Sputnik, the first artificial satellite to orbit the Earth, had a mass of 83.6 kg and travelled at 7574 m/s. The radius of the earth is 6371 km and its mass is 5.972 x 10^24 kg. (NOTE: You may find different numbers online since there was some uncertainty in the exact orbit. These numbers were chosen to keep this question consistent. Also, this question requires a subtraction, which can cause difficulty with the numerical tolerance. Keep about 5 figures as you go through the calculation. I have increased the tolerance to 10%). Sputnik was 578,000 m above ground.
What gravitational force did Sputnik apply to the earth during this orbit?
To solve this problem, we can use the equation for the gravitational force between two objects:
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, and r is the distance between the centers of the two objects.
First, we need to calculate the distance between Sputnik and the center of the Earth. We know that Sputnik was 578,000 m above the ground, so the distance from the center of the Earth to Sputnik is:
distance = radius_of_earth + height_of_Sputnik
distance = 6371 km + 578,000 m
Now, we can calculate the gravitational force using the given values for the mass of Sputnik, the mass of the Earth, and the distance between Sputnik and the Earth:
F = (G * m1 * m2) / r^2
F = (6.67430 x 10^-11 N(m/kg)^2 * 83.6 kg * 5.972 x 10^24 kg) / (distance)^2
Calculating this value:
F = (6.67430 x 10^-11 N(m/kg)^2 * 83.6 kg * 5.972 x 10^24 kg) / ((6371 km + 578,000 m)^2)
F = 8.31185 x 10^7 N
Therefore, the gravitational force that Sputnik applied to the Earth during this orbit was approximately 8.31185 x 10^7 N.