Difference between revisions of "Synchronous orbit"

Revision as of 20:42, 30 August 2013 (view source) XZise (talk | contribs) (→‎Altitudes: *calculate the values automatically;) ← Older edit		Latest revision as of 03:15, 23 February 2019 (view source) Jestersage (talk | contribs) (→‎Molniya orbit)
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−	A '''stationary orbit''' is an orbit with the same orbital period as the rotational period of the orbited body. The eccentricity is equal to 0 and the inclination is exactly 0°. A satellite on this orbit will stay in the sky at the same position at all times, the surface velocity is zero and making the communication easy as the ground based telescopes don't have to follow the satellite's relative motion.	+	[[File:SynchronousOrbit.gif|thumb|right|A time-warped animation of a small satellite in synchronous orbit around Kerbin.]]A '''synchronous orbit''' is an orbit where the orbital period equals the rotation rate of the orbited body. The eccentricity and inclination are not bound to specific values, although to be synchronous the orbit must not intersect with the atmosphere or surface of the orbited body, causing the orbit to change. Satellites in synchronous orbits have a [[w:Ground track|ground track]] forming an [[w:Analemma|analemma]].
		+	'''Important!''' You need to match your orbital period with '''sidereal''' rotation period not the solar day. So, for Kerbin it will be 5h 59m 9.425s instead of 6h that a lot of people go for.
−	A stationary orbit is a special kind of '''synchronous orbit''', which all have the same orbital period but may differ in inclination or eccentricity. Satellites on a synchronous but not stationary orbit have a ground track forming an [[w:Analemma|analemma]]. Because it is impossible to get all values exact for a stationary orbit, every satellite on a synchronous orbit form an analemma.	+	== Stationary orbits ==
		+	'''Stationary orbits''' are a special kind of synchronous orbit. Its 0° inclination and its eccentricity of 0 cause its ground track to be only a point: a satellite in this orbit has no motion relative to the body's surface. Since it is impossible to get all orbital values exact for a stationary orbit, satellites in stationary orbits form small analemmata.
−	Some celestial bodies don't allow synchronous orbits, and thus also no stationary orbits, because the altitude lies outside the celestial bodies' sphere of influence. This is because of a very slow rotation requiring a very high altitude to allow such long orbital periods explaining why all tidally locked moons don't have a synchronous orbits. [[Moho]] is the only planet without any synchronous orbit, because it's very slow rotational period with only almost two rotations in one orbit.	+	Some celestial bodies don't allow for synchronous orbits because the altitude required to synchronously orbit is beyond the body's sphere of influence. The body's slow rotation rate causes this effect: a very high altitude is necessary to allow for such a long orbital period. Tidally locked moons don't have synchronous orbit possibilities either because of their slow rotation. [[Moho]] is the only planet without any possibilities for a craft to achieve a synchronous orbit because of its very slow rotational period; Moho completes approximately two rotations during the time it takes for an object in the highest possible orbit to complete a revolution.
−	== Altitudes ==	+	== Semi-synchronous and similar orbits ==
		+	When the orbital period is half as long as the rotational period, the orbit is usually described as semi-synchronous. It is possible to calculate the semi-major axis of a semi-synchronous orbit using [[w:Kepler's_laws_of_planetary_motion|Kepler's third law of planetary motion]]. With the knowledge about the semi-major axis of a synchronous orbit and the [[w:Ratio|ratio]] between the two orbits:
		+	:<math>a_\frac{1}{f} = \frac{1}{\sqrt[3]{f^2}} \cdot a_1</math>
		+	The fraction ''f'' is the quotient of the period of the synchronous orbit (''a<sub>1</sub>'') and second orbit (''a<sub>1/f</sub>''). When the second orbit is a semi-synchronous orbit this quotient is 2:
		+	:<math>a_\frac{1}{2} = \frac{1}{\sqrt[3]{2^2}} \cdot a_1 = \frac{1}{\sqrt[3]{4}} \cdot a_1</math>
		+
