'', meaning “rock” or “stone”.
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;<span id="atmospheric entry">Atmospheric entry</span>
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{{Main article|Atmospheric entry}}
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:Entering atmosphere and using drag to decelerate a vessel to a groundwards trajectory. This causes intense heat stress on the object as the vessel requires sufficient speed to not "bounce" back from the atmosphere into space, and care must be taken not to overheat. This is usually called re-entry/reentry but in theory only correct in Kerbin's atmosphere; atmospheric entry being the more general term.
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;Burn
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:firing of the engines, usually to alter trajectory in some way.
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;Circularizing
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:Reducing an orbit's [[#ecc|eccentricity]] to 0 or close to it. This is usually achieved by a burn close to an apsis.
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;Gravity assist
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:Changing velocity (direction and/or magnitude) by encountering and interacting with a gravity well. In terms of vector addition, the vehicle has some relative velocity to the large body during the encounter, calculated by subtracting the large body's velocity from the vehicle's initial velocity. The vehicle travels in a hyperbolic path relative to the large body, and the inital and final velocities have equal magnitude but different directions. Then you add the large body's velocity again to get the final velocity in the beginning reference frame. The vehicle's speed increases when its velocity is deflected toward the large body's direction of motion. Larger deflection requires lower periapsis (without crashing) or greater large body mass.
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;Intercept
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:The entering of another celestial sphere of influence (SOI)
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;Maneuver node
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{{Main article|Maneuver node}}
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:A planned maneuver in the map view, so as to predict the effect of a [[#burn|burn]] in advance of performing it.
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;Radial-in burn
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:A burn performed directly towards the center of your orbit (perpendicular to both normal and prograde). It rotates the orbit counter-clockwise until the periapsis passes the center of mass of a celestial body. Opposite of radial-out burn. This is the fastest way of returning to the surface of the body you are orbiting, but not the most efficient.
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;Radial-out burn
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:A burn performed directly away from the center of your orbit. it rotates the orbit clockwise until the periapsis passes the center of mass of a celestial body. Opposite of radial-in burn.
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;Re-entry
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{{See also|#atmospheric entry|Atmospheric entry}}
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;Retroburn
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:A burn performed "backwards", e.g. with the engines facing towards prograde and nose towards retrogade (hence the name). This is a common maneuver to used to lower the [[#periapsis|periapsis]] or [[#apoapsis|apoapsis]].
  
