Difference between revisions of "Synchronous orbit"

Revision as of 05:26, 7 October 2014

A synchronous orbit is an orbit with the same orbital period as the rotational period of the orbited body. The eccentricity and inclination aren't bound to specific values, although the orbit shouldn't intersect with the atmosphere or surface of the orbited body. Satellites on a synchronous have a ground track forming an analemma.

A stationary orbit is a special kind of synchronous orbit where the ground track is only a point. Additionally to the orbital period is the eccentricity 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 and the surface velocity is zero. This makes the communication easy as the ground based antennae don't have to follow the satellite's relative motion. Because it is impossible to get all values exact for a stationary orbit, also satellites in stationary orbits form a small analemma.

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.

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

Semi-synchronous and similar orbits

When the orbital period is half as long as the rotational period, the orbit is usually called semi-synchronous orbit. 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 semi-synchronous orbits.

When dropping numerous payloads which should land nearby to each other from an orbit which is 1/f-synchronous -that is, an object that orbits it's parent celestial body f times within a sidereal day- it is possible to drop a payload f times in one day (of the celestial body). For example, a semi-synchronous orbit has f=2 so you could drop two different payloads within one sidereal day or, when orbiting kerbin, one every three hours.

One example for a semi-synchronous orbit in real world science is a Molniya orbit.

Altitudes and semi-major axes

The following table, contain the altitudes for a circular synchronous orbit around all celestial bodies, even when the altitude resides outside the SOI. The altitudes are from the body's surface, while the semi-major axes are from the body's center.

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

Sun-synchronous orbit

→ See also: Sun-synchronous orbit on Wikipedia

In the real world exists a sun-synchronous orbit, which isn't like a synchronous orbit around the Sun. Instead it describes an orbit around Earth which itself rotates, so it looks like the orbit stays the same relative to the Sun. As it requires an uneven gravitational field it is impossible to simulate in KSP.

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
• Heights for (semi-) synchronous orbits on the KSP forums; Includes a formula for calculating (semi)synchronous orbits