Difference between revisions of "Tutorial: Basic Orbiting (Technical)"

Revision as of 00:27, 16 July 2011

Orbiting Tutorial

Getting into space is relatively easy, but staying there without drifting endlessly into space or falling back down to Kearth can be challenging. This tutorial will teach you how to get into and remain in orbit, how to adjust your orbit to be circular or elliptical, and how to adjust to a higher or lower orbit.

Your first orbit

A good procedure for getting into orbit was posted by HarvesteR on the KSP forums (edited with a better horizontal speed based on the orbital tables below):

1. Launch straight up, and continue to climb up to about 10000 meters.
2. Then, gradually start leveling off. You will start gaining horizontal speed.
3. Now you're basically trading vertical speed for horizontal speed. The idea is to get to 0 vertical speed at about 40000 meters up, and be moving horizontally at about 2350 m/s.

This will put you in a stable orbit. The altitude at which you start leveling off and the altitude at which you reach orbital velocity will depend a lot on how your rocket is designed. The idea, however, is to get out of the thickest part of the atmosphere before you start adding horizontal speed, so that you aren't wasting energy adding horizontal speed which will just bleed off due to air resistance.

It is likely that you will overshoot or undershoot these figures by a wide margin on your first couple attempts. Don't worry! Manual orbit insertion is difficult, that's why NASA uses computer guidance! When you finally do get into a stable orbit, you'll probably be on an elliptical trajectory; that is, your ship will coast away from the planet, gradually losing speed. When it reaches its maximum altitude, it will start to fall back toward Kearth, picking up speed again. If you're going fast enough, you'll fall "past" Kearth instead of into it, and that's orbiting.

Controlling your orbit

During each orbit, your craft will reach maximum altitude, called apokee, and on the opposite side of the planet, it will reach minimum altitude, called perikee. At both apokee and perikee, your vertical speed will be zero. These points are the easiest points to make orbital corrections, because you can easily determine how fast to go when your vertical speed is zero. Note: The relative difference between your orbit's apokee and perikee is called its eccentricity. Orbits that are exactly circular have zero eccentricity, and highly "flattened-out" orbits have eccentricity close to 1.

First, in order to get into a nice, round orbit, you need to determine how fast to go. The higher your orbit, the less gravity you'll feel from Kearth, so the slower you'll need to go to be in a circular orbit. Consult the table below to determine the proper speed for your altitude at apokee or perikee. You'll probably want to watch your altimiter as you near one of the critical points, remember the altitude, look up the speed in the table, and make the correction on your next pass. If you want to "round out" your orbit from apokee, you need to speed up to avoid falling back down to perikee. Point your craft in the exact direction of travel (use the green circular indicator on the gimbal to line up), and apply thrust until you've gained enough speed. To round out an orbit from perikee, you need to slow down to avoid climbing back up to apokee. Point your craft in the opposite direction of travel (indicated on the gimbal by a green circle with an "X" through it), and apply thrust until you have slowed to the speed indicated by the table. You should then be in an orbit that is very close to circular! Depending on how eccentric your initial orbit was, you may need to make a large correction on your first pass followed by a small correction on a subsequent pass to get very stable.

Formulae and Tables

The relation between orbital speed and acceleration is given by the formula:

a = v² / r,

where a is the acceleration due to gravity, v is the horizontal speed, and r is the radius of orbit.

Of course, gravity varies depending on your distance from the planet, so we also need the following formula to determine a based on your altitude:

a = g * (R / (R + h))²,

where g is the acceleration due to gravity at sea level (9.81 m/s²), R is the radius of Kearth (600 km), and h is the altitude of your orbit.

Note: From here, we will substitute R + h for r, since the radius of your orbit is equal to the radius of Kearth plus your altitude.

Substituting for a and simplifying, we get:

g * (R / (R + h))² = v² / (R + h)

g * R² / (R + h) = v²

v = R * sqrt(g / (R + h))

Finally, substituting known values for g and R,

v = 600 000 m * sqrt(9.81 m/s² / (600 000 m + h))

From this formula, we can produce the table below:

Video Tutorial

Video Example Of Building A Rocket And Taking It To Orbit