This problem has 5 parts. I will type out the questions for each of these five parts and any additional info in the "Description" below.

Question

Space debris left from old satellites and their launchers is becoming a hazard to other satellites. One can estimate how long such a collision lasts; if an object of length l is travelling at a velocity v, it will cover a distance l in a time equal to l/v. This is the approximate time of interaction for an object being smashed against another object.

Part a) Calculate the speed (in m/s) of a satellite in an orbit 870 km above Earth's surface.

Part 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 speed (in m/s) of the rivet relative to the satellite just before striking it?

Part c) Given the rivet is 2.8 mm in size, how long will its collision with the satellite last? In this approximation, the rivet is completely destroyed and the collision does not slow the rivet down.

Part d) If its mass is 0.48 g, what is the average force it exerts on the satellite? The destroyed rivet is assumed to have zero velocity after the collision.

Part 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.)

Answer 1

a) v_sat=sqrt(GM_e/(r_e+altitude of satelite))=7495 m/s

b) v_rivet=v_sat thus v_rel=sqrt(7495+7495)=10600 m/s

c) trivet= .0028/10600=2.64E-7 seconds =dt

d) Fdt=mdv thus F= mdv/dt but part c) says dv=0 but is destroyed ... can't have it both ways! Let's assume dv=-7495 as the rivet is destroyed, thus F= .00048(-10600)/2.64E-7=1.93E7 Newtons

e) Energy of collision is 1/2(.00048)(10600)^2 = 26966 J