Difference between revisions of "Synchronous orbit"
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Revision as of 04:48, 26 September 2016
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.
Contents
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:
![a_{{\frac {1}{f}}}={\frac {1}{{\sqrt[ {3}]{f^{2}}}}}\cdot a_{1}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/37991efd4f38572751b603de65d9bc1d72836e0b)
The fraction f is the quotient of the period of the synchronous orbit (a1) and second orbit (a1/f). When the second orbit is a semi-synchronous orbit this quotient is 2:
![a_{{\frac {1}{2}}}={\frac {1}{{\sqrt[ {3}]{2^{2}}}}}\cdot a_{1}={\frac {1}{{\sqrt[ {3}]{4}}}}\cdot a_{1}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/61510cf2304d6941ea6fe7e9b88d1173ed8e5aa6)
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.
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
