Question

the acceleration of moon with respect to earth is 0.0027m/s2 and the acceleration of an apple falling on earth surface is about 10m/s2. assume that the radius of the moon is one fourth of the earth's radius .if the moon is stopped for an instant an then released , it will fall towards the earth .
1.what is the initial acceleration of the moon towards the earth
2.the acceleration of the moon just before it strikes the earth?

Answer 1

Task:

The acceleration of moon with respect to earth is $0.0027\frac{m}{s^2}$ and the acceleration of an apple falling on earth surface is about $10\frac{m}{s^2}$ . Assume that the radius of the moon is one fourth of the earth's radius. If the moon is stopped for an instant an then released, it will fall towards the earth.

1. What is the initial acceleration of the moon towards the earth

2. The acceleration of the moon just before it strikes the earth?

Solution:

$$F _ {g r a v i t a t i o n a l} = G \frac {m _ {1} m _ {2}}{d ^ {2}}$$

Gravitational acceleration with respect to Earth is $G \frac{M}{d^2}$ , where

$G$ - gravitational constant

$M$ - mass of the Earth

$d$ - distance from the center of the Earth to the center of the object

Given:

$G\frac{M}{\rho^2} = 0.0027\frac{m}{s^2}$ , where $\rho$ is the distance between Earth and Moon

$G\frac{M}{R^2} = 10\frac{m}{s^2}$ , where $R$ is the radius of the Earth

When the Moon is just about to strike the Earth

$$G \frac {M}{d ^ {2}} = G \frac {M}{(R + 0 . 2 5 R) ^ {2}} = \frac {G \frac {M}{R ^ {2}}}{1 . 5 6 2 5} = \frac {1 0 \frac {m}{s ^ {2}}}{1 . 5 6 2 5} = 6. 4 \frac {m}{s ^ {2}}$$

Answer:

1. $G\frac{M}{\rho^2} = 0.0027\frac{m}{s^2}$

2. $G\frac{M}{d^2} = 6.4\frac{m}{s^2}$