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1) On the way to the moon, the Apollo astro-
nauts reach a point where the Moon’s gravi-
tational pull is stronger than that of Earth’s.
Find the distance of this point from the
center of the Earth. The masses of the
Earth and the Moon are 5.98 × 1024 kg and
7.36 × 1022 kg, respectively, and the distance
from the Earth to the Moon is 3.84 × 108 m.
Answer in units of m

2) What would the acceleration of the astro-
naut be due to the Earth’s gravity at this
point if the moon was not there? The
value of the universal gravitational constant
is 6.672 × 10−11 N · m2/kg2.
Answer in units of m/s2

Respuesta :

Hagrid
(1) You must find the point of equilibrium between the two forces,

G * MTms / (R−x)^2 = G * MLms / x^2
MT / (R-x)^2 = ML / x^2

So,

x = R * sqrt(ML * MT) - ML / (MT - ML)
R = is the distance between Earth and Moon.

The result should be,
x = 3.83 * 10^7m
from the center of the Moon, and 

R - x = 3.46*10^8 m
from the center of the Earth.


(2) As the distance from the center of the Earth is the number we found before,
d = R - x = 3.46*10^8m
The acceleration at this point is
g = G * MT / d^2
g = 3.33*10^-3 m/s^2

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