=== Space Maneuvers ===
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== Physics ==
* Circularizing: a manouver (firing of the engines) that makes an orbit circular. This is usually achieved by a burn close to Apoapsis.
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;Acceleration
* Re-entry: the part of a rocket's flight where it hits atmosphere at high speed and uses the drag to decelerate the vessel back into a groundwards trajectory (this usually gets very hot, depending on speed - since air heats up when compressed rapidly by a fast-moving object).
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:Rate of change of velocity. Acceleration is a vector, measured in "m/s<sup>2</sup>".
* Burn: firing of the engines, usually to alter trajectory in some way.
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;Ballistic trajectory
* Retroburn: A burn performed "backwards", e.g. with the engines facing towards prograde and nose towards retrogade (hence the name). This is used to lower the velocity of the rocket and the height of the orbit, either to adjust to a new orbit or to put the rocket on a sub-orbital path home.
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:A freely falling object. In rocketry it usually indicates that the object in question is only influenced by gravity and does not exert any force (i.e. thrust) of its own.
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;Delta-v (Δv)
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:The change in a spacecraft's velocity measured in meters per second (m/s). Delta-v can describe a spacecraft accelerating over a period of time (dependent on mass, thrust and duration) or a maneuver from one trajectory to another (independent of a spacecraft's properties). This makes it a useful value for calculating a vehicle's effectiveness. For example, a launch vehicle requires about 4,500 m/s of delta-v to escape Kerbin's atmosphere and achieve a stable orbit, which is fulfilled by having appropriate mass, thrust, fuel, etc.
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:A general formula for the Delta-v of a vehicle with thrust ''T'' and mass ''m'',
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:<math>\Delta{v} = \int_{t_0}^{t_1} {\frac {|T|} {m}}\, dt</math>
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:For constant thrust in the direction of motion,
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: <math>\Delta{v} = \int_{t_0}^{t_1} {\frac {|T|} {m}}\ dt = \int_{t_0}^{t_1} {|a|}\ dt = | {v}_1 - {v}_0 |\,</math>
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:In terms of specific impulse,
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: <math>\Delta{v} = | {v}_1 - {v}_0 |_{max}\ = -\int_{t_0}^{t_1} {I_{sp} \cdot g\ \cdot \frac{\dot{m}} {m}}\ dt = {I_{sp} \cdot g \cdot ln( \frac {m_0} {m_1})}\,</math>
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;Energy
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{{See also||{{Wikipedia|Specific orbital energy}}}}
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:The energy of an object in an orbit is the sum of its potential and kinetic energy. The potential energy is <math>E_p = -\frac{G M m}{R}</math> and kinetic energy <math>E_k = \frac{1}{2} m v^2</math> where ''G'' is the [[w:Gravitational constant|gravitational constant]], ''M'' is the mass of the [[celestial body|body]], ''m'' is the mass of the [[craft]], ''R'' is the distance from the center of the body and ''v'' is the velocity. This results in <math>E = E_k + E_p = \frac{1}{2} m v^2 - \frac{G M m}{R}</math>. The total energy remains the same when no thrust or external forces are applied. When approaching periapsis, potential energy is transferred into kinetic energy. After passing the periapsis, kinetic energy is converted back into potential energy. When the energy or specific orbital energy is greater than zero, the vehicle is on an escape trajectory.
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:This is the basic idea behind Kepler's laws of planetary motion, which gives rise to KSP's patched conics approximation. An ellipse is the set of all points on a plane such that the sum of the distances to two points - the foci - is some constant. One focus of a Kepler orbit is the center of mass of the object being orbited; as an object approaches it, it exchanges potential energy for kinetic energy. As the object moves away from this focus - equivalently, if the orbit is elliptical, as the object approaches the other focus - it exchanges kinetic energy for potential energy. If the craft going directly towards or away from the object, the foci coincide with the apsides, where the kinetic (apoapsis) or potential (periapsis) energy is zero. If it's perfectly circular (e.g. the Mun's orbit around Kerbin), the two foci coincide and the locations of the apsides are undefined, since every point of the orbit is an apsis.
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:There is also the specific orbital energy (<math>\epsilon</math>) which doesn't require the mass of the craft: <math>E_p = \epsilon_p m</math>, <math>E_k = \epsilon_k m</math>, <math>E = \epsilon \, m = (\epsilon_k + \epsilon_p) m = -\frac{G M}{2 a}</math>. All orbits with the same semi-major axis (''a'') have the same specific orbital energy.
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;Escape Velocity
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:The velocity needed to escape a given planet's gravity well, as given by <math>v_e = \sqrt{\frac{2GM}{r}},</math> where G is the [[w:Gravitational constant|gravitational constant]], M is the mass of the planet, and r is the radius of the planet.
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;g-force (''g'')
