A 600-kg geosynchronous satellite has an orbital radious of 6.6 Earth radii. What gravitational force does Earth exert on the satellite?

F=mass*w^2*r

w=2PI/period. Period is 24 hrs, but you need to convert that to seconds. R= 6.6*
RadiusEarth

800 newtons

To calculate the gravitational force that Earth exerts on the geosynchronous satellite, we need to use Newton's law of universal gravitation:

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

Where:
F is the gravitational force
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of two objects
r is the distance between the centers of the two objects

In this case, Earth is one object, and the satellite is the other object. The mass of Earth is approximately 5.972 × 10^24 kilograms, and the mass of the satellite is 600 kilograms. The distance between Earth's center and the satellite is the sum of the orbital radius and the radius of Earth, which is 6.6 Earth radii.

Plugging in the values:

F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 * 5.972 × 10^24 * 600) / (6.6 * 6,371,000)

By simplifying this equation, we can calculate the gravitational force exerted by Earth on the satellite.

To determine the gravitational force that Earth exerts on the satellite, we can use Newton's law of universal gravitation. This law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

The formula to calculate the gravitational force (F) is given by:

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

Where:
- F is the gravitational force
- G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
- m1 and m2 are the masses of the two objects
- r is the distance between the centers of the two objects

In this case, we have:
- The mass of the satellite (m1) = 600 kg
- The mass of the Earth (m2) ≈ 5.972 × 10^24 kg (average mass of the Earth)
- The distance between the centers of the satellite and Earth (r) = 6.6 Earth radii

To use this formula, we need to convert the Earth radii to meters, as the gravitational constant is given in SI units. The average radius of the Earth is approximately 6,371 kilometers.

1 Earth radius ≈ 6,371 km ≈ 6,371,000 meters

Therefore, the distance between the centers (r) is:
r = 6.6 × 6,371,000 meters

Now we can substitute the values into the formula and calculate the gravitational force:

F = (6.67430 × 10^-11 N m^2/kg^2) * (600 kg) * (5.972 × 10^24 kg) / ((6.6 × 6,371,000 meters)^2)

After performing the calculation, we find the value of F.