Answer:
Gravitational forces: Earth: [tex]W = 650.969\,N[/tex], Mars: [tex]W = 246.449\,N[/tex], Pluto: [tex]W = 38.504\,N[/tex]
Explanation:
The weight ([tex]W[/tex]), measured in newtons, experimented by the person on the surface of the planet is defined by Newton's Laws of Motion:
[tex]W = m\cdot g[/tex] (1)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
From Newton's Law of Gravitation we derive this expression for gravitational acceleration:
[tex]g = \frac{G\cdot M}{R^{2}}[/tex] (2)
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.
By (2) we calculate the gravitational acceleration for each planet:
Earth ([tex]G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}[/tex], [tex]M = 5.97\times 10^{24}\,kg[/tex], [tex]R = 6.38\times 10^{6}\,m[/tex])
[tex]g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (5.97\times 10^{24}\,kg)}{(6.38\times 10^{6}\,m)^{2}}[/tex]
[tex]g = 9.789\,\frac{m}{s^{2}}[/tex]
Mars ([tex]G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}[/tex], [tex]M = 6.42\times 10^{23}\,kg[/tex], [tex]R = 3.40\times 10^{6}\,m[/tex])
[tex]g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (6.42\times 10^{23}\,kg)}{(3.40\times 10^{6}\,m)^{2}}[/tex]
[tex]g = 3.706\,\frac{m}{s^{2}}[/tex]
Pluto ([tex]G = 6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}}[/tex], [tex]M = 1.25\times 10^{22}\,kg[/tex], [tex]R = 1.20\times 10^{6}\,m[/tex])
[tex]g = \frac{\left(6.674\times 10^{-11}\,\frac{m^{3}}{kg\cdot s^{2}} \right)\cdot (1.25\times 10^{22}\,kg)}{(1.20\times 10^{6}\,m)^{2}}[/tex]
[tex]g = 0.579\,\frac{m}{s^{2}}[/tex]
Lastly, we calculate the gravitational force for each case by (1):
Earth ([tex]m = 66.5\,kg[/tex], [tex]g = 9.789\,\frac{m}{s^{2}}[/tex])
[tex]W =(66.5\,kg)\cdot \left(9.789\,\frac{m}{s^{2}} \right)[/tex]
[tex]W = 650.969\,N[/tex]
Mars ([tex]m = 66.5\,kg[/tex], [tex]g = 3.706\,\frac{m}{s^{2}}[/tex])
[tex]W = (66.5\,kg)\cdot \left(3.706\,\frac{m}{s^{2}} \right)[/tex]
[tex]W = 246.449\,N[/tex]
Pluto ([tex]m = 66.5\,kg[/tex], [tex]g = 0.579\,\frac{m}{s^{2}}[/tex])
[tex]W = (66.5\,kg)\cdot \left(0.579\,\frac{m}{s^{2}} \right)[/tex]
[tex]W = 38.504\,N[/tex]
