Geostationary Orbits

So, you wanna get a probe in a geostationary orbit? Well look no further! In this guide I'll explain how the geostationary orbit works and how to get it for every planet where it's possible!

What is a geostationary orbit?

A geostationary orbit, geostationary Earth orbit or geosynchronous equatorial orbit (GEO) is a circular orbit 35,786 kilometres (22,236 mi) above the Earth's equator and following the direction of the Earth's rotation. An object in such an orbit has an orbital period equal to the Earth's rotational period (one sidereal day), and thus appears motionless, at a fixed position in the sky, to ground observers. Source[en.wikipedia.org].

Do note that this term only applies to the Earth. The general term for an orbit that does not appear to move to ground observers is called a Stationary orbit. You may also see the term Synchronous orbit being used. The difference between a Synchronous and Stationary orbit, is that the Stationary orbit is a type of Synchronous orbit. An orbit is a Synchronous one if the orbital period matches the rotation rate of the orbited body. An orbit becomes a Stationary one if the inclination and eccentricity are 0, resulting in no relative motion relative to the ground.

In layman's terms, this means that one orbit takes the same amount of time as is takes for planet to turn a full circle,. and that the orbit needs to be aligned with the equator. On earth, this means that the orbit takes 24 hours to complete. The GIF beautifully demonstrates the concept:

This concept is particularly useful for communication satellites. By using this technique, we can put a satellite above the KSC, and have it beam the signal across the Kerbin system, or even the Kerbol system!

Do note that we are matching the rotation speed of a sidereal day, and not solar days. This short video by astrogirlwest illustrates the difference between the two:
https://youtu.be/lwVf-AvD8ds?t=5
The difference between a sidereal day and a solar day on earth is about 3 minutes and 56 seconds, but remember, this stacks up orbit after orbit! Getting these two confused will mean that your satellite will slowly drift away from your originally aligned position!

How do I achieve one?

Well, to get one you need an orbit which takes the exact time to complete as the planet needs to spin around it's axis. On kerbin this is 6 hours. The altitude linked to this time is 2 863.33 km. This orbit is called Keostationary, or KEO for short.

And now, for a whole chart:

• Kerbol (or sun) 1 508 045.29 km
  
• Eve 10 328.47 km
  
• Gilly 42.14 km
  
• Kerbin 2 863.33 km
  
• Minmus 357.94 km
  
• Duna 2 880.00 km (Be aware that this orbit intersects with Ike!)
  
• Dres 732.24 km
  
• Jool 15 010.46 km
  
• Eeloo 683.69 km

Some of you may be dissapointed to find out that for certain celestial bodies, it is impossible to achieve stationary orbits. Sadly the altitudes needed to match the rotation, is so far away, that it lies outside the sphere of influence, or SOI. This make a stationary orbit for this body impossible.

The source for these values can be found here[wiki.kerbalspaceprogram.com].

You're ready!

So, you've made it through the guide! I hope you can reach that orbit you like and enjoyed reading my guide.

If you're having issues making the small corrections needed to achieve this precise orbit, be sure to use the thrust limiter function on your engine(s) to maximise your precision during burns. Another solution would be designing probes with ion engines, but I'll leave that design choice onto you.

Edit: Thanks for the positivity for my guide guys! I really appreciate it!

Sources

• https://en.wikipedia.org/wiki/Geostationary_orbit
  
• https://wiki.kerbalspaceprogram.com/wiki/Synchronous_orbit
  
• https://wiki.kerbalspaceprogram.com/wiki/KEO
  
• https://www.youtube.com/watch?v=lwVf-AvD8ds

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