What is the distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal? The mass of Earth is 5.97 × 10²⁴ kg,the mass of the Moon is 7.35 × 10²² kg,the center-to-center distance between Earth and the Moon is 3.84 × 10⁸ m,and G = 6.67 × 10^-11 N ∙ m²/kg². A)3.45 × 10⁸ m B)3.84 × 10⁷ m C)4.69 × 10⁶ m D)3.83 × 10⁶ m E)4.69 × 10⁷ m

Question

Quizplus · Accepted Answer

The distance from the center of the Moon to the point between Earth and the Moon where the gravitational pulls of Earth and Moon are equal is known as the barycenter. The location of the barycenter can be calculated using the formula:

r = R (m1 / (m1 + m2))

where r is the distance from the center of the Moon to the barycenter, R is the distance between the centers of Earth and Moon, m1 is the mass of Earth, and m2 is the mass of the Moon.

Plugging in the given values, we get:

r = (3.84 × 10^8 m) (5.97 × 10^24 kg / (5.97 × 10^24 kg + 7.35 × 10^22 kg))
r = 3.84 × 10^8 m (0.987)
r = 3.79 × 10^8 m

Therefore, the distance from the center of the Moon to the barycenter is approximately 3.79 × 10^8 m. However, we need to add the radius of the Moon (1.74 × 10^6 m) to this value to get the distance from the surface of the Moon to the barycenter:

3.79 × 10^8 m + 1.74 × 10^6 m = 3.84 × 10^8 m

Hence, the best choice is B.

What Is the Distance from the Center of the Moon