How Do You Calculate Orbital Speed Using Kepler's Laws?

[vle1]

Homework Statement

http://img518.imageshack.us/img518/2716/question11mediumjj8.jpg

This was an extra question for final exam some years ago, i hope that some one can direct me to obtain the right answer. I could not good find equations that I learn to answer this

 

[andrevdh]

Navigate: Mechanics -> Orbits -> Kepler's laws. Then scroll down for more info on the subject on the page that you land on.

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html"

Note that Kepler's third law is also applicable to the circular orbit of the space station.

 

[nrqed]

Homework Statement

http://img518.imageshack.us/img518/2716/question11mediumjj8.jpg

This was an extra question for final exam some years ago, i hope that some one can direct me to obtain the right answer. I could not good find equations that I learn to answer this

You know the period you want.

Use Kepler's third law to find the semimajor axis of the orbit you need.

Once you know the semimajor axis, you know the total energy you will have at any point of your orbit (there is a simple formula giving the total energy at any point of an orbit in terms of the semimajor axis and the masses).

Now set that energy equal to $1/2 m v^2 - G m M /r$ where r is the initial distance from the center of the Earth. That will give you the speed you need.