A 610 kg satellite orbits at a distance from the Earth's center of about 5.3 Earth radii. What gravitational force does the Earth exert on the satellite?
M*g*(1/5.3)^2 = ____ newtons
The last "inverse square" term is the factor by which the weight is reduced due to the the large distance from Earth.
Plug in M and g and perform the calculation.
To determine the gravitational force exerted by the Earth on the satellite, we can 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 x 10^-11 N(m/kg)^2), m1 is the mass of one object (the Earth in this case), m2 is the mass of the other object (the satellite), and r is the distance between the centers of the two objects.
Given:
Mass of the Earth (m1) = 5.972 × 10^24 kg
Mass of the satellite (m2) = 610 kg
Distance from the Earth's center (r) = 5.3 Earth radii
First, let's calculate the distance from the Earth's center to the satellite. Since the distance is given in terms of Earth radii, we can use the radius of the Earth (6,371 kilometers) to convert it to meters.
Radius of the Earth = 6,371 km = 6,371,000 meters
Distance from the Earth's center to the satellite = 5.3 times the radius of the Earth = 5.3 * 6,371,000 meters
Next, we can substitute the values into the formula and calculate the gravitational force:
F = (6.67430 x 10^-11 N(m/kg)^2) * (5.972 × 10^24 kg) * (610 kg) / (5.3 * 6,371,000 meters)^2
Simplifying this equation will give us the gravitational force exerted by the Earth on the satellite.