Explanation Kepler’s third law states that the ratio of the squares of the periods of any two planets revolving around the sun is equal to the ratio of the cubes of their mean distances from the sun. The perihelion is the distance of a planetary orbit with major-axis 2 a from the sun. The aphelion is the farthest distance from the sun. Given: Saturn’s orbit has eccentricity e = 0.056 . The ratio T / a 3 2 is equal to a constant C for all planetary orbits around the sun, where T is the period (time for a complete orbit) and a is the semi major-axis. Formula Used: The perihelion and aphelion are calculated by: Perihelion = a ( 1 − e ) Aphelion = a ( 1 + e ) Calculation: a. A period for the earth is 365 days. It is given that C = T a 3 2 where T = 365 and the semi-major axis of the earth’s orbit a = 150 × 10 6 . So, C = T a 3 2 = 365 ( 150 × 10 6 ) 3 2 ≈ 2.433 × 10 − 6 days/kilometers Thus, C = 2.433 × 10 − 6 days/kilometers b. It is given that Saturn’s semi-major axis is approximately 1.43 × 10 9 km. So, C = T a 3 2 T = C a 3 2 T = 2.433 × 10 − 6 × 1...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 12.5, Problem 64E

To determine

We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.

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Chapter 12.5, Problem 63E

Chapter 12.5, Problem 65E

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Chapter 12 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150 × 10 6 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43 × 10 9 km. c. The perihelion and aphelion of Saturn.

Solution Summary: The author explains that Kepler's third law states that the ratio of squares of the periods of any two planets revolving around the sun is equal to their cubes.

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We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.

Want to see the full answer?

Chapter 12 Solutions

We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150 × 10 6 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43 × 10 9 km. c. The perihelion and aphelion of Saturn.

Solution Summary: The author explains that Kepler's third law states that the ratio of squares of the periods of any two planets revolving around the sun is equal to their cubes.

Concept explainers

Videos

We need to compute a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is 150×106 km. b. The period of Saturn’s orbit, given that its semi-major axis is approximately 1.43×109 km. c. The perihelion and aphelion of Saturn.

Want to see the full answer?

Chapter 12 Solutions

We need to compute

a. C in units of days and kilometers, given that the semi-major axis of the earth’s orbit is $150 \times 10^{6}$ km.

b. The period of Saturn’s orbit, given that its semi-major axis is approximately $1.43 \times 10^{9}$ km.

c. The perihelion and aphelion of Saturn.