Elliptical satellite orbit around the Earth
- 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.
- 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?
- 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.