Question

A 2160 kg satellite used in a cellular telephone network is in a circular orbit at a height of 800 km above the surface of the earth. What is the gravitational force on the satellite? What fraction is this force of the satellite's weight at the surface of the earth?

I've looked at other problems but I'm not getting the correct answer, I've gotten 21168 for the first one and 0.998 for the second part.

Answer 1

As acceleration due to gravity above earth's surface

Is g' = gR^2/(R+h)^2

At h = 800km

g' = 9.8×6400^2/(7200)^2 = 7.74 m/s^2

So force experienced is F = mg' = 2160×7.74 =16718.4N

Now fraction = mg' / mg = g'/g = 0.7901

Answer 2

To calculate the gravitational force on the satellite, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by:

F = (G * m1 * m2) / r^2

Where: F is the gravitational force G is the gravitational constant (approximately 6.67430 x 10^-11 N m^2/kg^2) m1 and m2 are the masses of the two objects (in this case, the satellite and the Earth) r is the distance between the centers of the two objects (in this case, the radius of the Earth plus the height of the satellite)

First, we need to calculate the distance between the satellite and the center of the Earth:

r = radius of the Earth + height of the satellite r = 6,371 km + 800 km r = 7,171 km

Converting the radius to meters: r = 7,171 km * 1000 m/km r = 7,171,000 m

Now we can calculate the gravitational force:

F = (G * m1 * m2) / r^2 F = (6.67430 x 10^-11 N m^2/kg^2 * 2160 kg * 5.972 x 10^24 kg) / (7,171,000 m)^2

Calculating this expression, we find:

F ≈ 1.981 x 10^4 N

So the gravitational force on the satellite is approximately 1.981 x 10^4 N.

To find the fraction of this force compared to the satellite's weight at the surface of the Earth, we can calculate the weight of the satellite at the Earth's surface using the formula:

Weight = mass * acceleration due to gravity

On the surface of the Earth, the acceleration due to gravity is approximately 9.8 m/s^2. So we can calculate the weight as:

Weight = 2160 kg * 9.8 m/s^2 Weight ≈ 21,168 N

Finally, we can find the fraction by dividing the gravitational force on the satellite by its weight:

Fraction = (gravitational force) / (weight) Fraction = (1.981 x 10^4 N) / (21,168 N) Fraction ≈ 0.938

Therefore, the gravitational force on the satellite is approximately 1.981 x 10^4 N, and it is about 0.938 (or 93.8%) of the satellite's weight at the surface of the Earth