A satellite is in a circular orbit about the Earth at a distance of d = 5 times the Earth's radius above the surface.What is the speed of the satellite? (The radius of the Earth is 6.4 × 10⁶ m. ) A)4.2E+2 m/s B)1.3E+5 m/s C)3.2E+3 m/s D)3.3E+6 m/s

Question

Quizplus · Accepted Answer

We can use the formula for the speed of a satellite in circular orbit:

v = sqrt(GM / r)

where v is the speed of the satellite, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the satellite.

First, we need to find r. Since the satellite is at a distance of 5 times the Earth's radius above the surface, we have:

r = (6.4 × 10^6 m) + (5 × 6.4 × 10^6 m) 
r = 32 × 10^6 m

Next, we can plug in the values for G, M, and r and solve for v:

v = sqrt((6.67 × 10^-11 N(m/kg)^2) * (5.97 × 10^24 kg) / (32 × 10^6 m)) 
v ≈ 3.2 × 10^3 m/s

Therefore, the best choice is C.

A Satellite Is in a Circular Orbit About the Earth