The International Space Station orbits 300 km above the surface of the earth. What is the gravitational force on a 1.0 kg sphere inside the International Space Station?

Video transcript

Hey everyone. So this problem is a pretty straightforward gravitational force problem. Let's see what they're asking us. A cylindrical object with a mass of 2.3 kg is located on a satellite that orbits Mars at an altitude of 400 kilometers from its surface determine the gravitational force experienced by this cylinder. The mass of Mars is given to us here 6.42 times 10 to the 23 kg And its radius is 3.34 times 10 to the six m. Our multiple choice answers for this problem are a 8. newtons, B, 6.63 newtons C 7. Newtons or D 9.21 Newtons. So the key to this problem is going to be recalling our gravitational force equation. And so that gravitational force F is given by G M one M two all divided by R squared. Now let's take each of these terms one by one, she is a gravitational constant. We can recall that that is 6. Times 10 to the -11 meters cubed per kilogram. Second squared. Our mass one is the mass of the cylindrical object. So that was given to us and the problem is 2.3 kg Mass two will be Mars. And that is given to us as 6.4, 2 times 10 to the 23 kg. And then our last term here is R. So this is the tricky part of the problem where we have to recall that the gravitational forces act from the center of the object of the body. So the distance are between the Mar, between the cylinder and Mars is going to be the radius of Mars plus the distance that the object is above the surface of Mars. So that will be that radius 3. times 10 to the six m plus That 400 km. So we can rewrite that in standard units, 400 km is equal to four times 10 to the 5th m. And so that means our radius is or sorry, our r the distance between the two objects Is 3.7, 4 times 10 to the 6th m. And from here it's just a plug and shug. So StF is equal to 6.67. Sorry, let's move this down a little bit. OK. F is equal to 6.67 times 10 to the negative 11 m cubed per kilogram second squared, multiplied by 2.3 kg, multiplied by 6.4, 2 times 10 to the 23rd kg. All over our distance are 3.7, 4 Times 10 to the six m squared, Plug that into our calculators and we get 7. newtons. So that is the answer to this problem. And that aligns with answer choice C So that's all we have for this one. We'll see you in the next video.