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Sergeu [11.5K]
3 years ago
5

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.
Physics
1 answer:
dolphi86 [110]3 years ago
5 0

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.

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