Question

This is a Gravity topic

1. A man lived in a rural America Ln Midwest home and went outside his house at 9pm on Friday on February 16 2008 to look at the stars. He saw the moon planet Mars and the constellation gemini. If the man weigh 85 kg how much gravitational force do the three (3) brightest stars of gemini exert on that man.

Answer 1

Use the law of universal gravitation:

$$F=G\frac{mM}{R^2},$$

where m is a mass of the man, M is a mass of the star. We have three starts, so, the man will be subjected to the action of three forces:

$$F=Gm\bigg(\frac{M_1}{R^2_1}+\frac{M_2}{R^2_2}+\frac{M_3}{R^2_3}\bigg).$$

In this equation:

β Gem: $M_1=1.7M_⊙, R_1=33.7\text{ l.y.}$

α Gem: $M_2=2.15M_⊙, R_2=49.8\text{ l.y.}$

γ Gem: $M_3=2.8M_⊙, R_3=105\text{ l.y.}$

The value of solar mass:

$M_⊙=1.988\cdot10^{30}\text{ kg}$

The value of a light year:

$1\text{ l.y.} ≡ 946\cdot10^{13}\text{ m}.$

It's time to substitute values!

$$F=6.673\cdot10^{-11}\cdot85\bigg(\frac{1.7}{33.7^2}+\frac{2.15}{49.8^2}+\frac{2.8}{105^2}\bigg)\frac{1.988\cdot10^{30}}{(946\cdot10^{13})^2}=\\\space\\ =3.298\cdot10^{-13}\text{ N}.$$

Too little to notice it.