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:A measurement of acceleration as expressed in the sea-level force of Earth's gravity with 1&nbsp;''g'' (not to be confused with the unit gram, or the local acceleration or the gravitational constant) being about 9.81&nbsp;m/s². An object at Earth's surface is accelerated at 1&nbsp;''g''. The object weighs twice as much when at 2&nbsp;''g'' acceleration and is weightless when accelerated with 0&nbsp;''g''. In free fall, like in orbit, and without an engine running or an atmosphere applying drag all objects experience no acceleration which can be expressed as 0&nbsp;''g''. (Strictly speaking an orbiting body still experiences acceleration, namely in the radial direction due to the gravitation of the body being orbited, but this is not usually included in an expression of g-force.)
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;Gravity
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:The force exerted by all objects with mass. Very weak (by comparison with the other fundamental forces, but the only one modelled directly by KSP and the only one that is noticeable over long distances). Usually only objects with very high mass - i.e. planets, moons - have any noticeable effect. Diminishes with the square of distance from the center of mass. So for an object twice as far, experiences only 1/2<sup>2</sup> = 1/4 of the gravity.
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;Gravity well
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:The area around a planet affected by gravity. Actually extends to infinity, but as gravity decreases quadratically with distance (after twice the distance the gravity is only a quarter), it is only significant within the body's sphere of influence. In fact, in KSP, gravity isn't simulated at all beyond a body's sphere of influence due to its use of the "patched conic approximation".
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;Orbit
 +
{{Main article|Orbit}}
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:When an object has sufficient tangential velocity (without external forces such as drag) so that the planet's surface curves away more than object's path curves due to gravity. Stable orbits are elliptical (with eccentricity between 0 and 1). If the object's tangential speed exceeds escape velocity its orbit will be hyperbolic (with eccentricity more than 1. Parabolic orbits require an eccentricity of exactly 1, and circular orbits require an eccentricity of exactly 0, which are impossible unless its orbit is defined as such, like the Mun).
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;<span id="isp">Specific Impulse (I<sub>sp</sub>)</span>
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{{Main article|Specific impulse}}
 +
:<math style="float:center">I_{sp}= \frac{T}{\dot m},</math><span style="padding:1em"></span><math style="float:center"> [I_{sp}] = \frac{m}{s}</math>
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:The I<sub>sp</sub> defines how effective a propulsion system is. The higher the I<sub>sp</sub> the more powerful is the thrust applied to the rocket with the same fuel mass. The I<sub>sp</sub> is usually given in ''seconds'' but actually the physically correct unit is ''distance per time'' which is usually given in ''meters per second'' or ''feet per second''. To avoid confusion which unit of speed is used, the physical correct I<sub>sp</sub> (in ''distance/time'') is divided by the surface gravity of Earth (9.81&nbsp;m/s²). This results in a value given in ''seconds''. To use this I<sub>sp</sub> in formulas it must be converted back into ''distance per time'' which requires multiplying with the surface gravity of Earth again. As this value is only used to convert between those two units, the '''specific impulse doesn't change when the gravity changes'''. It appears that KSP use a value like 9.82&nbsp;m/s² and thus using a little less fuel.
 +
:As the specific impulse is the ratio of thrust and fuel flow <math>\frac{Ns}{kg}</math> is sometimes given as the unit. This is mathematically another form of <math>\frac{m}{s} = kg \cdot \frac{m}{s^2} \cdot \frac{s}{kg}</math> because force is the multiplication of mass and acceleration defining <math>N = kg \cdot \frac{m}{s^2}</math>. So <math>1 \frac{Ns}{kg} = 1 \frac{m}{s}</math> with the latter being simply only in SI base units.
 +
;<span id="soi">Sphere of influence</span>
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{{Main article|Sphere of influence}}
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:The radius around a celestial body outside of which its gravity is negligible compared to the gravity of another body. Commonly known as SoI/SOI.
 +
;Tangential velocity
 +
:The component of the velocity that is tangential to the trajectory. Instantaneous velocity - velocity when the time of measurement approaches zero - is always tangential to the trajectory.
 +
;<span id="TWR">Thrust-to-weight ratio</span>
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{{See also|Thrust-to-weight ratio}}
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:<math style="float:right;padding:.5em;">\text{TWR} = \frac{T}{W} = \frac{T}{m \cdot g}</math>The Ratio between the total mass of the vehicle and the available thrust of all propulsion devices of the vehicle/current stage. A TWR greater than 1 means the craft will have enough thrust to accelerate vertically and gain altitude. A TWR below 1 means that the craft won't be able to counteract gravity and drag at low altitudes, although in space it only means that maneuvers will take longer. Because the weight (W) depends on the current gravitational acceleration (g) the TWR depends on which body is currently influencing the craft. The acceleration on the [[Mun]]'s surface is only 16.6 % of Kerbin's acceleration, so at the surface a TWR<sub>Kerbin</sub>&nbsp;=&nbsp;1 would be a TWR<sub>Mun</sub>&nbsp;=&nbsp;6.
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;Trajectory
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:A trajectory is the path that a moving object follows through space as a function of time.
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;Velocity
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:Rate of change of the position. It is the combination of speed with the direction. Velocity is a vector, measured in meters per second (m/s).
  
