Question

The gravitational force of a star on an orbiting planet 1 is F1. Planet 2, which is twice as massive as planet 1 and orbits at three times larger distance from the star, experiences gravitational force F2.
What is the ratio F2F1? You can ignore the gravitational force between the two planets.

Answer 1

Answer:

ratio = 1 : 4.5

Explanation:

If m₁ is the mass of the star and m₂ the mass of the planet, the force of gravity F₁ for planet 1 is given by:

$F_1=\frac{Gm_1m_2}{r^2}$

The force F₂:

$F_2=\frac{Gm_1(2m_2)}{(3r)^2}$

The ratio:

$\frac{F_2}{F_1}=\frac{2}{9}$

Answer 2

The gravitational force is a natural force that results in the attraction of planets or masses in the universe. The ratio of F1 and F2 is 2/9.

How do you calculate the ratio of F1 and F2?

Given that planet 1 has a force F1 and planet 2 has force F2.

Let us consider that planet 1 has a mass of m1 and the distance of the orbit is r1.  Planet 2 has a mass of m2 and the distance of the orbit is r2.  

Given the condition, planet 2 will have a mass of 2m1 and the distance of orbit will be 3r1.

$m_2 =2m_1$ and $r_2 = 3r_1$

The gravitational force for planet 1 is given below.

$F_1 = -G\dfrac{ m\times m_1}{r_1^2}$

The gravitational force for planet 2 is given below.

$F_2 = -G\dfrac {m\times m_2}{r_2^2}$

By putting the values of m2 and r2 in the above equation,

$F_2 = -G\dfrac {m\times 2m_1}{(3r_1)^2}$

Then the ratio of F1 and F2 is given below.

$\dfrac {F_1}{F_2} =\dfrac { -\dfrac {Gmm_1}{r_1^2}}{-\dfrac {Gm\times 2m_1}{(3r_1)^2}}$

$\dfrac {F_1}{F_2} = \dfrac{2}{9}$

Hence we can conclude that the ratio of gravitational forces of planet 1 to planet 2 is 2/9.

To know more about the gravitational force, follow the link given below.

https://brainly.com/question/21500344.