 An asteroid of mass 6 times 10 to the 14 kilograms is approaching Earth. What is the acceleration due to gravity that the asteroid experiences at A, 10,000 km above the Earth's surface, and B, 2,000 km above the Earth's surface? Well, we know from Newton's law of universal gravitation that the gravitational force Fg is equal to Big G, Big M, small m, divided by R squared, which is the universal constant of gravitation, the mass of the first object, the mass of the second object, multiplied together, divided by the distance between the centres of mass of the objects squared. We've been given the mass of the asteroid at 6 times 10 to the 14 kilograms, and the mass of the Earth we can look up and find is 6.0 times 10 to the 24 kilograms. Now let's find R, and we know that the asteroid is heading towards Earth and is 10,000 km above the surface. We also know that the radius of the Earth is 6,400 km. Therefore, we know that R is equal to 10,000 km plus 6,400 km, which gives us 16,400 km. Now, we know that the acceleration due to gravity on the asteroid is equal to the gravitational force divided by the mass of the asteroid because we know that F equals ma. Therefore, the acceleration due to gravity on the asteroid is equal to Big G, mass of the Earth, divided by R squared. And we can see that this is independent of the mass of the asteroid. So let's plug in our values. If we put our kilometres into metres and cancel out our kilograms and our kilometres, plugging this into our calculators, we get 1.49 with units newtons over kilograms. We know that newtons is kilogram metres over second squared, and therefore our answer is 1.49 metres per second squared. Now let's find the acceleration due to gravity of the asteroid at 2,000 km above the Earth's surface. Similarly to before, we know that the R value will even call above the Earth's surface plus the Earth's radius, which gives us 8,400 km. The acceleration due to gravity of the asteroid at 2,000 km is equal to Big G, Big M, divided by R squared. However, we already know the acceleration due to gravity of the asteroid at 10,000 km, which is 1.49 metres per second squared. Therefore, it should be easy to calculate the acceleration due to gravity at 2,000 km. This is just equal to the acceleration due to gravity at 10,000 km, multiplied by 16,400 km squared over 8,400 km squared. If we cancel our kilometres squared and plug this into our calculator, we find that the acceleration due to gravity of the asteroid at 2,000 km above the Earth's surface is equal to 5.68 metres per second. So even though the distance of the asteroid at 10,000 km above the surface is about twice the distance of the asteroid at about 2,000 km, we get an answer that is much larger than twice that distance. And this is due to the square of the distance.