Question

Find the speed (in m/s) needed to escape from the solar system starting from the surface of Neptune. Assume there are no other bodies involved, and do not account for the fact that Neptune is moving in its orbit.

Answer 1

Answer:

The speed needed to escape from the solar system starting from the surface of Neptune is approximately 23557.615 meters per second.

Explanation:

The escape speed needed to escape from the gravitational influence of a planet ($v_{e}$), measured in meters per second, is derived from Newton's Law of Gravitation and Principle of Energy Conservation and defined by the following formula:

$v_{e} = \sqrt{\frac{2\cdot G\cdot M}{R} }$ (1)

Where:

$G$ - Gravitational constant, measured in cubic meters per kilogram-square second.

$M$ - Mass of Neptune, measured in kilograms.

$R$ - Radius from the center to surface, measured in kilograms.

If we know that $G = 6.672\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}$, $M = 1.024\times 10^{26}\,kg$ and $R = 24.622\times 10^{6}\,m$, then the escape speed needed is:

$v_{e} =\sqrt{\frac{2\cdot \left(6.672\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (1.024\times 10^{26}\,kg)}{24.622\times 10^{6}\,m} }$

$v_{e} \approx 23557.615\,\frac{m}{s}$

The speed needed to escape from the solar system starting from the surface of Neptune is approximately 23557.615 meters per second.