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.
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To determine the magnitude of the net gravitational force on the moon, you can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the formula:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 N*(m/kg)^2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects.
In this case, we need to calculate the gravitational forces between the sun and the moon (Fs-m) and between the Earth and the moon (Fe-m).
First, let's calculate the gravitational force between the sun and the moon:
Fs-m = G * (mSun * mMoon) / rSM^2
Given:
mSun = 1.99 × 10^30 kg
mMoon = 7.35 × 10^22 kg
rSM = 1.50 × 10^11 m
Substituting the values into the formula:
Fs-m = (6.67430 x 10^-11 N*(m/kg)^2) * ((1.99 × 10^30 kg) * (7.35 × 10^22 kg)) / (1.50 × 10^11 m)^2
Now, calculate the gravitational force between the Earth and the moon:
Fe-m = G * (mEarth * mMoon) / rEM^2
Given:
mEarth = 5.98 × 10^24 kg
mMoon = 7.35 × 10^22 kg
rEM = 3.85 × 10^8 m
Substituting the values into the formula:
Fe-m = (6.67430 x 10^-11 N*(m/kg)^2) * ((5.98 × 10^24 kg) * (7.35 × 10^22 kg)) / (3.85 × 10^8 m)^2
Finally, to find the net gravitational force, subtract the magnitude of the force between the sun and the moon from the magnitude of the force between the Earth and the moon:
Net gravitational force = |Fe-m| - |Fs-m|
Keep in mind that the magnitudes of the forces represent the absolute values of those forces.