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Answer :
The altitude of the satellite is approximately 2.31 x 10^6 kilometers.
The gravitational force experienced by the satellite is 930 N. This force is provided by the Earth's gravitational pull on the satellite.
To find the radius of the satellite's orbit, we can use the formula for gravitational force:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, the satellite and the Earth), and r is the distance between their centers of mass (the radius of the orbit in this case).
Since we are given the gravitational force and the mass of the satellite, we can rearrange the formula to solve for the radius (r):
r = sqrt((G * m1 * m2) / F)
Plugging in the given values:
G = 6.67 x 10^-11 N m^2/kg^2
m1 = 128 kg
m2 = mass of the Earth (not given, but approximately 5.972 x 10^24 kg)
F = 930 N
Now we can calculate the radius:
r = sqrt((6.67 x 10^-11 N m^2/kg^2 * 128 kg * 5.972 x 10^24 kg) / 930 N)
r = sqrt(5.39 x 10^18 m^3/kg s^2)
r ≈ 2.32 x 10^9 meters
To convert this to kilometers, divide by 1000:
r ≈ 2.32 x 10^6 kilometers
Therefore, the radius of the satellite's orbit is approximately 2.32 x 10^6 kilometers.
To find the altitude of the satellite, we subtract the radius of the Earth from the radius of the orbit:
Altitude = Radius of orbit - Radius of Earth
The radius of the Earth is approximately 6,371 kilometers.
Altitude = 2.32 x 10^6 kilometers - 6,371 kilometers
Altitude ≈ 2.32 x 10^6 kilometers - 6,371 kilometers
Altitude ≈ 2.31 x 10^6 kilometers
Therefore, the altitude of the satellite is approximately 2.31 x 10^6 kilometers.
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