If the mass of the Moon is 7.4 x 1022 kg and its radius is 1.74 x 106 m, compute the speed with which an object would have to be fired in order to sail away from it, completely overcoming the Moon’s gravity pull.
To compute the speed required to overcome the Moon's gravity pull, we need to calculate the escape velocity. Escape velocity is the minimum speed an object needs to reach in order to escape the gravitational pull of a celestial body.
The formula for escape velocity (v) is given by:
v = sqrt(2 * G * M / r)
Where:
- v is the escape velocity
- G is the gravitational constant (approximately 6.67430 x 10^-11 m³ kg^(-1) s^(-2))
- M is the mass of the celestial body (in this case, the Moon)
- r is the distance between the object and the center of the celestial body (in this case, the radius of the Moon)
Now we can substitute the given values into the formula:
M = 7.4 x 10^22 kg
r = 1.74 x 10^6 m
G = 6.67430 x 10^-11 m³ kg^(-1) s^(-2)
v = sqrt(2 * (6.67430 x 10^-11 m³ kg^(-1) s^(-2)) * (7.4 x 10^22 kg) / (1.74 x 10^6 m))
Now let's calculate the value of v:
v = sqrt(2 * 6.67430 x 10^-11 x 7.4 x 10^22 / 1.74 x 10^6) m/s
v = sqrt(9.869077994 x 10^11) m/s
v ≈ 9932.82 m/s
Therefore, the speed with which an object would have to be fired to completely overcome the Moon's gravitational pull is approximately 9932.82 m/s.