Calculating orbital velocity at periastron

AI Thread Summary
To calculate the orbital velocity at periastron for a spacecraft near Sirius B, one must apply the conservation of energy principle, focusing on gravitational potential energy and kinetic energy. The initial kinetic energy and gravitational potential energy can be determined with the given parameters, allowing for the calculation of kinetic energy at periastron. The discussion emphasizes that only relevant information should be considered, as potential energy depends solely on distance and kinetic energy on speed. The period of the orbit can also be derived from these calculations. Understanding these concepts is crucial for solving the problem effectively.
ketkup
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Homework Statement


-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?

Homework Equations





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.
 
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Total energy is conserved, and the only contributions to energy here are gravitational potential energy and kinetic energy. You have all the information needed to calculate the initial kinetic energy and to calculate the gravitational potential energy initially and at periastron. You can therefore calculate the kinetic energy at periastron, and thence the velocity.
 
Welcome to PF!

ketkup said:
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.

Hi ketkup! Welcome to PF! :smile:

I suspect you're being put off by the fact that most of the information given is irrelevant! :rolleyes:

Hint: PE depends only on distance, and KE depends only on speed. :wink:

EDIT: rats! D H beat me to it! :smile:
 

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