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==See also==
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* [[Tutorials]]
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* [[Acronyms and Initialisms]]
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* [[Deep Space Kraken]]
  
=== Physics ===
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[[Category: Tutorials]]
 
 
* Trajectory: A trajectory is the path that a moving object follows through space as a function of time.
 
* Ballistic trajectory: A falling object's trajectory is ballistic. In rocketry it usually indicates that the object in question is only influenced by gravity and does not exert any force (ie. thrust) of its own.
 
* Orbit: When an object has sufficient tangential velocity (and is outside the atmosphere, so drag won't slow it down) so that it will keep falling "next" to the planet (never touching ground) its trajectory is called an orbit.
 
** Stable orbits are elliptical (a circle is an ellipse with zero eccentricity).
 
** If the objects tangential speed exceeds escape velocity it's orbit will be either para- or hyperbolic.
 
 
 
* Velocity: Rate of change of your position. Your speed and direction. Velocity is a vector. It's unit of measurement is "m/s".
 
* Tangential velocity: The component of your velocity that's perpendicular to your trajectory. Instantaneous velocity - velocity when the time of measurement approaches zero - is always tangential to your trajectory.
 
* Escape Velocity:  The velocity needed to escape a given planets gravity well.
 
 
 
* Acceleration:  Rate of change to your velocity. Acceleration is a vector. It's unit of measurement is "m/s<sup>2</sup>".
 
* G's:  A measurement of force as expressed in the sea-level force of Earth's gravity. In other words, right now you're under 1&nbsp;G. 2&nbsp;G's is equivalent to twice earths gravity at sea level, and so on.
 
 
 
* Gravity: The force exerted by all objects with mass. Very weak. Usually only objects with very high mass - ie. planets, moons - have any noticeable effect. Diminishes with the square of distance from the center of mass. So for an object twice as far, experiences only 1/2<sup>2</sup> = 1/4 of the gravity.
 
* Gravity Well:  The area around a planet effected by gravity. Actually extends to infinity, but for practical purposes only significant within its Sphere-Of-Influence.
 
* Sphere-Of-Influence: The radius around a celestial body where its gravity well is non-neglectable.
 
* Energy: The energy of an object in an orbit is the sum of it's potential and kinetic energy. Potential energy is E<sub>p</sub> = - GMm/R  and Kinetic Energy  E<sub>k</sub> = (1/2) m v<sup>2</sup> where G is the gravitational constant, M is the mass of the planet, m is the mass of the vehicle, R is the distance from the center of the planet and v is the velocity. So E = (1/2) m v<sup>2</sup>  - GMm/R . When the energy is greater than zero the vehicle is on an escape trajectory.  All orbits with the same semi-major axis have the same energy.
 
 
 
==See also==
 
[[Tutorials]]
 

Latest revision as of 18:25, 21 June 2021

In to KSP, there are many terms pertaining to orbiting and physics that often can be confusing to non-technicians. In addition, various other scientific terms and abbreviations are used to describe common terms.

This sheet is designed as a concise lookup table of necessary terms to help you get started down the road to being a full fledged astronaut!

