Question

A satellite is orbiting a distant planet of mass 9.5e25 kg and radius 66900 km. The satellite orbits at a height of 9960 km above the surface of the planet. a) Determine the acceleration due to gravity at the location of the satellite orbit.

Answer 1

1.43 m/s^2

Step-by-step explanation:

To determine the acceleration due to gravity at the location of the satellite's orbit, we can use the formula for gravitational acceleration:

g = G * (M / r^2)

where:

g is the gravitational acceleration,

G is the gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2),

M is the mass of the planet, and

r is the distance between the center of the planet and the satellite.

Given:

M = 9.5e25 kg (mass of the planet)

r = radius of the planet + height of the satellite

First, let's convert the given distances from kilometers to meters:

Radius = 66900 km * 1000 = 6.69e7 m

Height = 9960 km * 1000 = 9.96e6 m

Next, we calculate the total distance from the center of the planet to the satellite:

r = Radius + Height = 6.69e7 m + 9.96e6 m = 7.69e7 m

Now, we can calculate the gravitational acceleration:

g = G * (M / r^2)

= 6.67430 × 10^-11 m^3/kg/s^2 * (9.5e25 kg / (7.69e7 m)^2)

Evaluating this expression using a calculator, we find that the acceleration due to gravity at the location of the satellite's orbit is approximately 1.43 m/s^2.