What are the forces acting on a satellite?

Question

A satellite is put into a certain orbit in space at 1000 kilometer above see level. The total mass of satellite is 500 kilogram. Find the velocity of the satellite at which the orbit is maintained in space indefinitely. What is the centripetal force and the centrifugal force acting on the satellite during orbit? Thank you

Answer 1

The radius of Earth is 6370 km, so the satellite will be orbiting 7370 km from the earth's center.
The acceleration due to gravity is inversly proportional to the square of the distance, and (6370/7370)^2 is 0.747. Since at sea level, the acceleration due to garvity is 9.81 m/s^2, at 1000 km altitude it should be (0.747 * 9.81) = 7.238 m/s^2.

Angular motion equation is

AR = v^2/r

with AR being the centripetal acceleration, r the radius of the motion, and v the tengential vleocity. Solving for v returns a speed of 7349 m/s.

The centripetal force (and the centrifugal force) is provided by the force of gravity (the so called centrifugal by the motion of the satellite) and should be equal since they are balanced.
That acceleration of 0.747 g means a force of

F= m a

F = 500 kg (.747 * 9.81 m/s^2) = 3664 N

Answer 2

For a satellite in orbit around a planet, the centripetal force is supplied by the gravitational attraction between the satellite and the planet, and acts toward the center of mass of the two objects. The satellite has kinetic energy implies that it has some velocity.When the acceleration or force is normal to the direction of velocity, any object will have a curvilinear (Circular)path. The only force that acts on a satellite is the gravitational attraction force. Therefore there is no question of equal or opposite. When a single force acts in the direction of velocity the magnitude of the velocity changes, direction of force and velocity coincides. When a single force acts in the direction perpendicular to the velocity, the direction alone changes, magnitude of velocity remains the same. . when the force acts in any other direction both magnitude and direction of velocity change.

Answer 3

I assume you mean a circular orbit? If so, the above two answers are correct.

An elliptical orbit can also be maintained in space indefinitely, but the velocity and the forces would change constantly, making the question unanswerable. Only the angular momentum and total energy would remain constant.

Answer 4

Ok - this is a simple two body problem. The satellite has a centripital force given by:
Fc = mv^2/r where r = radisu of orbit

There is a gravitational force acting to pull it down:

Fg = GMm/r^2 where G is Newton's constant and M = mass of the earth. Now equate tehe two forces:

mv^2/r = GMm/r^2 ---> v = sqrt(GM/r)

G = 6.67 x 10^-11 Nt-m^2/kg M = 5.98 x 10^24 kg and r = 1000 + 6378 = 7378 km = 7.378 x 10^6 m

v = 7352.7 m/s

You can compute the force of gravity and the centripital force.