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Problem 35 Easy Difficulty

ssm The sun is more massive than the moon, but the sun is farther from the earth. Which one exerts a greater gravitational force on a person standing on the earth? Give your answer by determining the ratio $F_{\operatorname{sun}} / F_{\operatorname{mon}}$ of the magnitudes of the gravitational forces. Use the data on the inside of the front cover.

Answer

178

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Video Transcript

in this question, we have to couple into the following reshoot the magnitude of the gravitational force exerted on the earth by the sun, divided by the magnitude of the gravitational force exerted on the earth by the moon. Remember that the magnitude of the gravitational force is given by the Newtown constant times the mass off the object one in this case, the mass of the Sun Times the mass of the earth divided by the distance between the earth and the sun squared on the denominator. We have the magnitude off the gravitational force exerted by the moon. And this is given by the Newton constant times the mass off the moon times the mass off the earth divided by the distance between here and the moon squared So note that there will be a lot of simplifications here Nearly is equals to g times And as times m e divided by r. P s squared times r e m squared divided by G and m times m e. So these are simply fired and the masses off the earth are also simply fired. So we got r e m squared divided by R E s squared times m s divided by M m. As the result off the ratio between the magnitudes off the rotational forces. Then they plug in the values that were given by the problem we got the following the ratio is it goes to 3.85 time stand to eat, squared, divided by 1.5 I'm stand 11. It's weird times the mass off the sun 1.99 times 10 to the 30 divided by the mass of the moon 7.35 times Stand in the 22 and these givers approximately 170 feet. So the gravitational force exerted on the earth by the sun is 178 times bigger than the gravitational force exerted on the earth by the moon.