weaker gravity?

Question

You are explaining to friends why astronauts feel weightless orbiting in the space shuttle, and they respond that they thought gravity was just a lot weaker up there. Convince them and yourself that it isn't so by calculating how much weaker gravity is at h = 490 km above the Earth's surface.

Answer 1

At this altitude gravity is weakened by a factor of 1.163, this a small amount, one feels weightless because one is in free fall when in orbit.

Answer 2

You'll need to know R, the radius of the Earth, as well as M, the mass of the Earth, and G, the gravitational constant. Simply calculate GM / R^2, which should be equal to 9.8 m/s^2, acceleration due to gravity at the surface of the Earth. Then calculate GM / (R + 490 km)^2, the acceleration due to the Earth's gravity inside the space shuttle, and compare to the first value. You should find that the second value is only about 1 m/s^2 smaller. But don't forget to convert the distances to meters before performing the calculations.

You can also get the answer without using G or M, but you will still need R. If we assume you know that g = 9.8 m/s^2 is the acceleration due to gravity at the Earth's surface, you can say that the acceleration inside the space shuttle is equal to g*(R^2) / (R + 490 km)^2, due to the inverse dependence on the square of distance. This time, it doesn't matter if you convert to meters, as long as R and the distance above the surface (given as 490 km) are in the same units as each other.

Answer 3

just compare the radius of the earth to the height h=490 km. If the height is not a significant distance, then the gravitational force between two bodies does not really change.

So lets see . . .

radius of earth: about 6,356.750 km

height h = 490 km

radius of earth >>>>> h

safe to approximate that gravity at h=0 km is almost the same as h=490 km