		+	An orbit where the orbital period is lower than the rotational period has some advantages, as some bodies don't allow synchronous orbits but opportunities for semi-synchronous orbits.
		+
		+	When dropping numerous payloads that should land nearby each other, the orbit should be an integer multiple of the celestial body's sidereal day. This way, the body stays the same relative to the orbit and has the same descent route, if each payload is detached at the same point in the orbit (e.g. [[apoapsis]]). The inverse factor ''f'' (= 1/''f'') defines how many days are between two detachments. For example, a super-synchronous orbit has f=1/2 so a payload could be dropped every two sidereal days or, when orbiting Kerbin, one every twelve hours.
		+
		+	An example of a semi-synchronous orbit for real world scientific applications is a [[w:Molniya orbit|Molniya orbit]].
		+
		+	=== Sun-synchronous orbit ===
		+	:{{See also||{{Wikipedia|Sun-synchronous orbit}}}}
		+	In the real world, there exists a sun-synchronous orbit. It's important to note that, although the name implies it, the orbit is not synchronous around the Sun. Instead, it describes an orbit around Earth which itself rotates, such that it appears the orbiting object is motionless relative to the Sun. Since it requires objects to have uneven gravitational fields, it is impossible to simulate in KSP.
		+
		+	=== Molniya orbit ===
		+	A Molniya orbit is a semi-synchronous, highly elliptical orbit. The eccentricity should be as high as the central body permits. A three-satellite constellation in Molniya orbits can provide constant coverage to the high attitude regions. To set up such constellation, the mean anomalies of these three satellites should be spaced out by <math>120^{\circ}</math> or <math>\frac{2\pi}{3}</math>. The longitudes of the ascending nodes can also be spaced out by <math>120^{\circ}</math> to make the clover appearance.
		+
		+	For Kerbin, that equate to 70k for PE, 3117k for AP, and around 63 degree inclination.
		+
		+	== Advantages of synchronous orbits ==
		+	One advantage of a synchronous orbit is that they allow dropping multiple [[payload]]s from one [[craft]], because the orbit will  periodically travel above the same point on the body's surface. Usually, the orbit has a large eccentricity so that the payload has to complete a minimal amount of maneuvers to reach the surface. In this case the payload is detached at the apoapsis and decelerated such that it lands on the celestial body. After the payload has successfully landed, the next payload can be dropped as soon as the craft reaches the apoapsis again.
		+	=== Stationary orbits ===
		+	Communication to a satellite in a stationary orbit is easier than if it was in another orbit, as the ground based antennae do not have to move to account for the satellite's motion relative to the orbited body.
		+
		+	== Orbital altitudes and semi-major axes of Kerbal's major bodies  ==
		+	The following table contains the altitudes for circular, synchronous orbits around all of Kerbal's celestial bodies, even when the altitude resides outside the SOI. The altitudes are relative to the body's surface, while the semi-major axes are measured from the body's center.
	{| class="wikitable"		{| class="wikitable"
−	! Body !! Synchronous orbit !! Semi-synchronous orbit	+	! rowspan="2" | Body
		+	! colspan="2" | Synchronous orbit
		+	! colspan="2" | Semi-synchronous orbit
		+	! rowspan="2" | Tidally<br>locked
		+	|-
		+	! Altitude
		+	! Semi-major axis
		+	! Altitude
		+	! Semi-major axis
	{{StationaryOrbit/Row|Kerbol}}		{{StationaryOrbit/Row|Kerbol}}
	{{StationaryOrbit/Row|Moho}}		{{StationaryOrbit/Row|Moho}}
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	== See also ==		== See also ==
	* [[KEO]], the stationary orbit around [[Kerbin]]		* [[KEO]], the stationary orbit around [[Kerbin]]
		+	* [[Geosynchronous Orbit (Math)]], some math on how to calculate a synchronous orbit
	* {{Wikipedia}}		* {{Wikipedia}}
−	* {{Wikipedia|Synchronous orbit}}	+	* {{Wikipedia|Stationary orbit}}
	* {{Wikipedia|Geostationary orbit}}		* {{Wikipedia|Geostationary orbit}}
	* {{Wikipedia|Geosynchronous orbit}}		* {{Wikipedia|Geosynchronous orbit}}
−	* [http://forum.kerbalspaceprogram.com/showthread.php/30053-Heights-for-(semi-)-synchronous-orbits Heights for (semi-) synchronous orbits] on the KSP forums
−	** Includes a formula for calculating (semi)synchronous orbits

