and gravitational force is equal to:
so:
Satellite Speed
In order for an object to orbit the earth, the centripetal force
holding the object in a circle must equal the gravitational force acting on
the object. If the gravitational force is too weak, the object will move away
from the earth. If the gravitational force is too strong, the object will move
towards the earth. Remember centripetal force is equal to:
and gravitational force is equal to:
so:
 |
Where m on the left hand side is equal to m1 on the right hand side so those terms will cancel. |
Solving for V we get the equation:
What this equation tells us is that in order for a satellite to orbit at a
certain distance from the earth, it must have a certain speed. The closer
the satellite is to the earth (The smaller r is) the quicker the satellite
has to move. The further away the satellite is from the earth (The larger
r is) the slower it will move. This should make sense because the acceleration
of gravity gets smaller as you move further from the earth and gets larger
the closer you get to the earth. Click Here to see how
to calculate the acceleration due to gravity acting on objects near the earth.
Is it possible to make these satellites stay over a certain spot on the planet?