The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force SM that the sun exerts on the moon is perpendicular to the force EM that the earth exerts on the moon. The masses are: mass of sun = 1.99 1030 kg, mass of earth = 5.98 1024 kg, mass of moon = 7.35 1022 kg. The distances shown in the drawing are rSM = 1.5 1011 m and rEM = 3.85 108 m. Determine the magnitude of the net gravitational force on the moon.

To determine the magnitude of the net gravitational force on the moon, we can use the formula for gravitational force:

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

Where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, we have three gravitational forces acting on the moon: the force from the sun (FSM), the force from the earth (FEM), and the net force (Fnet) which is the vector sum of the two forces.

To find the magnitude of the net gravitational force, we need to calculate the individual gravitational forces and then find their vector sum.

1. Calculate the force FSM from the sun on the moon:
FSM = (G * mSun * mMoon) / rSM^2

Substitute the given values:
mSun = 1.99 × 10^30 kg
mMoon = 7.35 × 10^22 kg
rSM = 1.5 × 10^11 m

Plug the values into the formula:
FSM = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (1.99 × 10^30 kg) * (7.35 × 10^22 kg) / (1.5 × 10^11 m)^2

2. Calculate the force FEM from the earth on the moon:
FEM = (G * mEarth * mMoon) / rEM^2

Substitute the given values:
mEarth = 5.98 × 10^24 kg
mMoon = 7.35 × 10^22 kg
rEM = 3.85 × 10^8 m

Plug the values into the formula:
FEM = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (5.98 × 10^24 kg) * (7.35 × 10^22 kg) / (3.85 × 10^8 m)^2

3. Calculate the net force Fnet:
Fnet = √(FSM^2 + FEM^2)

Calculate the squared magnitudes of the individual forces:
FSM^2 = (FSM)^2
FEM^2 = (FEM)^2

Calculate the net force using the formula:
Fnet = √(FSM^2 + FEM^2)

Substitute the calculated values into the formula and compute the square root.

The resulting value will be the magnitude of the net gravitational force on the moon.