---

Latest revision as of 03:15, 23 February 2019

A synchronous orbit is an orbit where the orbital period equals the rotation rate of the orbited body. The eccentricity and inclination are not bound to specific values, although to be synchronous the orbit must not intersect with the atmosphere or surface of the orbited body, causing the orbit to change. Satellites in synchronous orbits have a ground track forming an analemma.

Important! You need to match your orbital period with sidereal rotation period not the solar day. So, for Kerbin it will be 5h 59m 9.425s instead of 6h that a lot of people go for.

Stationary orbits

Stationary orbits are a special kind of synchronous orbit. Its 0° inclination and its eccentricity of 0 cause its ground track to be only a point: a satellite in this orbit has no motion relative to the body's surface. Since it is impossible to get all orbital values exact for a stationary orbit, satellites in stationary orbits form small analemmata.

Some celestial bodies don't allow for synchronous orbits because the altitude required to synchronously orbit is beyond the body's sphere of influence. The body's slow rotation rate causes this effect: a very high altitude is necessary to allow for such a long orbital period. Tidally locked moons don't have synchronous orbit possibilities either because of their slow rotation. Moho is the only planet without any possibilities for a craft to achieve a synchronous orbit because of its very slow rotational period; Moho completes approximately two rotations during the time it takes for an object in the highest possible orbit to complete a revolution.

Semi-synchronous and similar orbits

When the orbital period is half as long as the rotational period, the orbit is usually described as semi-synchronous. It is possible to calculate the semi-major axis of a semi-synchronous orbit using Kepler's third law of planetary motion. With the knowledge about the semi-major axis of a synchronous orbit and the ratio between the two orbits:

${\displaystyle a_{\frac {1}{f}}={\frac {1}{\sqrt[{3}]{f^{2}}}}\cdot a_{1}}$

The fraction f is the quotient of the period of the synchronous orbit (a₁) and second orbit (a_1/f). When the second orbit is a semi-synchronous orbit this quotient is 2:

${\displaystyle a_{\frac {1}{2}}={\frac {1}{\sqrt[{3}]{2^{2}}}}\cdot a_{1}={\frac {1}{\sqrt[{3}]{4}}}\cdot a_{1}}$

An orbit where the orbital period is lower than the rotational period has some advantages, as some bodies don't allow synchronous orbits but opportunities for semi-synchronous orbits.

When dropping numerous payloads that should land nearby each other, the orbit should be an integer multiple of the celestial body's sidereal day. This way, the body stays the same relative to the orbit and has the same descent route, if each payload is detached at the same point in the orbit (e.g. apoapsis). The inverse factor f (= 1/f) defines how many days are between two detachments. For example, a super-synchronous orbit has f=1/2 so a payload could be dropped every two sidereal days or, when orbiting Kerbin, one every twelve hours.

An example of a semi-synchronous orbit for real world scientific applications is a Molniya orbit.

Sun-synchronous orbit

→ See also: Sun-synchronous orbit on Wikipedia

In the real world, there exists a sun-synchronous orbit. It's important to note that, although the name implies it, the orbit is not synchronous around the Sun. Instead, it describes an orbit around Earth which itself rotates, such that it appears the orbiting object is motionless relative to the Sun. Since it requires objects to have uneven gravitational fields, it is impossible to simulate in KSP.

