# Elliptical satellite orbit around the earth

## Exercise

Elliptical satellite orbit around the Earth
1. Run the simulation. Calculate the speed necessary to travel in a circular orbit with radius 8400 km, i.e. the distance from the center of the earth to the satellite when the simulation starts. Also find the period. Problems with the calculations? Go to the parameters page and change the speed to the value that you calculated. Run the simulation to check if your value is correct.
2. Change the speed back to 8100 m/s. Stop the simulation when the satellite has the maximum distance from the earth. Note the distance and the speed. Then calculate this speed using the known distance. Problems with the calculations?
3. Make a sketch of the elliptical orbit. Draw acceleration vectors at some points on the orbit with approximately correct directions and mutual lengths. Check the menu item Show, Acceleration Vector, run the simulation and compare with your drawing. Study the acceleration vectors and explain their directions. Which effect will the acceleration vector have on the velocity at various points on the orbit? (Consider the components of the acceleration vector along the orbit and perpendicular to the orbit.)

Comment to b.
If the velocity and the distance are known in the point closest to the earth, we may find both the velocity and distance in the farthest point. It turns out that This is a special case of Kepler's third law, which follows from the law of conservation of angular momentum.

Combined with conservation of mechanical energy we have two equations with two unknowns.