Question

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?

Answer 1

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;

$g = \frac{GM}{r^2} \\\\G = \frac{gr^2}{M}$

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

$g_2 = \frac{GM_2}{r_2^2}$

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

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