Question

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 90°. What is the velocity of the rivet relative to the satellite just before striking it? (c) If its mass is 0.500 g, and it comes to rest inside the satellite, how much energy in joules is generated by the collision? (Assume the satellite’s velocity does not change appreciably, because its mass is much greater than the rivet’s.)

a) 7.5 km/s
b) 10.6 km/s
c) 15.2 km/s
d) 20.1 km/s

Answer 1

The speed of a satellite in an orbit 900 km above Earth's surface is approximately 7.5 km/s. The velocity of the rivet relative to the satellite just before striking it is approximately 10.6 km/s. The energy generated by the collision between the satellite and the rivet is approximately 15.2 km/s.

The correct option is;c) 15.2 km/s;

Step-by-step explanation:

(a) To calculate the speed of a satellite in an orbit 900 km above Earth's surface, we can use the formula for orbital velocity:

v = √(GM/r)

Where G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2), M is the mass of the Earth (5.9722 x 10^24 kg), and r is the radius of the orbit (900 km + the radius of the Earth).

Plugging in the values, we get:

v = √((6.67430 x 10^-11) x (5.9722 x 10^24) / (9000000 + 6371000))

Simplifying, we find that the speed of the satellite in this orbit is approximately 7.5 km/s.

(b) To find the velocity of the rivet relative to the satellite just before striking it, we can use the formula for relative velocity:

v_relative = v_rivet - v_satellite

Since the angle between the rivet's orbit and the satellite's orbit is 90°, the relative velocity is equal to the sum of their individual velocities. Therefore, the velocity of the rivet relative to the satellite just before striking it is approximately 10.6 km/s.

(c) The energy generated by the collision can be calculated using the formula:

Ek = (1/2) * m * v^2

Where m is the mass of the rivet and v is the velocity of the rivet relative to the satellite. Plugging in the values, we get:

Ek = (1/2) * 0.0005 kg * (10.6 km/s)^2

Simplifying, we find that the energy generated by the collision is approximately 15.2 km/s.