Position satellite in stationary orbit of Minmus

[Kurld]

So, I get this contract. Is there an easy way to do this without sitting just inside the target orbit and waiting until the target looks like it is directly underneath your satellite, then circularizing?

[Spricigo]

 

Maybe that is the easy way.

The other one that I know is setting up a 'rendezvous' with the target position in the required orbit. That a bit difficult since is not possible to target a imaginary vessel but you can calculate things considering that the required orbital period is known (and unfortunately is also long).

[WanderingKid]

I typically put my apo on the correct orbit, periapsis as low as possible, then guesstimate with KAC when I should come back and care for circularization.

[bewing]

You want to start in a low circular orbit, because that lets you get near your target ground point quickly. You can calculate an altitude so that you know exactly how many degrees your satellite will gain as it climbs to the minsynch altitude, or you can just do it by eye. But you wait until you are X degrees behind your target point, then burn to set your Ap, then circularize again at your Ap to complete the contract.

 

[Kurld]

I've kind of been doing it by eye, and it works OK, but If somebody can point to the maths for this, that would be awesome.

[Spricigo]

 

The math behind it is the Kepler's Laws, more specifically the 3rd one:

Since the target orbit is circular , its orbital velocity is constant. If you are at the desired altitude, an angle ϕ apart from the required position, you want to complete one orbit while the target complete one orbit plus or minus ϕ, so you desired orbital period is:

     (for angle in radians, substitute 2π for 360º if you are using degrees )

In the end , we don't even need to know the orbital period, as we get the formulas together  it get canceled out and we end with:

Edit: this tool may help,  it's meant to help deploying a number of satellites equally spaced in a circular orbit but the math is exactly the same. 

 

Edited August 4, 2017 by Spricigo

[Kurld]

Awesome, thank you!

 

[Spricigo]

57 minutes ago, Kurld said:

Awesome, thank you!

Welcome.  

I guess it can be clarified a bit (proper statement of what is what in the formula for example), but as long no one complains I will just assume is well explained enough. (laziness pays out faster than work ) 

[Kurld]

By all means, feel free to expand on your answer.  I can probably figure out the math if I stare at it long enough, but a layman's explanation never hurts.