Ch 13: Newton's Theory of Gravity

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 13: Newton's Theory of Gravity

Problem 2

Chapter 13, Problem 2

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

Verified step by step guidance

Step 1: Begin by identifying the formula for gravitational force, which is given by Newton's law of gravitation:

F = G rac{m_1 m_2}{r^2}

, where

G

is the gravitational constant,

m_1

and

m_2

are the masses of the two objects, and

r

is the distance between their centers.

Step 2: To find the gravitational force exerted by the Sun on you, substitute the mass of the Sun (

m_{Sun} = 1.989 	imes 10^{30} \(\text{ kg}\)

), your mass (

m_{you}

), and the average distance between the Sun and Earth (

r_{Sun-Earth} = 1.496 	imes 10^{11} \(\text{ m}\)

) into the formula.

Step 3: To find the gravitational force exerted by the Earth on you, substitute the mass of the Earth (

m_{Earth} = 5.972 	imes 10^{24} \(\text{ kg}\)

), your mass (

m_{you}

), and the radius of the Earth (

r_{Earth} = 6.371 	imes 10^{6} \(\text{ m}\)

) into the formula.

Step 4: Calculate the ratio of the Sun's gravitational force to the Earth's gravitational force by dividing the two expressions:

rac{F_{Sun}}{F_{Earth}} = rac{G rac{m_{Sun} m_{you}}{r_{Sun-Earth}^2}}{G rac{m_{Earth} m_{you}}{r_{Earth}^2}}

. Notice that

G

and

m_{you}

cancel out.

Step 5: Simplify the ratio to

rac{F_{Sun}}{F_{Earth}} = rac{m_{Sun} / r_{Sun-Earth}^2}{m_{Earth} / r_{Earth}^2}

. Substitute the known values for

m_{Sun}

m_{Earth}

r_{Sun-Earth}

, and

r_{Earth}

to compute the ratio.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gravitational Force

Gravitational force is the attractive force between two masses, described by Newton's law of universal gravitation. It states that every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This fundamental concept is crucial for understanding how objects interact under gravity.

Mass and Weight

Mass is a measure of the amount of matter in an object, while weight is the force exerted by gravity on that mass. Weight can be calculated using the formula W = mg, where W is weight, m is mass, and g is the acceleration due to gravity. Understanding the distinction between mass and weight is essential for analyzing gravitational forces from different celestial bodies.

Ratio of Forces

The ratio of forces compares the gravitational force exerted by one body to that exerted by another. In this context, it involves calculating the gravitational force from the sun and the earth on a person and expressing it as a fraction. This concept helps in understanding how different gravitational influences affect an object based on their respective masses and distances.