Mathematics

Cartesian coordinate system - Uses rectangular coordinates
Polar (spherical) coordinate system - Uses only angles and one length
Elliptical
Oval shaped, often in reference to your orbit.
Hyperbolic
Open smooth curve, often in reference to escape trajectories.
Normal vector
A vector perpendicular to a plane. (Usually the direction of the north pole if you are in an equatorial orbit.)
Scalar
A single value without a direction. Scalars are usually followed by a unit of measurement that tells what the scalar's dimension is. eg 3 m/s, 3 m,3 s are scalar: they have units which denote speed, length/distance, and time respectively, but have no direction.
Vector
A set of a direction and a value. eg. heading (direction) and speed together give a velocity. How a vector is expressed depends on what the coordinate system is, and how many dimensions are taken into consideration. <35°, 12> is a two dimensional polar vector, where <14, 9, -20> is a three dimensional Cartesian vector. There are other coordinate systems but these are the most utilized.
<35°, 12> looks like an arrow which is 12 units long, starting from the origin (zero, angle does not matter because it is a point with no length) and ending at a point 35° from the base axis (typically the x-axis, positive angles progress counter-clockwise)
<14, 9, -20> looks like an arrow starting from the origin (<0,0,0>) and ending at a point where the x coordinate is at 14, the y coordinate = 9 and the z coordinate = -20.
The upside to using Cartesian coordinates is that you know exactly where the terminal position is, but it is more difficult to figure the length, however in polar coordinates it is trivial to find the length, the downside is its more difficult to know the position.
The following physical qualities are all vectors: velocity, acceleration, force

A 3D coordinate systems needs:

  • A point of reference. This is your origin.
  • 3 base-vectors. These define your base unit of measurement along the axis and the direction of said axis.
  • A mix of 3 scalars, that could be either angles or co-ordinates to express locations in your co-ordinate space.

Orbital Terms

Visualization of the most common orbital parameters
Apoapsis
Periapsis
Apsis
→ See also: “Apoapsis and periapsis” section in Orbit
Every elliptical orbit has two apsides. The periapsis (q) is at the closest point to the body being orbited (the lowest point in the orbit) and the apoapsis (Q) is on the other side of the orbit and is the farthest from the body being orbited (the highest point in the orbit). The apsides are usually given from the body's surface while most formula require the distance from the center of the body so the radius usually needs to get added.
Peri-* and Apo-*
When speaking of orbits, oftentimes the words "periapsis" and "apoapsis" will be modified to specify which planet or moon the orbit is around. For example, -kee and -kerb are both commonly used to describe orbits around Kerbin, resulting Perikee/Perikerb and Apokee/Apokerb. (This is not to be confused with "Apogee" and "Perigee", which are used for Earth orbit.) The periapsis is the lowest point in your orbit while the apia-sis is the highest point in your orbit.
Ascending node
The point (orbital node) at which the orbit crosses the reference plane moving north. Here, "north" means the direction of the orbit normal of the reference plane.
Descending node
The point (orbital node) at which the orbit crosses the reference plane moving south.
Eccentricity
→ See also: “Eccentricity” section in Orbit

A scalar describing how non-circular an orbit is.
  • ecc = 0 → circular orbit.
  • 0 < ecc < 1 → elliptical orbit.
  • ecc = 1 → parabolic orbit - this is an escape orbit.
  • ecc > 1 → hyperbolic orbit - this is an escape orbit.
Inclination
→ See also: “Inclination” section in Orbit
The angle between an orbital plane relative to a reference plane (e.g. an orbit with 90° inclination to an equatorial reference plane would be called polar).
Low orbit
An orbit that is only just high enough to indefinitely avoid succumbing to hazards of the body being orbited, such as atmospheric drag. Low orbits are typically used as parking orbits, where spacecraft will wait after ascent and before burning to a future destination, as it allows the exit burn to be performed in any direction, requires the least amount of fuel to reach from the body's surface, and generally allows for some downtime as the craft shuts down its engines and coasts safely while the next series of maneuvers is planned and scheduled. A low orbit for Kerbin is at least 70km but is generally considered to extend up to 100km. Bodies with no atmosphere can theoretically allow an orbit at any height above the ground, but below 10km the risk of crashing into mountains or other elevated terrain becomes very high. The time warp is restricted to lower values while in low orbits.
Orbital node (astronomical definition)
The point at which the orbit crosses the reference plane. At the ascending node the craft is moving in the direction of the orbit normal of the reference plane. Ususally the ascending direction is pointing north while the descending direction is pointing south.
Orbital nodes (as in game)
Specific points of reference in any orbit such as Apoapsis, Periapsis, intersect points with other orbits etc.
Orbit normal
A normal vector of the Orbital Plane. Produced by cross multiplying the ship's velocity and gravity. Since this follows the right hand rule, from a perspective where the ship is orbiting counter-clockwise it will point "up", while for a ship orbiting "clockwise" it will point down. "Up" is also often labeled as "North" or "N+", and in tandem with that "Down" is labeled "Anti-Normal", "South" or "N-".
Orbital plane
The imaginary disk described by the path of an orbit around a body (commonly used when describing inclinations).
Orbital speed
The orbital speed of an orbiting body, is the speed at which it orbits around the barycenter of the system, usually around a more massive body. It can be used to refer to either the mean orbital speed, i.e. the average speed as it completes an orbit, or the speed at a particular point in its orbit.
Prograde
The direction in which a ship is traveling along its orbital path. Since orbits are elliptical, it is always tangent to the orbit at the point where the ship is.
Retrograde
The reverse of Prograde, backwards along the orbital path.
Reference plane
Any plane used as a reference for describing your current orbit. For local orbits around a planet, this is often the equatorial plane. When multiple bodies in a solar system are involved, the ecliptic plane can be used. For intercepting another orbiting body, the orbital plane of the body to be intercepted is used. An orbital plane can be fully described by giving the inclination and the longitude of the ascending node relative to a reference plane.
Semi-major axis

