   # A planet ( m = 5.542 ×10 26 kg) is in orbit around a star ( M = 1.056 ×10 31 kg) in another part of our galaxy. a. What is the total energy of the planet if its orbit is circular with a radius of 6.35 × 10 12 m? b. What is the total energy of the planet if its orbit is instead elliptical and if its maximum distance is 7.21 × 10 12 m from the star? ### Physics for Scientists and Enginee...

1st Edition
Katz + 1 other
Publisher: Cengage Learning
ISBN: 9781133939146

#### Solutions

Chapter
Section ### Physics for Scientists and Enginee...

1st Edition
Katz + 1 other
Publisher: Cengage Learning
ISBN: 9781133939146
Chapter 8, Problem 83PQ
Textbook Problem
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## A planet (m = 5.542 ×1026 kg) is in orbit around a star (M = 1.056 ×1031 kg) in another part of our galaxy. a. What is the total energy of the planet if its orbit is circular with a radius of 6.35 × 1012 m? b. What is the total energy of the planet if its orbit is instead elliptical and if its maximum distance is 7.21 × 1012 m from the star?

(a)

To determine

The total energy of the planet if its orbit is circular.

### Explanation of Solution

Write the equation for the total energy of a planet in circular orbit.

E=12(GMmr)                                                                                                       (I)

Here, E is the energy of the planet, G is the universal gravitation constant, M is the mass of the star, m is the mass of the planet and r is the radius of the orbit.

Conclusion:

Given that the mass of the star is 1.056×1031 kg , the mass of the planet is 5.542×1026 kg and its radius is 6.35×1012 m . The value of G is 6.67×1011 Nm2/kg2 .

Substitute 6.67×1011 Nm2/kg2 for G, 1

(b)

To determine

The total energy of the planet if its orbit is elliptical.

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