How Do You Solve Orbital Mechanics Problems Involving Central Forces?

[Otto31]

Homework Statement

1) A satellite having a mass of 5000 kg describes a circular path around the Earth of radius
8000 km. Find (a) its angular momentum and (b) its potential, (c) kinetic and (d) total
energy. Also calculate (e) the orbital period.

2) Assume the satellite in the previous problem is given an horizontal velocity 20% greater
than the velocity required to achieve a circular orbit. Find (a) its new angular momentum
and (b) total energy, and determine (c) the shape of the orbit, including its maximum and/or
minimum distance to the Earth's center.

3) A comet is observed at a distance of 1011 m from the Sun, traveling toward it with a velocity
5.16 x 104 m/s at an angle of 45° with the radius vector from the Sun. Determine (a) the
shape of the orbit and (b) its closest approach to the Sun.

Homework Equations

L = r x p

E = Ek + U(r)

Our teacher gave us the following link in order to resolve the exercises:
http://www-physics.ucsd.edu/students/courses/fall2010/physics110a/LECTURES/CH09.pdf

The Attempt at a Solution

My attemp at a solution was first, calculate the angular momentum and the Total Energy in each problem, then with the graphic E(r) I should calculate the shape of the orbit, but this is where the problem get stuck. In all three exercises I know how to calculate L and E, but I can't "imagine" the proper way to continue solving the problems. Sorry if It something is wrong with this thread, but this is my first post.

 

[raopeng]

For question I I think it doesn't need to be so complicated, after all in the case of a circular orbit there is an easy identity to exploit(U= -2T)