A 5,000 kg satellite is orbiting the Earth in a circular path.The height of the satellite above the surface of the Earth is 800 km.The time it takes for the satellite to travel around the Earth is (Me = 5.98 $\times$ 10²⁴ kg, Re = 6.37 $\times$ 10⁶ m, G = 6.67 $\times$ 10^-11 N.m²/kg²) A) 0.750 hours. B) 0.950 hours. C) 1.25 hours. D) 1.68 hours. E) 2.01 hours.

Question

Quizplus · Accepted Answer

We can use the formula T = 2π√(r³/GM), where T is the period of the satellite (the time it takes to complete one orbit), r is the radius of the orbit (which is equal to the sum of the radius of the Earth and the height of the satellite), G is the gravitational constant, M is the mass of the Earth.

r = Re + h = 6.37 × 10^6 m + 8 × 10^5 m = 7.17 × 10^6 m

Plugging in the values, we get:

T = 2π√((7.17 × 10^6)^3 / (6.67 × 10^-11 × 5.98 × 10^24))
T = 1.68 hours

Therefore, the correct answer is D) 1.68 hours.

A 5,000 Kg Satellite Is Orbiting the Earth in a Circular