The Force Exerted on the Moon In FIGURE 5-37 we show the...

The Force Exerted on the Moon In FIGURE $5-37$ we show the Earth, Moon, and Sun (not to scale) in their relative positions at the time when the Moon is in its third-quarter phase. Though few people realize it, the force exerted on the Moon by the Sun is actually greater than the force exerted on the Moon by the Earth. In fact, the force exerted on the Moon by the Sun has a magnitude of $F_{\mathrm{sM}}=4.34 \times 10^{20} \mathrm{N},$ whereas the force exerted by the Earth has a magnitude of only $F_{\mathrm{EM}}=1.98 \times 10^{20} \mathrm{N}$ . These forces are indicated to scale in Figure $5-37 .$ Find (a) the direction and (b) the magnitude of the net force acting on the Moon. (c) Given that the mass of the Moon is $M_{M}=7.35 \times 10^{22} \mathrm{kg}$ , find the magnitude of its acceleration at the time of the third- quarter phase.

The Force Exerted on the Moon In FIGURE $5-37$ we show the Earth,
Moon, and Sun (not to scale) in their relative positions at the
time when the Moon is in its third-quarter phase. Though few
people realize it, the force exerted on the Moon by the Sun is
actually greater than the force exerted on the Moon by the
Earth. In fact, the force exerted on the Moon by the Sun has a magnitude of $F_{\mathrm{sM}}=4.34 \times 10^{20} \mathrm{N},$ whereas the force exerted by
the Earth has a magnitude of only $F_{\mathrm{EM}}=1.98 \times 10^{20} \mathrm{N}$ . These
forces are indicated to scale in Figure $5-37 .$ Find (a) the direction
and (b) the magnitude of the net force acting on the Moon.
(c) Given that the mass of the Moon is $M_{M}=7.35 \times 10^{22} \mathrm{kg}$ ,
find the magnitude of its acceleration at the time of the third-
quarter phase.

Key Concepts

Gravitational Forces

Gravitational forces are the attractive forces that act between two masses. In celestial mechanics, they govern the interactions between bodies such as the Earth, Moon, and Sun. This concept is critical for understanding how objects in space influence each other’s motion and how these forces are calculated using Newton's law of universal gravitation.

Vector Addition

Vector addition is the process of combining multiple forces, taking into account both their magnitudes and directions, to determine a single resultant force. This concept is essential when forces are applied in different directions, as it allows one to calculate the net force acting on an object using methods such as decomposing the forces into their components.

Newton’s Second Law

Newton’s second law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, succinctly expressed as F = ma. This principle is used to compute the acceleration of any object when the net force and the object's mass are known, making it fundamental in analyzing motion resulting from combined forces.

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