(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Orbit Question

1. The problem statement, all variables and given/known data

A satellite is in a circular earth orbit of altitude 400km. Determine the new perigee and apogee altitudes if the satellite on-board engine gives the satellite a radial (outward) component of velocity of 240m/s.

Answers: Z_apogee = 621km, Z_perigee = 196km

2. Relevant equations

mu = 398600km^3/sec^2

h (specific angular momentum) = r*v_perpendicular

a = semimajor axis of ellipse

2*a = perigee radius + apogee radius

v^2/2 + mu/r = -mu/(2*a) ( specific energy equation )

e= eccentricity of the orbit

theta = the true anomaly angle ( angle between eccentricity vector and the position vector)

r_perigee = a(1-e)

radius of the earth = 6378km

r = h^2/mu * (1+e*cos(theta))

V_cir = sqrt(mu/r)

3. The attempt at a solution

I started off by getting the magnitude of the velocity (v_perp^2 + v_radial^2)^.5

then calculated the escape velocity to see if it would be a closed orbit.

I found that it was still an ellipse (i also calculated the specific energy and found that it was negative... thus being an ellipse) from the specific energy i got 'a' ( -mu/(2*a) )

and using rp = a(1-e) = h^2/mu*(1+e)^-1 (at theta = 0 for rp)

however... when i did this I used the same h that i got from the satellite being a circular orbit.. which i am unsure if that was incorrect to do..

finally after solving for e, i plugged it back into rp = a(1-e) to get ~ 6543km... then the altitude zp = 6543- 6378 = 165km.. which is incorrect... can anyone help?? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orbit Question

**Physics Forums | Science Articles, Homework Help, Discussion**