How does the gravitational force attraction between two masses depend on distance between them?

Answer 1

The size of the gravitational attraction between two masses depends on two things:

The masses of both objects, and the distance between their centers of mass.

-- Regarding the masses, the strength of the force between them is proportional to

the product of the masses. It doesn't matter how big one is or how small the other

one is. All that matters is the product . . . (mass-#1) multiplied by (mass-#2).

When that product doubles, the force doubles.

-- Your question is regarding the distance. The strength of the force between the

two objects is inversely proportional to the square of the distance between them.

This tells you two things about how the distance affects the force.

First, the relationship is inverse, so greater distance means less force.

Second, it's the square of the distance. So triple the distance means 1/32 = 1/9 as much force.

Ten times the distance means 1/102 = 1/100 as much force, and so on.

Talking about the distance, we also need to understand that the 'distance' is the

distance between the 'center of mass' or the 'center of gravity' of the objects. For

purposes of gravity, an object behaves as of all of its mass is right there at the

center. So, for example, your weight on Earth depends on your distance from the

center of the Earth, and that's about 4,000 miles.

Answer 2

Newton'slaw of gravity describes a force that decreases with the SQUARE of the distance. For every factor of 2 the distance increases, the gravitational attraction decreases by a factor of 2 × 2 = 4.

Some remarks before we calculating:

# Mass and weight are two different things. # An object's mass doesn't change (unless you remove some!), but its weight can change. # It is technically wrong to talk about weight in kilograms (or pounds) # An objects weight is how hard gravity is pulling on it. # Sometimes people say "kilogram force" (kgf) or "pound force" (lbf) to show that they are talking about the force that the mass exertsbecause gravity is pulling down on it. # The correct unit for that force is the Newton (1 kg·m/s2) which is abbreviated N. # Gravity makes a 1 kilogram mass exert about 9.8 Newtons of force. So a 100kg mass really weighs about 980 Newtons. And now the example:

John Doe has a mass of 63.5 kilograms, so he weighs 623 newtons (=140 pounds) on the Earth's surface.

If he moves up 1 Earth radius (= 6378 kilometers) above the surface, he will be two times farther away from the Earth's center (remember that distances are measured from center-to-center!)

So his weight will be ''four times less, or 623/4 newtons = 155.8 newtons (= 140/4 pounds)

NOT two times less, or 623/2 newtons = 311.5 newtons.

If he moves up another Earth radius above the surface, he will be three times farther away than he was at the start, so his weight will drop by a factor of nine times.

NOT 3 times.

His weight will be 623/9 newtons = 69.22 newtons (= 140/9 pounds)

NOT 623/3 newtons = 207.7 newtons.

His mass will still be 63.5 kilograms.

''

Answer 3

It is inversely proportional to the square of the distance. That means that:

a) The force decreases at greater distances

b) The factor by which it decreases is equivalent to the square of the ratio of the distances. E.g., if the distance increases by a factor of 10, the force will decrease by a factor of 10 squared = 100.