Answer:
The mass of Neptune is [tex]1.023\times 10^{26}[/tex] kilograms.
Explanation:
From Newton's Law of Gravitation, the gravitational acceleration of Neptune is determined by the following formula:
[tex]g = \frac{G\cdot M}{R^{2}}[/tex] (1)
Where:
[tex]G[/tex] - Gravitational constant, measured in cubic meters per kilogram-square second.
[tex]M[/tex] - Mass of the planet, measured in kilograms.
[tex]R[/tex] - Radius of the planet, measured in meters.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
If we know that [tex]G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}[/tex], [tex]g = 11.529\,\frac{m}{s^{2}}[/tex] and [tex]R = 24.340\times 10^{6}\,m[/tex], then the mass of Neptune is:
[tex]M = \frac{g\cdot R^{2}}{G}[/tex]
[tex]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}} }[/tex]
[tex]M = 1.023\times 10^{26}\,kg[/tex]
The mass of Neptune is [tex]1.023\times 10^{26}[/tex] kilograms.