→ See also: “Semi-major axis” section in Orbit
The major-axis is the long axis of an ellipse, and the semi-major axis (a) is half of this. It's the average of the apoapsis (Q) and periapsis (q) computed relative to the center of the body. As both are relative to the body's surface, the radius (R) must be added. All orbits with the same semi-major axis have the same period, regardless of their eccentricity.
Sidereal period
The sidereal period is the temporal cycle that it takes an object to make a full orbit, relative to the stars. This is the orbital period in an inertial (non-rotating) frame of reference.
Sub-orbital
Describes an orbit where the periapsis is below the surface of a planetary body. If a suborbital path is followed for too long the orbiter will collide with the body being orbited.
Synodic period
The synodic period is the temporal interval that it takes for an object to reappear at the same point in relation to two or more other objects, e.g. when the Mun relative to Kerbol as observed from Kerbin returns to the same illumination phase. The synodic period is the time that elapses between two successive conjunctions with the Kerbol–Kerbin line in the same linear order. The synodic period differs from the sidereal period due to Kerbin orbiting around Kerbol.
True Anomaly
The polar angle (counterclockwise and in the orbital plane) measured from the periapsis to the spacecraft's position.

Ship Orientation

The ship orientation is always relative to a specific object. The terms are usually defined relative to the cockpit.

Attitude

The ship's orientation with respect to its direction of motion (prograde).

Zenith
Direction in space from the observer pointing away from the parent body (i.e. orbited planet). Opposite of nadir.
Nadir
Direction in space from the observer pointing towards the orbited body. Opposite of zenith.
Port
Left side of the ship. Opposite of starboard.
Starboard
Right side of the ship. Opposite of port.
Forward (Fore)
Front side/end of the ship which is usually towards the nose or prograde. Opposite of aft.
Aft
Back side/end of the ship which usually houses the primary rockets and faces retrograde. Opposite of forward.

