The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force that the sun exerts on the moon is perpendicular to the force 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 = 1.50 × 1011 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon. I tried to solve for Force by writing down F=squareroot[(6.67x10^-11)(7.35x10^22/(3.85x10^8)^2)^2+(5.98x10^24/1.50x10^11)^2)^2 and I came out to get F=265.81N, however it is saying that the answer is wrong. Please help!

To determine the magnitude of the net gravitational force on the moon, we need to find the individual gravitational forces exerted on the moon by the sun and the earth, and then sum them up.

The gravitational force between two objects can be calculated using the formula:

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

Where:
F is the gravitational force,
G is the gravitational constant (6.67 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between the centers of the two objects.

First, let's calculate the gravitational force exerted on the moon by the sun:

Fsun = (G * mSun * mMoon) / rSM^2

Substituting the given values:
mSun = 1.99 × 10^30 kg
mMoon = 7.35 × 10^22 kg
rSM = 1.50 × 10^11 m

Fsun = (6.67 × 10^-11 N m^2 / kg^2) * (1.99 × 10^30 kg) * (7.35 × 10^22 kg) / (1.50 × 10^11 m)^2
Fsun = 1.91 × 10^20 N

Next, let's calculate the gravitational force exerted on the moon by the earth:

Fearth = (G * mEarth * mMoon) / rEM^2

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

Fearth = (6.67 × 10^-11 N m^2 / kg^2) * (5.98 × 10^24 kg) * (7.35 × 10^22 kg) / (3.85 × 10^8 m)^2
Fearth = 1.97 × 10^20 N

Now, we can calculate the net gravitational force on the moon by summing up the individual forces:

Fnet = √(Fsun^2 + Fearth^2)

Substituting the calculated values:

Fnet = √((1.91 × 10^20 N)^2 + (1.97 × 10^20 N)^2)
Fnet = √(3.65 × 10^40 N^2 + 3.88 × 10^40 N^2)
Fnet = √7.53 × 10^40 N^2
Fnet = 2.75 × 10^20 N (approximately)

Therefore, the magnitude of the net gravitational force on the moon is approximately 2.75 × 10^20 N.