The mass of an object doubles. What happens to the gravitational force between it and another object, assuming they remain the same distance apart?
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1 point
The amount of the gravitational force decreases by one-half.
The amount of the gravitational force quadruples.
The amount of the gravitational force doubles.
The amount of the gravitational force remains the same.
The amount of the gravitational force doubles.
Based on Kepler's observations about planetary motion, what is the relationship between a planet's orbital velocity and its distance from the sun?
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1 point
The greater the distance, the slower the orbital velocity.
Distance has no effect on orbital velocity.
The greater the distance, the greater the orbital velocity.
As distance is cut in half, orbital velocity decreases.
The greater the distance, the slower the orbital velocity.
The amount of the gravitational force doubles.
To determine what happens to the gravitational force between two objects when the mass of one object doubles, you need to understand the relationship between mass and gravitational force.
According to Newton's Law of Universal Gravitation, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Mathematically, this relationship can be expressed as:
F = (G * m1 * m2) / (r^2)
Where F represents the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.
Since we are assuming the distance between the objects remains the same, let's focus on the effect of doubling the mass.
When the mass of one object doubles, it means that m1 becomes 2m1 (assuming the mass of the other object remains the same).
So, the equation for the new gravitational force becomes:
F' = (G * 2m1 * m2) / (r^2)
By simplifying the equation, we find that:
F' = 2 * (G * m1 * m2) / (r^2)
Comparing this with the original equation, we can see that the new gravitational force (F') is twice the original gravitational force (F).
Therefore, the amount of the gravitational force doubles when the mass of the object doubles. Hence, the correct answer is: The amount of the gravitational force doubles.