Find the net force of gravity on the moon (Mm = 7.35 x 10^22 kg) from the earth and the sun (Ms = 1.99 x 10^30). Assume that the two forces are perpendicular to each other. Give the angle in relationship to the sun.

To find the net force of gravity on the moon from the Earth and the Sun, we need to consider the gravitational forces exerted individually by each body and their directions.

1. Gravitational force from the Earth:
The magnitude of gravitational force between two objects is given by the equation: F = G * (m1 * m2) / r^2, where 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.

The mass of the Moon (Mm) = 7.35 x 10^22 kg, and we assume the distance from the center of the Moon to the center of the Earth is the radius of the Earth (Re) + distance from the center of the Earth to the center of the Moon (d).

2. Gravitational force from the Sun:
Similar to the Earth-Moon force, the gravitational force between the Sun and the Moon depends on the mass of the Sun (Ms) = 1.99 x 10^30 kg and the distance between their centers of mass.

Since we are assuming that the Earth-Moon and Moon-Sun forces are perpendicular to each other, we can calculate the net force using vector addition. The magnitude of the net force is given by the Pythagorean theorem.

To find the angle in relation to the Sun, we can use trigonometry. The tangent of the angle can be found by taking the ratio of the perpendicular component (force of gravity from the Sun) to the horizontal component (force of gravity from the Earth).

Now, let's calculate the net force and the angle:

Step 1: Calculate the gravitational force from the Earth:
F1 = G * (Mm * Me) / (Re + d)^2

Step 2: Calculate the gravitational force from the Sun:
F2 = G * (Mm * Ms) / R^2

Step 3: Calculate the net force (F_net) using vector addition:
F_net = sqrt(F1^2 + F2^2)

Step 4: Calculate the angle (θ):
tan(θ) = F2 / F1
θ = atan(F2 / F1)

Plug in the values for the masses and constants to get the numerical answer.