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 = 1.50 1011 m and rEM = 3.85 108 m. Determine the magnitude of the net gravitational force on the moon.
Perform a vector addition of the two perpendicular forces, to get the magnitude of the resultant. Use the Pythagorean theorem, since they are perpendicular. The individual forces due to Earth and sun can be computed using Newton's Universal law of Gravity, with which you should be familiar.
sun------------moon
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Earth
I still don't get the problem...the resultant vector founded did not solve it please help
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To determine the magnitude of the net gravitational force on the moon, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for the gravitational force between two objects is given as:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers.
In this scenario, we need to calculate the gravitational force exerted on the moon by both the sun (SM) and the earth (EM). Since the forces are perpendicular, we can use the Pythagorean theorem to find the net gravitational force (FM) on the moon.
FM^2 = SM^2 + EM^2
First, let's calculate the force SM exerted by the sun on the moon:
SM = G * (mass of sun * mass of moon) / rSM^2
Substituting the given values:
mass of sun = 1.99 x 10^30 kg
mass of moon = 7.35 x 10^22 kg
rSM = 1.50 x 10^11 m
SM = (6.67 x 10^-11 Nm^2/kg^2) * (1.99 x 10^30 kg * 7.35 x 10^22 kg) / (1.50 x 10^11 m)^2
Next, let's calculate the force EM exerted by the earth on the moon:
EM = G * (mass of earth * mass of moon) / rEM^2
Substituting the given values:
mass of earth = 5.98 x 10^24 kg
rEM = 3.85 x 10^8 m
EM = (6.67 x 10^-11 Nm^2/kg^2) * (5.98 x 10^24 kg * 7.35 x 10^22 kg) / (3.85 x 10^8 m)^2
Now, we can use the Pythagorean theorem to find the net gravitational force FM:
FM^2 = SM^2 + EM^2
Finally, take the square root of both sides to find the magnitude of the net gravitational force on the moon:
FM = √(SM^2 + EM^2)
By substituting the calculated values for SM and EM into the equation above, you can determine the magnitude of the net gravitational force on the moon.