Integrated Concepts

Space debris left from old satellites and their launchers is becoming a hazard to other satellites. (a) Calculate the speed of a satellite in an orbit 900 km above Earth’s surface. (b) Suppose a loose rivet is in an orbit of the same radius that intersects the satellite’s orbit at an angle of 90º relative to Earth. What is the velocity of the rivet relative to the satellite just before striking it? (c) Given the rivet is 3.00 mm in size, how long will its collision with the satellite last? (d) If its mass is 0.500 g, what is the average force it exerts on the satellite? (e) How much energy in joules is generated by the collision? (The satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)

Solution 48PE

Step 1 of

(a)

In part (a) we need to calculate the speed of satellite in an orbit of above the earth’s surface. Since the gravitational force acting on the satellite depending on the distance of the satellite from the earth’s. They possess different speed in different orbits.

The centripetal force acting on the satellite is given by,

Using newton's laws of motion

………...1

Where is centripetal force, m is mass of satellite and is centripetal acceleration of satellite.

Using centripetal acceleration for a satellite revolving with speed in an orbit around earth with orbital radius .

Equation 1 becomes,

……………..2