The mass of the sun is 2.0 x 10^30 kg. A 5.0 x 10^14 kg comet is 75 million kilometers from the sun. What is the magnitude of the comet's acceleration toward the sun?

Video transcript

Hey everyone. So this problem is dealing with gravitational forces. Let's see what it's asking us if the distance between Earth and a geostationary satellite weighing 1600 kg is approximately 35,800 km, determine the satellite's acceleration towards Earth. Using the equations of motion. The mass of the earth is given to us as 5.9 times 10 to the 24 kg. Our multiple choice answers here are a 0.405 m per second squared. B 0.307 m per second squared, C 0.501 m per second squared or D 0.42, m/s squared. So if we were to draw a free body diagram of our satellite, the only force acting on the satellite is the gravitational force between the satellite and the earth, we can recall that this gravitational force is given by the equation G multiplied by mass of the first object multiplied by mass of the second object all over D squared. So from our problem, we were told that the mass of the first object, the satellite is 1600 kg. The mass of the second object, the earth is oops 5.9 Multiply, it times 10 to the 24 kg. And our distance, the distance between the two objects is 3:35,800 km which we can rewrite In standard units of m as 3.5, 8 times 10 to the seven m. Lastly, we can recall that G is our gravitational constant And that is 6.674, 3 Times 10 to the -11. And that has units of m cubed her kg multiplied by 2nd squared. When we recall uh Newton's second law where the sum of the forces is equal to mass multiplied by the acceleration. And recognizing that the only force acting on this satellite is our gravitational force. We can then solve for acceleration. So the force this gravitational force multiplied or is equal to the mass of the satellite which we've deemed M1 multiplied by the acceleration. So acceleration will be our gravitational force divided by that mass of the satellite. So when we plug in our equation for gravitational force and recognizing that the mass of the satellite cancels, we are left with the gravitational constant multiplied by mass two, which is the mass of the earth divided by D or distance squared. We plug in our known values that we've established here and then it is a plug and chug to get to our answer. So we have G gravitational constant 6.6743 times 10 to the minus 11 m cubed per kilogram second cubed Multiplied by 5.9 times 10 to the kg divided by 3.58 times 10 to the seven m. And that quantity squared plug that into our calculators and we get 0.307 meters per second squared. So that is the answer to this problem. And that aligns with answer choice B so that's all we have for this one, we'll see you in the next video.