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 Fsun/Fmoon of the magnitudes of the gravitational forces. Use the data on the inside of the front cover.
To determine the ratio Fsun/Fmoon, we can use Newton's law of universal gravitation. The law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Let's denote the mass of the Sun as Msun, the mass of the Moon as Mmoon, and the distances between the Earth and the Sun and Moon as Rsun and Rmoon, respectively.
The gravitational force between the Earth and the Sun is given by:
Fsun = (G * Msun * Mearth) / Rsun^2
where G is the gravitational constant and Mearth represents the mass of the Earth.
Similarly, the gravitational force between the Earth and the Moon is given by:
Fmoon = (G * Mmoon * Mearth) / Rmoon^2
We are asked to determine the ratio Fsun/Fmoon, so we divide the equation for Fsun by the equation for Fmoon:
Fsun/Fmoon = (G * Msun * Mearth) / Rsun^2 / (G * Mmoon * Mearth) / Rmoon^2
Mearth cancels out in the equation, leaving us with:
Fsun/Fmoon = (Msun / Mmoon) * (Rmoon / Rsun)^2
Based on the given information, we know that the Sun is more massive than the Moon, so Msun > Mmoon. Additionally, the Sun is farther from the Earth than the Moon, so Rsun > Rmoon.
Since both Msun/Mmoon and (Rmoon/Rsun)^2 are greater than 1, we can conclude that Fsun/Fmoon is greater than 1. Therefore, the Sun exerts a greater gravitational force on a person standing on the Earth compared to the Moon.
To determine the ratio of the magnitudes of the gravitational forces exerted by the sun and the moon on a person standing on Earth, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Let's break down the steps to calculate the ratio of the magnitudes of the gravitational forces:
1. Check the data on the inside of the front cover: Find the mass of the sun and the mass of the moon.
2. Calculate the gravitational force exerted by the sun: Multiply the mass of the person (which we assume to be constant) by the mass of the sun, and divide by the square of the distance between the person and the sun.
3. Calculate the gravitational force exerted by the moon: Multiply the mass of the person by the mass of the moon, and divide by the square of the distance between the person and the moon.
4. Divide the magnitude of the gravitational force exerted by the sun by the magnitude of the gravitational force exerted by the moon. This will give you the desired ratio Fsun/Fmoon.
Remember to use consistent units of measurement when performing these calculations.