Newton: Force of gravity that one object exerts on another decreases like one divided by the square of the distance between them.

More precisely: between a small object (e.g., a space station or an astronaut) and a large object that is approximately a sphere (e.g., the Earth, Moon or Sun), the force of gravity decreases like one divided by the square of the distance between the small object and the** center **of the large spherical object.

Distance from center of Earth to an object on the earth’s surface: 3,960 miles (6,370 km)

Distance from surface of Earth to the space station: 230 miles (370 km)

Distance from center of Earth to the space station: 3,960 + 230 = 4190 miles (6370 + 370 = 6740 km)

Thus the distance from Earth’s center to the space station is 1.06 = 4190/3960 times larger than the distance from Earth’s center to Earth’s surface — i.e, the distance is 6% larger.

And the *square* of the distance from Earth’s center to the space station is (1.06)² = 1.12 times larger than *square* of the distance from Earth’s center to Earth’s surface — i.e., the *square* of the distance is 12% larger.

**And therefore the force of the Earth’s gravity on an astronaut is 12% smaller if the astronaut is in the space station than it would be on the ground.**

## 6 Responses

on the issue of the rocket wall that has to be protected against gravity, what must be done. i think the walls of the rocket should be shielded with a neutron absorber which is boron. what do you think.

I do not understand how would you use the equation to work out your weight 100 miles away from earth centre. 3960/100 = 39.6. 39.6 * 39.6 =1568. so somebody 100 miles away from earth centre weighs 1568 as much as on the surface. I believe you are weigtless on centre of earth so how do you do the equations ?

That equation takes into account that the hole mass of earth is centralized at one point. Not the hole mass of the earth is compresses at that point. The equation only is correct from the earth surface and above.

mass of the earth is compressed at that point*

oops

More like 11%, wouldn’t you agree?