How Does Distance Affect Gravitational Force?

[Physix1233]

Homework Statement

If an apple at the surface of the Earth has a weight of 1 N, its weight three times as far away from the centre of the Earth is

Homework Equations

f = m1m2/d^2

The Attempt at a Solution

1N/3times

so is it 1/3?
or since it's three times

1/9?

 

[berkeman]

Homework Statement

If an apple at the surface of the Earth has a weight of 1 N, its weight three times as far away from the centre of the Earth is

Homework Equations

f = m1m2/d^2

The Attempt at a Solution

1N/3times

so is it 1/3?
or since it's three times

1/9?

Welcome to the PF. I'd suggest that you be a little more careful and rigerous in writing the equations.

On your first equation, you are missing a constant, right? It may not be important in the calculation you are doing, but gravitational force is not equal to what you wrote as m1m2/d^2. It is proportional to that, but not equal.

And put some variables into the equation to get the ratio, don't just guess. Call the radius of the Earth R, and write the two force equations for the two spots. Then divide them -- what do you get?

 

[kerimek]

As a scientist, it is important to be precise and accurate in our measurements and calculations. In this case, we need to use the equation for gravitational force, which is F = G(m1m2)/d^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and d is the distance between them. We also need to consider that weight is a measure of the force of gravity on an object, so we can use the same equation to calculate the weight of the apple at a different distance from the center of the Earth.

Using this equation, we can see that if the apple's weight at the surface of the Earth is 1 N, its weight at three times the distance from the center of the Earth would be 1/9 N. This is because the distance from the center of the Earth has increased by a factor of 3, but the force of gravity decreases with the square of the distance.

Therefore, the correct answer is 1/9 N. It is important to use the correct equation and units in scientific calculations to ensure accuracy and precision.