A 600-kg geosynchronous satellite has an orbital radius of 6.6 Earth radii. What gravitational force does Earth exert on the satellite?
A. 13.8 N
B. 90.9 N
C. 138 N
D. 909 N
Well, Earth doesn't really exert a gravitational "force" on the satellite. It's more like a gravitational hug, you know? But to give you a more scientific answer, we can use Newton's law of universal gravitation. The formula is F = (G * m1 * m2) / r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between them.
In this case, m1 would be the mass of the satellite (600 kg), m2 would be the mass of Earth, and r would be the orbital radius (6.6 Earth radii). Unfortunately, I don't have the exact mass of Earth off the top of my head, so I can't calculate the exact force. But I can tell you that the force will be a lot bigger than just 13.8 N or 138 N. So, B and C are out. That leaves us with A. 13.8 N is a bit too weak, so let's go with D. 909 N. Earth gives a firm, but friendly, gravitational hug!
To calculate the gravitational force that Earth exerts on the satellite, we can use Newton's Law of Universal Gravitation, which states that the gravitational force between two objects is given by the formula:
F = (G * m1 * m2) / r^2
Where:
F = Gravitational force
G = Gravitational constant (approximately equal to 6.674 x 10^-11 N m^2 / kg^2)
m1 = Mass of the first object (Earth)
m2 = Mass of the second object (Satellite)
r = Distance between the centers of the two objects (orbital radius)
In this case, the mass of the satellite is given as 600 kg, and the orbital radius is given as 6.6 Earth radii. Since the mass of the Earth is much greater than the mass of the satellite, we can consider the mass of the satellite to be negligible compared to the mass of the Earth.
Plugging in the values into the formula, we get:
F = (G * (mass of Earth) * (mass of satellite)) / r^2
Since the mass of the satellite is negligible compared to the mass of the Earth, we can ignore it in the calculation.
F = (G * (mass of Earth)) / r^2
Now, substituting the known values:
F = (6.674 x 10^-11 N m^2 / kg^2 * (5.98 x 10^24 kg)) / (6.6 Earth radii)^2
To convert Earth radii to meters, we multiply by the average radius of the Earth (approximately 6.37 x 10^6 m).
F = (6.674 x 10^-11 N m^2 / kg^2 * (5.98 x 10^24 kg)) / (6.6 * 6.37 x 10^6 m)^2
F ≈ 90.9 N
Therefore, the gravitational force that Earth exerts on the satellite is approximately 90.9 N.
The correct answer is B. 90.9 N.
To find the gravitational force that the Earth exerts on the satellite, 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 (approximately 6.67 x 10^-11 N*m^2/kg^2)
- m1 and m2 are the masses of the two objects involved (in this case, the Earth and the satellite)
- r is the distance between the centers of the two objects
Given:
- The mass of the satellite is 600 kg
- The orbital radius of the satellite is 6.6 Earth radii
First, we need to find the mass of the Earth. The mass of the Earth is approximately 5.97 x 10^24 kg.
Next, we convert the Earth radii to meters. The average radius of the Earth is approximately 6.37 x 10^6 meters. So, the orbital radius of the satellite is 6.6 * 6.37 x 10^6 meters.
Plugging the values into the formula:
F = (6.67 x 10^-11 N*m^2/kg^2 * (5.97 x 10^24 kg) * (600 kg)) / ((6.6 * 6.37 x 10^6 meters)^2)
Calculating this, the answer is approximately 138 N.
Therefore, the correct answer is C. 138 N.