Jump to content

Calculating non-circular synchronous orbits


wasmic

Recommended Posts

So, I've been looking around for an equation for calculating orbital period, but I haven't found anything that deals with two bodies; one massive and one of negligible mass. All of the equations that I have found seem to be dealing with two more-or-less massive bodies.

Also, is it possible to calculate orbital period from semi-major axis, semi-minor axis, planet density and planet mass, or should semi-major axis, eccentricity, planet density and planet mass be used? Are there any other things that I forget to factor in?

My real reason for wanting to know this, is that I want a formula where I can put a semi-major axis in, and then calculate what the semi-minor axis should be to achieve synchronous orbit. This would be useful for setting things like Molniya orbits up in KSP.

Link to comment
Share on other sites

For a given central body and a small orbiter, the orbital period only depends on the semi-major axis and none of the other parameters you mention. So just take a circular synchronous orbit and make the sum of the apoapsis and periapsis height match two times the apo/periapsis height of that circular orbit.

Link to comment
Share on other sites

For a given central body and a small orbiter, the orbital period only depends on the semi-major axis and none of the other parameters you mention. So just take a circular synchronous orbit and make the sum of the apoapsis and periapsis height match two times the apo/periapsis height of that circular orbit.

Oh, right, thanks. I completely forgot what semi-major and semi-minor axes were alltogether :P

Thanks a lot, again. It'll help a lot.

Link to comment
Share on other sites

Real world orbits do depend on inclination and ellipticity of the orbit, but only because Earth is not perfectly spherical. In KSP, all planets are assumed to be perfect spheres, and therefore, period of any orbit depends on semi-major axis only. The game does, also, take an approximation that mass of the ship is negligible, yielding a formula T = 2À Sqrt(a³/μ). The gravitational parameter μ is equal to GM, where M is mass of the planet, but in KSP, the value for μ is stored directly in the game's data.

Link to comment
Share on other sites

This thread is quite old. Please consider starting a new thread rather than reviving this one.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...