The gravitational force between two objects in space is 800 million newtons. If the distance between them is doubled, what size will the gravitational force be (in millions of newtons)?

200 million

1600 million

To find the new size of the gravitational force when the distance between the objects is doubled, we can use the inverse square law of gravity. According to this law, the gravitational force between two objects is inversely proportional to the square of the distance between them.

Here's how you can calculate it:

1. Determine the original force: The original gravitational force is given as 800 million newtons.

2. Calculate the scaling factor due to the change in distance: When the distance between the objects is doubled, the new distance is twice the original distance. Since the force is inversely proportional to the square of the distance, the scaling factor for the gravitational force is the square of the reciprocal of the distance scaling factor. In this case:

Distance scaling factor = New distance / Original distance = 2 / 1 = 2
Force scaling factor = (1 / Distance scaling factor)^2 = (1 / 2)^2 = 1/4

3. Calculate the new force: Multiply the original force by the scaling factor to get the new force.

New force = Original force * Force scaling factor = 800 million newtons * (1/4) = 200 million newtons

Therefore, the new size of the gravitational force will be 200 million newtons (or 200 million/1 million = 0.2 billion newtons) when the distance between the objects is doubled.