Figuring Mun orbits for sat deployment.

[Chocki]

I need to figure out 2 orbits to deploy 4 com sats. The main orbit should be a high Mun equatorial orbit, the second should have an Ap equal to the main orbit, but be a quater of the main orbits orbital period. The point is to allow me to deploy a sat, and circulaize at Ap, leaving the deploy vehicle to make 1 orbit and be ready to deploy the next sat at a 90 degree angle to the first. 4 orbits, would mean a 4 sats equally spaced along the main orbit.

My question is how would I go about figuring out what orbits would work, without using trial and error. I know the orbital period needs to be a 1/4 ratio (deploy orbit / final) but I am lost as to what figures, equations I would need.

[Banbite]

This is a great use for keplers third law: (orbital period)^2 is proportional to (semi major axis)^3, or T^2=k*a^3 where k is an arbitrary constant which is the same for all orbits around a body. I just did something similar but with 3 instead of 4 satellites so I know this works. So math:

Seeing your problem the second orbit should actually have a orbital period that is 3/4 of the equitorial orbit, so T2 = 3/4*T1 where T1 is the orbital period of the equitorial orbit and T2 is the period of the "deploy" orbit. This will make the satellite end up 90 degrees in front of the other satellite

This gives that T1^2/a1^3 = T2^2/a2^3 => (T2/T1)^2 = (a2/a1)^3 which gives: a2=(T2/T1)^(2/3)*a1

This gives us the ratio between the "final orbit" and the "deploy orbit", and if T2/T1=3/4 then a2=(3/4)^(2/3)*a1 = 771/934*a1 = 0.8255*a1

To see what this gives for Pe for the deploy orbit use the following formula: a = (Pe + Ap + 2*R)/2, where R is the radius of the body, for the Mun R = 200km.

Assuming the "final orbit" is circular the Pe of the "deploy orbit" gets:

a1 = Ap+R; a2 = (Pe + Ap + 2*R)/2; a2=0.8255*a1;

Pe = 2*0.8255*(Ap + R) -Ap - 2*R

Example: If your final orbit has an altitude of 500km then your Pe becomes: Pe = 2*0.8255*(500 + 200) - 500 - 2*200 = 255.7 km

Just punch in your own Ap to get your value of Pe. When you're deploying the satellites you can make one orbit with the first, two orbits with the second, and three orbits with the third and you should have everyone in a nice 90 degree separation. Or you can redo the calculations with T2/T1 = 1/2 and 1/4 and do everything in one orbit, but you're likely to crash on the 1/4 one if you're Ap is to low.

[duncan1297]

[Chocki]

I almost feel the same way, but I got formulas, and understood most of it. I am at least headed in the right direction. That, and I'm awsome at plug and chug math.