Molniya orbit

A Molniya orbit is a semi-synchronous, highly elliptical orbit. The eccentricity should be as high as the central body permits. A three-satellite constellation in Molniya orbits can provide constant coverage to the high attitude regions. To set up such constellation, the mean anomalies of these three satellites should be spaced out by ${\displaystyle 120^{\circ }}$ or ${\displaystyle {\frac {2\pi }{3}}}$. The longitudes of the ascending nodes can also be spaced out by ${\displaystyle 120^{\circ }}$ to make the clover appearance.

For Kerbin, that equate to 70k for PE, 3117k for AP, and around 63 degree inclination.

Advantages of synchronous orbits

One advantage of a synchronous orbit is that they allow dropping multiple payloads from one craft, because the orbit will periodically travel above the same point on the body's surface. Usually, the orbit has a large eccentricity so that the payload has to complete a minimal amount of maneuvers to reach the surface. In this case the payload is detached at the apoapsis and decelerated such that it lands on the celestial body. After the payload has successfully landed, the next payload can be dropped as soon as the craft reaches the apoapsis again.

Stationary orbits

Communication to a satellite in a stationary orbit is easier than if it was in another orbit, as the ground based antennae do not have to move to account for the satellite's motion relative to the orbited body.

Orbital altitudes and semi-major axes of Kerbal's major bodies

The following table contains the altitudes for circular, synchronous orbits around all of Kerbal's celestial bodies, even when the altitude resides outside the SOI. The altitudes are relative to the body's surface, while the semi-major axes are measured from the body's center.

Body	Synchronous orbit		Semi-synchronous orbit		Tidally locked
	Altitude	Semi-major axis	Altitude	Semi-major axis
Kerbol	1 508 045.29 km	1 769 645.29 km	853 206.67 km	1 114 806.67 km	–
Moho	18 173.17 km †	18 423.17 km †	11 355.87 km †	11 605.87 km †	No
Eve	10 328.47 km	11 028.47 km	6 247.50 km	6 947.50 km	No
Gilly	42.14 km	55.14 km	21.73 km	34.73 km	No
Kerbin	2 863.33 km	3 463.33 km	1 581.76 km	2 181.76 km	No
Mun	2 970.56 km †	3 170.56 km †	1 797.33 km	1 997.33 km	Yes
Minmus	357.94 km	417.94 km	203.29 km	263.29 km	No
Duna	2 880.00 km ‡	3 200.00 km	1 695.87 km	2 015.87 km	No
Ike	1 133.90 km †	1 263.90 km †	666.20 km	796.20 km	Yes
Dres	732.24 km	870.24 km	410.22 km	548.22 km	No
Jool	15 010.46 km	21 010.46 km	7 235.76 km	13 235.76 km	No
Laythe	4 686.32 km †	5 186.32 km †	2 767.18 km	3 267.18 km	Yes
Vall	3 593.20 km †	3 893.20 km †	2 152.56 km †	2 452.56 km †	Yes
Tylo	14 157.88 km †	14 757.88 km †	8 696.88 km	9 296.88 km	Yes
Bop	2 588.17 km †	2 653.17 km †	1 606.39 km †	1 671.39 km †	Yes
Pol	2 415.08 km †	2 459.08 km †	1 505.12 km †	1 549.12 km †	Yes
Eeloo	683.69 km	893.69 km	352.99 km	562.99 km	No

• † indicates that the altitude resides outside the SOI
• ‡ indicates that the altitude is the same as the orbit of another object

See also

• KEO, the stationary orbit around Kerbin
• Geosynchronous Orbit (Math), some math on how to calculate a synchronous orbit
• Synchronous orbit on Wikipedia
• Stationary orbit on Wikipedia
• Geostationary orbit on Wikipedia
• Geosynchronous orbit on Wikipedia