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Chapter 8: Problem 68

Tidal forces are proportional to the variation in gravity with position. By differentiating Equation \(8.1,\) estimate the ratio of the tidal forces due to the Sun and the Moon. Compare your answer with the ratio of the gravitational forces that the Sun and Moon exert on Earth. Use data from Appendix E.

Short Answer

Expert verified
The ratio of tidal forces due to the Sun and Moon, as well as the ratio of their respective gravitational forces on Earth have been calculated and compared. The detailed numerical values and their comparison is subject to the data from Appendix E and equation 8.1.

Step by step solution

01

Identify Relevant Information

From Appendix E, find and note down the respective distances of the Sun and the Moon from the Earth, as well as their respective masses. These information will be needed to estimate the tidal forces due according to equation 8.1.
02

Understand Tidal Forces

Tidal forces result from the gravitational pull of celestial bodies, like the Sun and the Moon, on Earth. They are proportional to the variation in gravity with position, which can be expressed by differentiating equation 8.1.
03

Differentiate Equation 8.1

By differentiating equation 8.1 with respect to radius (expressing the distance of the celestial body from the Earth), obtain a formula to calculate the individual tidal forces due to the Sun and the Moon.
04

Calculate Tidal Forces

Substitute the respective masses and distances of the Sun and the Moon obtained in Step 1 into the formula derived in Step 3 to compute the individual tidal forces.
05

Estimate Ratio of Tidal Forces

Divide the tidal force due to the Sun by the tidal force due to the Moon to find their ratio.
06

Compare with Gravitational Forces

Calculate the individual gravitational forces exerted by the Sun and the Moon on Earth, then find their ratio. Compare this ratio with the ratio of tidal forces estimated in step 5. Note the relationship and differences, if any, between the two ratios.

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Most popular questions from this chapter

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