An 76 kg satellite orbits a distant planet with a radius of 4500 km and a period of 280 min. From the radius and period, you calculate the satellite's acceleration to be 0.63 m/s2. What is the gravitational force on the satellite?

gravity is the centripetal force keeping the satellite in orbit

g = m a = 76 kg * .63 m/s^2

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

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, the satellite is being attracted towards the planet, so the mass of the planet (m2) is larger than the mass of the satellite (m1). Therefore, we can consider m1 to be the mass of the satellite, which is 76 kg.

To calculate the gravitational force, we need to find the mass of the planet and the distance between the centers of the planet and the satellite.

Step 1: Find the mass of the planet
To find the mass of the planet, we can use the formula for the acceleration due to gravity:

a = (G * M) / r^2

where:
a is the acceleration due to gravity
M is the mass of the planet
r is the radius of the planet

We are given that the acceleration due to gravity (a) is 0.63 m/s^2 and the radius of the planet (r) is 4500 km. However, we need to convert the radius to meters, so it becomes 4500 km * 1000 m/km = 4,500,000 m.

Plugging in these values into the equation, we can solve for M:

0.63 m/s^2 = (6.67430 × 10^-11 N m^2 / kg^2 * M) / (4,500,000 m)^2

Simplifying, we can solve for M:

M = (0.63 m/s^2 * (4,500,000 m)^2) / (6.67430 × 10^-11 N m^2 / kg^2)

M ≈ 5.26 × 10^24 kg

Step 2: Find the distance between the centers of the planet and the satellite
The distance between the centers of the planet and the satellite is equal to the radius of the planet, which is 4,500,000 m.

Step 3: Calculate the gravitational force
Now that we have the mass of the planet (M = 5.26 × 10^24 kg) and the distance between the centers of the planet and the satellite (r = 4,500,000 m), we can calculate the gravitational force (F):

F = (G * m1 * m2) / r^2
F = (6.67430 × 10^-11 N m^2 / kg^2 * 76 kg * 5.26 × 10^24 kg) / (4,500,000 m)^2

Calculating this expression will give you the gravitational force on the satellite in newtons.