Space Maneuvers

Atmospheric braking
→ Main article: Aerobraking
Lowering the periapsis so it is inside a planetary atmosphere. This will lead to the vessel being slowed by atmospheric drag. Can lead to atmospheric entry, but also is used to reduce the necessary burn time for significant orbit alterations.
Lithobraking
→ See also: Lithobraking on Wikipedia
An attempted aerobrake using the ground instead of air. Usage of this term implies jokingly that the resulting crash-landing was not in the original plan. An adaptation of the term aerobraking where aero was replaced by the Greek word lithos, meaning “rock” or “stone”.
Atmospheric entry
→ Main article: Atmospheric entry
Entering atmosphere and using drag to decelerate a vessel to a groundwards trajectory. This causes intense heat stress on the object as the vessel requires sufficient speed to not "bounce" back from the atmosphere into space, and care must be taken not to overheat. This is usually called re-entry/reentry but in theory only correct in Kerbin's atmosphere; atmospheric entry being the more general term.
Burn
firing of the engines, usually to alter trajectory in some way.
Circularizing
Reducing an orbit's eccentricity to 0 or close to it. This is usually achieved by a burn close to an apsis.
Gravity assist
Changing velocity (direction and/or magnitude) by encountering and interacting with a gravity well. In terms of vector addition, the vehicle has some relative velocity to the large body during the encounter, calculated by subtracting the large body's velocity from the vehicle's initial velocity. The vehicle travels in a hyperbolic path relative to the large body, and the inital and final velocities have equal magnitude but different directions. Then you add the large body's velocity again to get the final velocity in the beginning reference frame. The vehicle's speed increases when its velocity is deflected toward the large body's direction of motion. Larger deflection requires lower periapsis (without crashing) or greater large body mass.
Intercept
The entering of another celestial sphere of influence (SOI)
Maneuver node
→ Main article: Maneuver node
A planned maneuver in the map view, so as to predict the effect of a burn in advance of performing it.
Radial-in burn
A burn performed directly towards the center of your orbit (perpendicular to both normal and prograde). It rotates the orbit counter-clockwise until the periapsis passes the center of mass of a celestial body. Opposite of radial-out burn. This is the fastest way of returning to the surface of the body you are orbiting, but not the most efficient.
Radial-out burn
A burn performed directly away from the center of your orbit. it rotates the orbit clockwise until the periapsis passes the center of mass of a celestial body. Opposite of radial-in burn.
Re-entry
→ See also: Atmospheric entry
Retroburn
A burn performed "backwards", e.g. with the engines facing towards prograde and nose towards retrogade (hence the name). This is a common maneuver to used to lower the periapsis or apoapsis.

