Question

An astronaut weighs 200 pounds at sea level about 4000 miles from Earth's center. Find an equation of F.f(d)= ____.

a) 200-GM/(d+4000)^2
b) 200-GM/d^2
c) 200- GM/(d-4000)^2
d) 200-GM/d^2+4000^2

Answer 1

The equation that represents gravitational force at a given distance from Earth's center is F.f(d) = 200 - GM / (d + 4000)^2 (option a).

Step-by-step explanation:

The equation that represents gravitational force at a distance d from Earth's center is F.f(d) = 200 - GM / (d + 4000)^2 (option a).

In this equation, F is the force, G is the gravitational constant (approximately 6.67 × 10^-11 Nm^2/kg^2), M is the mass of Earth (approximately 5.97 × 10^24 kg), and d is the distance from Earth's center in meters.

The equation accounts for the decrease in gravitational force as the distance from Earth's center increases.