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The planet Gallifrey has 2 times the gravitational field strength and 2 times the radius of the Earth.
How does the mass of the planet Gallifrey compare with the mass of Earth?

Sagot :

onyebuchinnaji

The mass of the planet Gallifrey is 8 times the mass of the Earth.

  • let the gravitational field of Earth = g
  • let the radius of the Earth = R
  • gravitational field of Gallifrey = 2g
  • radius of Gallifrey = 2R

What is gravitational potential energy?

  • This is the work done in moving an object to a certain distance against gravitational field.

The gravitational field strength of the Earth is given as follows;

[tex]g = \frac{GM}{r^2} \\\\G = \frac{gr^2}{M}[/tex]

The gravitational field strength of the Planet Gallifrey is calculated as follows;

[tex]g_2 = \frac{GM_2}{r_2^2}[/tex]

[tex]G = \frac{g_2r_2^2}{M_2} \\\\\frac{g_2r_2^2}{M_2} = \frac{gr^2}{M}\\\\M_2gr^2 = Mg_2r_2^2\\\\M_2 = \frac{Mg_2r_2^2}{gr^2} \\\\M_2 = \frac{M \times 2g \times (2r)^2}{gr^2} \\\\M_2 = \frac{M \times 2g \times 4r^2}{gr^2} \\\\M_2 = 8M[/tex]

Thus, the mass of the planet Gallifrey is 8 times the mass of the Earth.

Learn more about gravitational field strength here:  https://brainly.com/question/14080810

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