The earth exerts a force of 1400 N on an orbiting communications satellite that is 35 mi above the Earth.
What is the magnitude of the force the
satellite will exert on the earth?
Answer in units of N.
1400n
To calculate the magnitude of the force the satellite exerts on the Earth, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
The force exerted by the Earth on the satellite is given as 1400 N. According to Newton's third law, the force exerted by the satellite on the Earth will be equal in magnitude but in the opposite direction.
Therefore, the magnitude of the force the satellite exerts on the Earth is also 1400 N.
To find the magnitude of the force the satellite will exert on the Earth, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction.
Step 1: Convert the distance from miles to meters.
Given that the satellite is 35 miles above the Earth, we need to convert this distance to meters to use the correct unit in the calculation.
1 mile = 1609.34 meters
So, the distance above the Earth in meters is: 35 miles * 1609.34 meters/mile = 56,281.9 meters.
Step 2: Calculate the gravitational force between the Earth and the satellite.
The gravitational force between two objects can be calculated using the equation:
F = (G * m1 * m2) / r^2
Where F is the force of gravity, G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
In this case, the mass of the Earth will cancel out in the equation as we are trying to find the force exerted on the Earth by the satellite. The mass of the satellite is also not given. However, we are given the force exerted by the Earth on the satellite, which is 1400 N. So we can rearrange the equation and solve for the mass of the satellite.
Solving for m2:
F = (G * m1 * m2) / r^2
Rearranging the equation:
m2 = (F * r^2) / (G * m1)
Plugging in the given values:
m2 = (1400 N * (56,281.9 m)^2) / (6.67430 × 10^-11 N(m/kg)^2 * m1)
Step 3: Calculate the force exerted by the satellite on the Earth.
Now that we have the mass of the satellite, we can calculate the force exerted by the satellite on the Earth using the same equation for gravitational force:
F = (G * m1 * m2) / r^2
Plugging in the values:
F = (6.67430 × 10^-11 N(m/kg)^2 * m1 * m2) / r^2
Given that F is the force exerted on the Earth by the satellite, we substitute the mass of the satellite (m2) into the equation in Step 3 to calculate the magnitude of the force exerted on the Earth.
Note: The mass of the satellite is obtained in Step 2.
So, the magnitude of the force the satellite will exert on the Earth is given by the equation:
F = (6.67430 × 10^-11 N(m/kg)^2 * m1 * m2) / r^2
Please provide the mass of the satellite (m1) to continue with the calculation.