math and orbiter not coinciding...?

[markl316]

Hi. So my friend had a physics question:

A satellite of 1000 kg in orbit around earth is at 5.6E6 meters in altitude and 7100 m/s at perigee (so Rp=11971000 and Vp=7100). His task was to use conservation of energy and conservation of angular momentum to find radial distance and velocity at apogee. Solving

mRpVp=mRaVa

and

.5*m*vp^2 - GMm/rp = .5*m*va^2 - GMm/ra

I got velocity at apogee to be 2300 m/s. But simulating this problem in orbiter, it says velocity should be 1361. I'm wondering where I went wrong. Because 2300 m/s and the corresponding radius (which can easily be calculated from va=2300 m/s) satisfies both of the above equations, while orbiter's value of 1361 does not. Thanks for any help.

 

[RisingFury]

Rp = 5.6 * 10^6 = 5 600 000 m

You gave a number Rp=11 971 000 m.... how did you get that?

 

[markl316]

Rp = 5.6 * 10^6 = 5 600 000 m

You gave a number Rp=11 971 000 m.... how did you get that?

5 600 000 meters was given as the altitude above the surface, so 5.6E6 + 6.371E6 is 11 971 000 m which is radial distance at perigee.

 

[Wolfer]

[deleted by author]

 

[RisingFury]

Ah, yes! Stupid me! It's not like a *stable* orbit around Earth can exist with a Rp=5.6E6 :lol:

Well, the velocity at any given point of the orbit (if you have altitude of periapsis) is given by:

v[r] = Sqrt[2*G*M*r/(Rp*(r+Rp))]


Of course, you need to find the altitude of apoapsis, but I'm running into a nasty equation that I'm having no luck in solving...

Your approach is correct though.

v1*r1 = v2*r2 (from conservation of angular momentum)
and
v1^2/2 - M*G/r1 = v2^2/2 - M*G/r2 (from conservation of energy)

are the equations you can use. Keep in mind, mass doesn't matter

 

[TJohns]

Maths is right...

Well, according to my OCalc program, your maths is right...

 

[Chode]

How are you reading the velocity in Orbiter? I get an apoapsis velocity of 2280 when I run a simulation.

Regards

 

[markl316]

Yeah, I ran it again, and 2280 works. I must have set something wrong. Thanks for the help everybody.