3) A satellite is orbiting Earth at a distance of 57 kilometers. The satellite has a mass of 96 kilograms. What is the force between the planet and the satellite? (Hint: Don't forget that the distance between them in the equation represents the distance to the center of the earth, you might have to do a bit of Googling to determine the radius of the earth as well as the mass of the earth).
i'm thinking you multiply the satelite's mass by 9.8 (N/kg) then what?
At 57 km above the earth, the acceleration due to gravity is no longer 9.8 m/s².
The force between the satellite and the earth is governed by Newton's law of gravitation, GMm/r², which says that the force of gravitational attraction is proportional to the product of the masses, and inversely proportional to the square of the distance between them. For the distance r, it is important that you calculate the distance from the centre of each object, as suggested in the question.
Here's a site that will help you understand the law. Feel free to do some calculations and post your result for verification.
http://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation
To calculate the force between the planet and the satellite, you need to use Newton's law of universal gravitation. The formula for gravitational force is:
F = (G * (m1 * m2)) / r^2
Where:
F is the gravitational force between two objects,
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2),
m1 and m2 are the masses of the two objects respectively, and
r is the distance between the centers of the two objects.
However, in this case, since the satellite is orbiting Earth, it is easier to calculate the force using Newton's second law, which states that force equals mass times acceleration. The acceleration due to gravity on Earth's surface is approximately 9.8 m/s^2.
So, using Newton's second law, the force (F) between the planet and the satellite can be calculated by multiplying the satellite's mass (m) by the acceleration due to gravity (g):
F = m * g
For the given problem, the mass of the satellite is 96 kg. So, you can calculate the force between the planet and the satellite by multiplying 96 kg by 9.8 m/s^2:
F = 96 kg * 9.8 m/s^2
F = 940.8 N
So, the force between the planet and the satellite is approximately 940.8 Newtons.