-Suppose you have traveled to Sirius B with its radius of 5,842,200 m and mass of 1.945 x 10^30 kg. You are traveling in a spaceship 100 meters long. After arriving at close to the speed of light, you slow your spacecraft down to a velocity of only 43.19km/sec at a distance of 1 million km from the center of the star. This puts you into an elliptical orbit with a periastron only 1,000 km above the star's surface. What will be your orbital velocity at periastron. Hint: use conservation of energy.
What is the period of your orbit?
The Attempt at a Solution
I know that I am going to be finding potential and kinetic energy in order to complete this problem, but I'm not exactly sure what I am supposed to do with them.