If Earth's mass were suddenly and magically reduced to half its present value, the Sun's gravitational force on Earth would

A. be reduced by a factor of 2.
B. be reduced by a factor of 4.
C. increase by a factor of 2.
D. remain the same.

I was told it remained the same but I thought it would be C.increase by a factor of 2

To determine the effect of Earth's mass decreasing on the Sun's gravitational force on Earth, we need to understand the relationship between gravitational force and mass.

The gravitational force between two objects is given by the equation:

F = G * (m1 * m2) / r^2

Where F is 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 of mass.

Now, let's consider the scenario where Earth's mass is suddenly reduced by half. If we denote Earth's initial mass as m and its final mass after reduction as m/2, we can analyze the effect on the gravitational force between the Earth and the Sun.

Using the equation above, the original gravitational force between the Sun and Earth can be denoted as F_initial = G * (M_sun * m) / r^2, where M_sun is the mass of the Sun.

After reducing Earth's mass to m/2, the gravitational force can be denoted as F_final = G * (M_sun * (m/2)) / r^2.

To compare the two forces, let's divide F_final by F_initial:

F_final / F_initial = (G * (M_sun * (m/2)) / r^2) / (G * (M_sun * m) / r^2)

Canceling out common terms, we get:

F_final / F_initial = (m/2) / m = 1/2

Therefore, the ratio of the final force to the initial force is 1/2. This indicates that the Sun's gravitational force on Earth would be reduced by a factor of 2 if Earth's mass were reduced to half its present value.

Hence, the correct answer is A. be reduced by a factor of 2.