[spacefight mechanics]how to find true anomaly and eccentricity?

[smalllittle]

Homework Statement

An Earth satellite has a speed of 7km/s and a flight path angle of 15 degree when its radius is 9000km calculate the true anomaly and eccentricity of the orbit.

Homework Equations

r=h^2/u(1+ecostheta)

The Attempt at a Solution

The problem statement just doesn't seem provided enough information. The direction to the solution should deal with lagrange coefficients. Express r and v in the standard Earth refrence frame using flight pitch angle, then transfer them to the perifocal fame.
Then in perifocal fame:
h=r cross v (in perifocal fame)
e=1/u*(r cross v) -r(vector)/r
But i don't know how to find the r and v vectors in the standard Earth ref frame :(
correct me if my approach is incorrect >.>

the answer given is theta=83.35degree, e=0.2785

 

[D H]

The Attempt at a Solution

The problem statement just doesn't seem provided enough information. The direction to the solution should deal with lagrange coefficients. Express r and v in the standard Earth refrence frame using flight pitch angle, then transfer them to the perifocal fame.
Then in perifocal fame:
h=r cross v (in perifocal fame)
e=1/u*(r cross v) -r(vector)/r
But i don't know how to find the r and v vectors in the standard Earth ref frame :(
correct me if my approach is incorrect >.>

the answer given is theta=83.35degree, e=0.2785

The problem does provide all the information needed. You do not need to find the r and v vectors in "the standard Earth ref frame", just some earth-centered non-rotating reference frame.

BTW, your equation for the eccentricity vector is incorrect.