[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.

 

[Mene]

I would first clarify the problem statement to make sure all the necessary information is provided. In this case, it seems like the problem is asking for the true anomaly and eccentricity of an Earth satellite with a given speed, flight path angle, and radius at a specific point in its orbit. However, more information is needed, such as the position of the satellite in its orbit (i.e. its longitude or time since periapsis) and the mass of the Earth.

Assuming this information is known, the approach provided in the attempt at a solution seems correct. The r and v vectors can be found by converting the given speed and flight path angle into Cartesian coordinates in the Earth reference frame. From there, they can be transformed into the perifocal frame and the true anomaly and eccentricity can be calculated using the provided equations.

It would also be helpful to provide a diagram or figure to better visualize the situation and to make sure all the calculations are being done correctly. it is important to double check all calculations and make sure all assumptions are valid before arriving at a final answer.