Chapter 13: Q4P (page 379)

The Sun and Earth each exert a gravitational force on theMoon. What is the ratio $F_{s u n} / F_{E a r t h}$ of these two forces? (The average Sun–Moon distance is equal to the Sun–Earth distance.)

Short Answer

Expert verified

The value of the ratio $\frac{F_{s u n}}{F_{e a r t h}} is 2.16 \times 10^{4}$

Step by step solution

The given data

Mass of Sun, $m_{s} = 1.99 \times 10^{30} k g$

Mass of Earth, $m_{s} = 5.98 \times 10^{24} k g$

Distance between Earth and Moon, $r_{m s} = 3.82 \times 10^{10} m$

Distance between Sun and Moon, $r_{e m} = 1.5 \times 10^{11}$

Understanding the concept of Newton’s law of gravitation

According to Newton’s law of gravitation, the force between two objects is directly proportional to their masses and inversely proportional to the square of distance between them.

Formula:

Gravitational force between two particles, $^{F = \frac{G m_{1} m_{2}}{r^{2}}}$ (i)

Calculating the value of the ratio,FsunFearth

Using equation (i), Force between Sun & Moon can be given as:

$F_{s m} = \frac{G \times m_{s} \times m_{m}}{r_{m s}^{2}}$

Using equation (i), Force between Earth & Moon can be given as:

$F_{e m} = \frac{G \times m_{m} \times m_{e}}{r_{e m}^{2}}$

Ratio of two forces becomes:

$\frac{F_{s m}}{F_{e m}} = \frac{G \times m_{s} \times m_{m}}{r_{m s}^{2}} \times \frac{r_{e m}^{2}}{G \times m_{m} \times m_{e}} = \frac{m_{s}}{m_{e}} \times \frac{r_{e m}^{2}}{r_{s m}^{2}} = \frac{1.99 \times 10^{30}}{5.98 \times 10^{24}} \times \frac{(3.82 \times 10^{10})}{(1.5 \times 10^{11})} = 2.16 \times 10^{4}$

The value of the ratio is $2.16 \times 10^{4}$

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The Sun and Earth each exert a gravitational force on theMoon. What is the ratio $F_{s u n} / F_{E a r t h}$ of these two forces? (The average Sun–Moon distance is equal to the Sun–Earth distance.)

Short Answer

Step by step solution

The given data

Understanding the concept of Newton’s law of gravitation

Calculating the value of the ratio,FsunFearth

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The Sun and Earth each exert a gravitational force on theMoon. What is the ratioFsun/FEarthof these two forces? (The average Sun–Moon distance is equal to the Sun–Earth distance.)

Short Answer

Step by step solution

The given data

Understanding the concept of Newton’s law of gravitation

Calculating the value of the ratio,FsunFearth

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Waves Physics

Electromagnetism

Turning Points in Physics

Modern Physics

Thermodynamics

Study anywhere. Anytime. Across all devices.

The Sun and Earth each exert a gravitational force on theMoon. What is the ratio $F_{s u n} / F_{E a r t h}$ of these two forces? (The average Sun–Moon distance is equal to the Sun–Earth distance.)