Question

Calculate Neptune's mass given the acceleration due to gravity at the north pole is 11.529 m/s2 and the radius of Neptune at the pole is 24,340 km.

Answer 1

Answer:

The mass of Neptune is $1.023\times 10^{26}$ kilograms.

Explanation:

From Newton's Law of Gravitation, the gravitational acceleration of Neptune is determined by the following formula:

$g = \frac{G\cdot M}{R^{2}}$ (1)

Where:

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

$M$ - Mass of the planet, measured in kilograms.

$R$ - Radius of the planet, measured in meters.

$g$ - Gravitational acceleration, measured in meters per square second.

If we know that $G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}$, $g = 11.529\,\frac{m}{s^{2}}$ and $R = 24.340\times 10^{6}\,m$, then the mass of Neptune is:

$M = \frac{g\cdot R^{2}}{G}$

$M = \frac{\left(11.529\,\frac{m}{s^{2}}\right)\cdot (24.340\times 10^{6}\,m)^{2} }{6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} }$

$M = 1.023\times 10^{26}\,kg$

The mass of Neptune is $1.023\times 10^{26}$ kilograms.