The planets orbit the Sun in elliptical orbits withthe Sun at one focus. Theequation of an ellipse whose dimensions are 2a in the x-directionand 2b in the y-direction is(x2/a2) +(y2/b2) = 1.Let d2 denote the square of the distance from a planet tothe center of the ellipse at (0, 0). Integrate over the interval[-a, a] to show that the average value of d2 is(a2 + 2b2)/3 aEarthb.Sun

The planets move in elliptical orbits around the Sun. Celestial dance is dictated by the fundamental…

Answered: Integrate over the interval [-a, a] to…

Applications and Investigations in Earth Science (9th Edition)

9th Edition

ISBN:9780134746241

Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa

Chapter1: The Study Of Minerals

Section: Chapter Questions

Problem 1LR

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Question

The planets orbit the Sun in elliptical orbits with
the Sun at one focus. The
equation of an ellipse whose dimensions are 2a in the x-direction
and 2b in the y-direction is(x²/a²) +(y²/b²) = 1.
Let d2 denote the square of the distance from a planet to
the center of the ellipse at (0, 0). Integrate over the interval
[-a, a] to show that the average value of d2 is(a² + 2b²)/3