   Chapter 7, Problem 38P

Chapter
Section
Textbook Problem

Use the data of Table 7.3 to find the point between Earth and the Sun at which an object can be placed so that the net gravitational force exerted by Earth and the Sun on that object is zero.

To determine

The point at which the zero net gravitational force exerted on the object due to Earth and the Sun.

Explanation

The object is placed at a distance r from the center of Earth and (1.496×1011mr) from the center of the Sun. At this point, the magnitude of gravitational force on the object duo to Earth and the Sun are equal but their directions are opposite. Hence the net gravitational force on the object is zero at that point. It can be proved by the following relation GmEmr2=Gmsm(1.496×1011mr)2 and reduced for the location of the point.

Given Info: The mass of the Sun is 1.991×1030kg, mass of Earth is 5.98×1024kg, the mean distance of Earth from the sun is 1.496×1011m.

The formula for the point between Earth and the sun at which the an object can be placed so that the zero net gravitational force exerted by Earth and the Sun on the object is,

mEr2=ms(1.496×1011mr)2

• mE is mass of Earth

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