(a) Calculate the magnitude of the gravitational force exerted on a 430-kg satellite that is a distance of 2.81 times earth radii from the center of the earth. (b) What is the magnitude of the gravitational force exerted on the earth by the satellite? (c) Determine the magnitude of the satellite's acceleration. (d) What is the magnitude of the earth's acceleration?

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To calculate the magnitude of the gravitational force, we can use the formula:

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

where:
F is the magnitude of the gravitational force,
G is the gravitational constant (approximated as 6.674 × 10^-11 N(m/kg)^2),
m1 and m2 are the masses of the objects involved (in this case, the mass of the satellite and the mass of the Earth),
and r is the distance between the centers of the two objects.

(a) To calculate the magnitude of the gravitational force exerted on the satellite:
Given:
Mass of the satellite (m1) = 430 kg
Distance from the center of the Earth (r) = 2.81 times Earth radii

First, we need to find the distance between the satellite and the center of the Earth. Earth's radius is approximately 6,371 km.

Distance from the center of the Earth (r) = 2.81 * Earth radii = 2.81 * 6371 km

Next, we convert the distance from km to meters:
Distance from the center of the Earth (r) = 2.81 * 6371 km * 1000 m/km

Now we can substitute the values into the formula to calculate the magnitude of the gravitational force:

F = (G * m1 * m2) / r^2
F = (6.674 × 10^-11 N(m/kg)^2 * 430 kg * Earth's mass) / (2.81 * 6371 km * 1000 m/km)^2

Given that Earth's mass is approximately 5.972 × 10^24 kg, we can substitute this value:

F = (6.674 × 10^-11 N(m/kg)^2 * 430 kg * 5.972 × 10^24 kg) / (2.81 * 6371 km * 1000 m/km)^2

Calculating this equation will yield the magnitude of the gravitational force exerted on the satellite.

(b) To calculate the magnitude of the gravitational force exerted on the Earth by the satellite:
The magnitude of the gravitational force between two objects is the same, regardless of the masses of the objects. Therefore, the magnitude of the gravitational force exerted on the Earth by the satellite is the same as the magnitude of the gravitational force exerted on the satellite.

Once you calculate the magnitude of the gravitational force using the formula in part (a), that will be the answer to part (b) as well.

(c) To determine the magnitude of the satellite's acceleration:
We can use Newton's second law of motion:

F = m * a

where:
F is the magnitude of the gravitational force,
m is the mass of the satellite,
and a is the acceleration of the satellite.

Rearranging the equation to solve for a:

a = F / m

Substitute the calculated magnitude of the gravitational force and the mass of the satellite into the equation to get the magnitude of the satellite's acceleration.

(d) To calculate the magnitude of the Earth's acceleration:
The Earth's acceleration due to gravity can be calculated using the equation:

a = F / m

where:
F is the magnitude of the gravitational force between the Earth and the satellite,
m is the mass of the Earth.

Substitute the calculated magnitude of the gravitational force and the mass of the Earth into the equation to get the magnitude of the Earth's acceleration.