Orbital mechanics- change of inclination

[subsonicyouth]

Homework Statement

I'm trying to solve this problem: What's the delta-v required to change a satellite's inclination from Earth's to Mars' plane? Where should the plane change be done for the minimum velocity change? ( Satellite's transfer will be done with Hohmann transfer orbit.)

Homework Equations

I've found an equation on wikipedia (http://en.wikipedia.org/wiki/Orbital_inclination_change)
: dVi= [2sin(di/2)*(thesquarerootof(1-e^2))*cos(W+f)*n*a]/ (1+ecos(f))
where e is the eccentiricity,
W is the argument of perigee,
f is the true anomaly and n is the mean motion.

The Attempt at a Solution

You have to find the mean motion which is the square root of (G*(M+m))/a^3 where M and m are masses of the bodies to solve the eq. What I don't understand, which 2 bodies am I going to use? The masses of Earth and Mars, or Sun and Mars? And, how can I calculate the argument of perigee? Also, I'm not sure but I thought that for the minimum delta-v change the plane change should be done on the apogee. Is it correct?

Thank you.

 

[gneill]

Take a look at the attached figure. can you spot where it would be "easiest" to make the orbit inclination change with minimal delta-V?

 

[subsonicyouth]

I think it should be at the intersection point where mars' and Earth's inclination are equal.

 

[gneill]

I think it should be at the intersection point where mars' and Earth's inclination are equal.

You mean where the latus rectum of the spacecraft 's orbit meets the spacecraft 's trajectory?

 

[subsonicyouth]

You mean where the latus rectum of the spacecraft 's orbit meets the spacecraft 's trajectory?

Yes, am I wrong?

 

[gneill]

Yes, am I wrong?

No, you are right.

 

[subsonicyouth]

:) All right, thanks for your help.

 

[gneill]

:) All right, thanks for your help.

Glad to help.

 

[rubangeorge]

in order to change orbital plane impulse velocity should be applied at the nodes