A satellite used in a cellular telephone network has a mass of 2160 kg and is in a circular orbit at a height of 670 km above the surface of the earth.
What is the gravitational force Fgrav on the satellite?
Take the gravitational constant to be = 6.67×10−11 N*m^2/kg^2, the mass of the earth to be = 5.97×1024 kg, and the radius of the Earth to be = 6.38×106 m.
Express your answer in newtons.
easy. think on Newton.
Fg= GMe*M/distance^2
distance= re+670km
A simpler method to do this
Fg= 2160*9.8 (re/(re+670))^2
To find the gravitational force on the satellite, we can use the formula for gravitational force:
Fgrav = (G * m1 * m2) / r^2
where
Fgrav is the gravitational force,
G is the gravitational constant (6.67×10^(-11) N*m^2/kg^2),
m1 and m2 are the masses of the objects (in this case, the satellite and the Earth),
and r is the distance between the centers of the two objects.
In this case, the mass of the satellite (m1) is 2160 kg, the mass of the Earth (m2) is 5.97×10^24 kg, and the distance from the center of the Earth to the orbit of the satellite (r) is the sum of the radius of the Earth (6.38×10^6 m) and the height of the orbit (670×10^3 m).
Plugging the values into the formula, we get:
Fgrav = (6.67×10^(-11) N*m^2/kg^2 * 2160 kg * 5.97×10^24 kg) / (6.38×10^6 m + 670×10^3 m)^2
Calculating this expression will give us the gravitational force on the satellite.
To find the gravitational force (Fgrav) on the satellite, we can use the formula for gravitational force:
Fgrav = (G * m1 * m2) / r^2
where G is the gravitational constant, m1 and m2 are masses of the objects involved, and r is the distance between their centers of mass.
In this case, the satellite is being pulled towards the Earth, so the masses involved are the mass of the satellite (m1) and the mass of the Earth (m2). The gravitational constant (G) is given to be 6.67×10^(-11) N*m^2/kg^2.
We are given the mass of the satellite (m1) to be 2160 kg.
Now, to calculate the distance (r) between the satellite and the center of the Earth, we need to take into account the height of the satellite above the surface of the Earth. The height given is 670 km, which means the distance from the center of the Earth to the satellite is the sum of the radius of the Earth and the height: 6.38×10^6 m + 670×10^3 m.
Given:
Mass of Earth (m2) = 5.97×10^24 kg
Radius of Earth (r) = 6.38×10^6 m
Height of satellite above Earth's surface = 670 km = 670×10^3 m
Mass of satellite (m1) = 2160 kg
Gravitational constant (G) = 6.67×10^(-11) N*m^2/kg^2
Using these values, we can calculate the gravitational force (Fgrav) on the satellite:
r = Radius of Earth + Height of satellite
r = 6.38×10^6 m + 670×10^3 m
Now, substitute the values into the formula:
Fgrav = (G * m1 * m2) / r^2
Fgrav = (6.67×10^(-11) N*m^2/kg^2 * 2160 kg * 5.97×10^24 kg) / (r^2)
Calculate r and substitute it back into the formula to find Fgrav.