If the distance between two asteroids is doubled, the gravitational force they exert on each other willGroup of answer choicesbe four times greater.also be doubled.be half as great.will be the same.be one fourth as great.
Question
If the distance between two asteroids is doubled, the gravitational force they exert on each other willGroup of answer choicesbe four times greater.also be doubled.be half as great.will be the same.be one fourth as great.
Solution
The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force is proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, this is expressed as F = G * (m1 * m2 / r^2), where:
- F is the force between the masses,
- G is the gravitational constant,
- m1 and m2 are the two masses, and
- r is the distance between the centers of the two masses.
So, if the distance between the two asteroids is doubled (i.e., r is multiplied by 2), then the new force F' = G * (m1 * m2 / (2r)^2) = G * (m1 * m2 / 4r^2) = F/4.
Therefore, if the distance between two asteroids is doubled, the gravitational force they exert on each other will be one fourth as great.
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