The planet Saturn has a mass that is 95 times Earth's mass and a radius that is 9.4 times Earth's radius. What is the acceleration due to gravity on Saturn?

Respuesta :

Answer:

10.55111 m/s²

Explanation:

M = Mass of Saturn = [tex]95\times 5.972\times 10^{24}\ kg[/tex]

r = Radius of Saturn = [tex]9.4\times 6.371\times 10^6\ m[/tex]

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

Acceleration due to gravity is given by

[tex]g=\dfrac{GM}{r^2}\\\Rightarrow g=\dfrac{6.67\times 10^{-11}\times 95\times 5.972\times 10^{24}}{(9.4\times 6.371\times 10^6)^2}\\\Rightarrow g=10.55111\ m/s^2[/tex]

The acceleration due to gravity on Saturn is 10.55111 m/s²

The planet Saturn has a mass that is 95 times Earth's mass and a radius that is 9.4 times Earth's radius. The acceleration due to gravity on Saturn is 10.55 m/s².

The mass of the Earth is 5.972 × 10²⁴ kg. Saturn has a mass that is 95 times the Earth's mass, so it is:

[tex]R = 95 \times 5.972 \times 10^{24} kg = 5.673 \times 10^{26} kg[/tex]

The radius of the Earth is 6.371 × 10⁶ m. Saturn has a radius that is 9.4 times the Earth's radius, so it is:

[tex]M = 9.4 \times 6.371 \times 10^{6} m = 5.989 \times 10^{7} m[/tex]

We can calculate the acceleration due to gravity on Saturn (g) using the following expression.

[tex]g = G \frac{M}{R^{2} } = \frac{6.67 \times 10^{-11}N.m^{2} }{kg^{2} } \frac{5.673\times 10^{26}kg }{(5.989 \times 10^{7} m )x^{2} } = 10.55 m/s^{2}[/tex]

where,

  • G: gravitational constant

The planet Saturn has a mass that is 95 times Earth's mass and a radius that is 9.4 times Earth's radius. The acceleration due to gravity on Saturn is 10.55 m/s².

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