The star has a mass n_1 times that of the planet, which orbits this star. For a person on the planet, the average distance to the center of the star is n_2 times the distance to the center of the planet. In magnitude, what is the ratio of the star's gravitational force on you to the planet's gravitational force on you?

Gravity force is directly prop to mass, and inversely prop to square of distance.

Ratio= n1/(n2)^2

n_1/(n_2)^2

To find the ratio of the star's gravitational force on you to the planet's gravitational force on you, you can use the formula for gravitational force:

F = G * (m1 * m2) / r^2

Where:
- F is the gravitational force
- G is the gravitational constant
- m1 and m2 are the masses of the objects (the star and the planet)
- r is the distance between the center of the star and the center of the planet

Since we are interested in the ratio of the forces, we can cancel out the gravitational constant, G. Now, let's consider the following variables:
- M is the mass of the star
- m is the mass of the planet
- R is the average distance from the planet to the center of the star
- r is the average distance from the planet to the center of the person

Given that the star has a mass n1 times that of the planet (M = n1 * m) and the average distance to the center of the star is n2 times the distance to the center of the planet (R = n2 * r), we can substitute these values into the formula:

F_star = G * (M * m) / R^2
F_planet = G * (m * m) / r^2

Now, let's calculate the ratio of the two forces:

Ratio = F_star / F_planet
= (G * (n1 * m * m) / (n2 * r)^2) / (G * (m * m) / r^2)
= (n1 * m * m) / (n2^2 * m * m)
= n1 / n2^2

Therefore, the magnitude of the ratio of the star's gravitational force on you to the planet's gravitational force on you is n1 / n2^2.