What is the gravitational field strength at the location of a satellite that is orbiting the Earth at an altitude of 5,000 km? (G = 6.67 × 10^-11 N m²/kg², the mass of the Earth is 5.98 × 10²⁴ kg, and the radius of the Earth is 6.38 × 10⁶ m.) A) 9.55 N/kg. B) 8.43 N/kg. C) 3.08 N/kg. D) 6.33 N/kg. E) 5.28 N/kg.

Question

Quizplus · Accepted Answer

The gravitational field strength at a distance r from the center of the Earth is given by:

$g = \frac{GM}{r^2}$

where 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 location of interest.

In this case, we are interested in the gravitational field strength at a distance of 5,000 km above the surface of the Earth. The total distance from the center of the Earth to this location is:

$r = R_{Earth} + 5,000 	ext{ km}$

where $R_{Earth}$ is the radius of the Earth.

Substituting the given values, we get:

$r = 6.38 	imes 10^6 	ext{ m} + 5.00 	imes 10^6 	ext{ m} = 1.338 	imes 10^7 	ext{ m}$

$g = \frac{G M}{r^2} = \frac{(6.67 	imes 10^{-11} N \cdot m^2/kg^2)(5.98 	imes 10^{24} kg)}{(1.338 	imes 10^7 	ext{ m})^2} \approx 3.08 	ext{ N/kg}$

Therefore, the best choice is C.

What Is the Gravitational Field Strength at the Location of a Satellite