The Physics of Everyday Phenomena
The Physics of Everyday Phenomena
8th Edition
ISBN: 9780073513904
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
Question
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Chapter 5, Problem 6SP

(a)

To determine

The fraction of total orbital period of earth through which it move in one period of the moon’s orbit.

(a)

Expert Solution
Check Mark

Answer to Problem 6SP

The fraction of total orbital period of earth through which it move in one period of the moon’s orbit is 7.5%.

Explanation of Solution

Given Info: The period of moon’s orbit about the Earth is 27.3 days.

The period of orbital motion of Earth is 365.25 days. Therefore fraction of total orbital period of earth through which it move in one period of moon’s orbit is obtained by taking the ratio of period of moon’s orbit about earth to total orbital period of earth.

Write the expression for the fraction of total orbital period of Earth through which it move in one period of the moon’s orbit.

Period of moon's orbit about EarthPeriod of orbital motion of Earth=27.3 days365.25 days=0.075

Write the fraction 0.075 to percentage.

0.075=0.075×100=7.5%

Conclusion:

Thus, the fraction of total orbital period of earth through which it move in one period of the moon’s orbit is 7.5%.

(b)

To determine

The sketch of the sun, the Earth and the moon with the moon in the Full moon condition and also the sketch of the position where the moon would be in 27.3 days later when the Earth is in its new position and to determine whether it will be a full moon if the moon is in the same position relative to Earth as it was 27.3 days earlier.

(b)

Expert Solution
Check Mark

Answer to Problem 6SP

The sketch of the sun, the Earth and the moon with the moon in the Full moon condition is  given in figure 1.and the sketch of the position where the moon would be in 27.3 days later when the Earth is in its new position is given in figure 2.

The moon will not be a full moon since the apparent advance of the moon in 27.3days is only 333°.

Explanation of Solution

When the moon is full, it is on the opposite side of the Earth from the sun. The sketch of the sun, the Earth and the moon with the moon in the Full moon condition is plotted in figure 1.

The Physics of Everyday Phenomena, Chapter 5, Problem 6SP , additional homework tip  1

Figure 1

Write the expression for the angle through which the moon or the Earth advances in one day.

θ=θTT (1)

Here,

θ is the angle through which moon or earth advances in one day

θT is the total angle advanced by earth or moon in one day

T is the time period

Substitute 360 ° for QT and 27.3 days for T in equation (1) to find the angle through which the moon advances in one day.

θ=360°27.3 days=13.2°/day

Substitute 360 ° for QT and 365.25 days for T in equation (1) to find the angle through which the earth advances in one day.

θ=360 °365.25 days1 °/day

Find the apparent advance of the moon relative to sun earth system in one day.

θnet=13.2°/day1°/day=12.2°/day

Here,

θnet is the apparent advance of the moon relative to sun earth system in one day

Find the apparent advance of the moon in 27.3 days.

(12.2 °/day)×(27.3 days)=333 °360 °

The moon is not full moon yet.

The sketch of the position where the moon would be in 27.3 days later when the Earth is in its new position is drawn in figure (2).

The Physics of Everyday Phenomena, Chapter 5, Problem 6SP , additional homework tip  2

Figure 2

Conclusion:

Thus, the sketch of the sun, the Earth and the moon with the moon in the Full moon condition is plotted in figure 1 and the sketch of the position where the moon would be in 27.3 days later when the Earth is in its new position is plotted in figure 2. The moon will not be a full moon since the apparent advance of the moon in 27.3days is only 333°.

(c)

To determine

The extra angle through which the moon have to go to reach the full moon condition and to show it represents approximately an extra two days.

(c)

Expert Solution
Check Mark

Answer to Problem 6SP

The extra angle through which the moon has to go to reach the full moon condition is 27 ° and it takes 2.2 days more which is approximately extra two days.

Explanation of Solution

From part (b), the angle advanced by moon in 27.3 days is 333 °.

Therefore the extra angle that it can have to go to reach the full moon condition is obtained by subtracting apparent angle advanced by moon to total angle.

Find the extra angle for the moon to reach full moon condition.

Δθ=360 °333 °=27 °

Here,

Δθ is the extra angle for the moon to reach full moon condition.

Write the expression for the time taken to reach full moon condition.

t=Δθθnet

Here,

t is the time taken to reach full moon condition

Substitute 27° for Δθ and 12.2 °/day for θnet in the above equation to get t.

t=27 °12.2 °/day=2.2 days2 days

Conclusion:

Thus, the extra angle through which the moon has to go to reach the full moon is condition 27° and it takes approximately an extra two days.

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The Physics of Everyday Phenomena

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