Chapter 13: Q. 53 (page 355)

How much energy would be required to move the earth into a circular orbit with a radius $1.0 k m$ larger than its current radius?

Short Answer

Expert verified

Total of $1.89 \times 10^{25} J$ energy would be required to move the earth into a circular orbit with a radius $1.0 k m$ .

Step by step solution

Given Information

New radius of the circular orbit is $1.0 k m$ larger than the current radius.

Formula used

Excess energy $∆ E = \frac{G M m}{2 R} - \frac{G M m}{2 (R + r)}$

Here, gravitational constant $G = 6.67 \times 10^{- 11} N \cdot m^{2} / k g^{2}$ .

Mass of the sun, localid="1648185717314" $M = 1.989 \times 10^{30} k g$ .

Mass of the earth, $m = 5.97 \times 10^{24} k g$ .

Initial radius of earth's orbit, localid="1648185813557" $R = 1.5 \times 10^{11} m$ .

New radius of earth's orbit, $R + r = (1.5 \times 10^{11} + 10^{3}) m$ .

: Calculation

Substitute the values and obtain $∆ E$ .

∆ E = \frac{G M m}{2 R} - \frac{G M m}{2 (R + r)} ∆ E = \frac{G M m}{2} [\frac{1}{R} - \frac{1}{R + r}] ∆ E = \frac{6.67 \times 10^{- 11} N \cdot m^{2} / k g^{2} \times 1.989 \times 10^{30} k g \times 5.97 \times 10^{24} k g}{2} [\frac{1}{1.5 \times 10^{11} m} - \frac{1}{1.5 \times 10^{11} m + 10^{3} m}] ∆ E = 39.6 \times 10^{43} \times 4.78 \times 10^{- 20} J ∆ E = 1.89 \times 10^{25} J

Final Answer

Total of $1.89 \times 10^{25} J$ energy would be required to move the earth into a circular orbit with a radius $1.0 k m$ .

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How much energy would be required to move the earth into a circular orbit with a radius $1.0 k m$ larger than its current radius?

Short Answer

Step by step solution

Given Information

Formula used

: Calculation

Final Answer

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How much energy would be required to move the earth into a circular orbit with a radius 1.0km larger than its current radius?

Short Answer

Step by step solution

Given Information

Formula used

: Calculation

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Measurements

Magnetism and Electromagnetic Induction

Energy Physics

Rotational Dynamics

Linear Momentum

Study anywhere. Anytime. Across all devices.

How much energy would be required to move the earth into a circular orbit with a radius $1.0 k m$ larger than its current radius?