Question

What is the ratio of the sun’s gravitational force on you to the
earth’s gravitational force on you?

Short answer

Ratio sun's gravitational force on me to earth's gravitational force on me is

F_s/F_e=5.98 x 10^-4

Step-by-step solution

Given information

Mass of earth: M_e=5.97 x 10²⁴ kg
Mass of sun: M_e=1.98 x 10³⁰ kg
Radius of earth: r_e}=6.37 x 10⁶ m
Distance from sun to earth: r_se=1.5 x 10¹¹m

Explanation

We can calculate Gravitational force by

$F=\frac{GMm}{r^2}$

First find the gravitation force of Earth on you

$F_e=\frac{Gm{M}_e}{r_e^2}=\frac{Gm\left(5.97\times {10}^{24}\mathrm{kg}\right)}{{\left(6.37\times {10}^6\mathrm{m}\right)}^2}............................\left(1\right)$

now find Sun's gravitational force

$F_S=\frac{Gm{M}_s}{r_{se}^2}=\frac{Gm\left(1.98\times {10}^{30}\mathrm{kg}\right)}{{\left(1.5\times {10}^{11}\mathrm{m}\right)}^2}.....................\left(2\right)$

Now find the ratio

we get

$\frac{F_s}{F_e}=5.98\times {10}^{-4}$