Physics

Acceleration
Rate of change of velocity. Acceleration is a vector, measured in "m/s2".
Ballistic trajectory
A freely falling object. In rocketry it usually indicates that the object in question is only influenced by gravity and does not exert any force (i.e. thrust) of its own.
Delta-v (Δv)
The change in a spacecraft's velocity measured in meters per second (m/s). Delta-v can describe a spacecraft accelerating over a period of time (dependent on mass, thrust and duration) or a maneuver from one trajectory to another (independent of a spacecraft's properties). This makes it a useful value for calculating a vehicle's effectiveness. For example, a launch vehicle requires about 4,500 m/s of delta-v to escape Kerbin's atmosphere and achieve a stable orbit, which is fulfilled by having appropriate mass, thrust, fuel, etc.
A general formula for the Delta-v of a vehicle with thrust T and mass m,
For constant thrust in the direction of motion,
In terms of specific impulse,
Energy
→ See also: Specific orbital energy on Wikipedia
The energy of an object in an orbit is the sum of its potential and kinetic energy. The potential energy is and kinetic energy where G is the gravitational constant, M is the mass of the body, m is the mass of the craft, R is the distance from the center of the body and v is the velocity. This results in . The total energy remains the same when no thrust or external forces are applied. When approaching periapsis, potential energy is transferred into kinetic energy. After passing the periapsis, kinetic energy is converted back into potential energy. When the energy or specific orbital energy is greater than zero, the vehicle is on an escape trajectory.
This is the basic idea behind Kepler's laws of planetary motion, which gives rise to KSP's patched conics approximation. An ellipse is the set of all points on a plane such that the sum of the distances to two points - the foci - is some constant. One focus of a Kepler orbit is the center of mass of the object being orbited; as an object approaches it, it exchanges potential energy for kinetic energy. As the object moves away from this focus - equivalently, if the orbit is elliptical, as the object approaches the other focus - it exchanges kinetic energy for potential energy. If the craft going directly towards or away from the object, the foci coincide with the apsides, where the kinetic (apoapsis) or potential (periapsis) energy is zero. If it's perfectly circular (e.g. the Mun's orbit around Kerbin), the two foci coincide and the locations of the apsides are undefined, since every point of the orbit is an apsis.
There is also the specific orbital energy () which doesn't require the mass of the craft: , , . All orbits with the same semi-major axis (a) have the same specific orbital energy.
Escape Velocity
The velocity needed to escape a given planet's gravity well, as given by where G is the gravitational constant, M is the mass of the planet, and r is the radius of the planet.
g-force (g)
A measurement of acceleration as expressed in the sea-level force of Earth's gravity with 1 g (not to be confused with the unit gram, or the local acceleration or the gravitational constant) being about 9.81 m/s². An object at Earth's surface is accelerated at 1 g. The object weighs twice as much when at 2 g acceleration and is weightless when accelerated with 0 g. In free fall, like in orbit, and without an engine running or an atmosphere applying drag all objects experience no acceleration which can be expressed as 0 g. (Strictly speaking an orbiting body still experiences acceleration, namely in the radial direction due to the gravitation of the body being orbited, but this is not usually included in an expression of g-force.)
Gravity
The force exerted by all objects with mass. Very weak (by comparison with the other fundamental forces, but the only one modelled directly by KSP and the only one that is noticeable over long distances). Usually only objects with very high mass - i.e. planets, moons - have any noticeable effect. Diminishes with the square of distance from the center of mass. So for an object twice as far, experiences only 1/22 = 1/4 of the gravity.
Gravity well
The area around a planet affected by gravity. Actually extends to infinity, but as gravity decreases quadratically with distance (after twice the distance the gravity is only a quarter), it is only significant within the body's sphere of influence. In fact, in KSP, gravity isn't simulated at all beyond a body's sphere of influence due to its use of the "patched conic approximation".
Orbit
→ Main article: Orbit
When an object has sufficient tangential velocity (without external forces such as drag) so that the planet's surface curves away more than object's path curves due to gravity. Stable orbits are elliptical (with eccentricity between 0 and 1). If the object's tangential speed exceeds escape velocity its orbit will be hyperbolic (with eccentricity more than 1. Parabolic orbits require an eccentricity of exactly 1, and circular orbits require an eccentricity of exactly 0, which are impossible unless its orbit is defined as such, like the Mun).
Specific Impulse (Isp)
→ Main article: Specific impulse
The Isp defines how effective a propulsion system is. The higher the Isp the more powerful is the thrust applied to the rocket with the same fuel mass. The Isp is usually given in seconds but actually the physically correct unit is distance per time which is usually given in meters per second or feet per second. To avoid confusion which unit of speed is used, the physical correct Isp (in distance/time) is divided by the surface gravity of Earth (9.81 m/s²). This results in a value given in seconds. To use this Isp in formulas it must be converted back into distance per time which requires multiplying with the surface gravity of Earth again. As this value is only used to convert between those two units, the specific impulse doesn't change when the gravity changes. It appears that KSP use a value like 9.82 m/s² and thus using a little less fuel.
As the specific impulse is the ratio of thrust and fuel flow is sometimes given as the unit. This is mathematically another form of because force is the multiplication of mass and acceleration defining . So with the latter being simply only in SI base units.
Sphere of influence
→ Main article: Sphere of influence
The radius around a celestial body outside of which its gravity is negligible compared to the gravity of another body. Commonly known as SoI/SOI.
Tangential velocity
The component of the velocity that is tangential to the trajectory. Instantaneous velocity - velocity when the time of measurement approaches zero - is always tangential to the trajectory.
Thrust-to-weight ratio
→ See also: Thrust-to-weight ratio
The Ratio between the total mass of the vehicle and the available thrust of all propulsion devices of the vehicle/current stage. A TWR greater than 1 means the craft will have enough thrust to accelerate vertically and gain altitude. A TWR below 1 means that the craft won't be able to counteract gravity and drag at low altitudes, although in space it only means that maneuvers will take longer. Because the weight (W) depends on the current gravitational acceleration (g) the TWR depends on which body is currently influencing the craft. The acceleration on the Mun's surface is only 16.6 % of Kerbin's acceleration, so at the surface a TWRKerbin = 1 would be a TWRMun = 6.
Trajectory
A trajectory is the path that a moving object follows through space as a function of time.
Velocity
Rate of change of the position. It is the combination of speed with the direction. Velocity is a vector, measured in meters per second (m/s).

See also