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Q. 53

Found in: Page 772


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

Measurements indicate that Earth’s orbital eccentricity is 0.0167 and its semimajor axis is 1.00000011 astronomical units.

(a) Write a Cartesian equation for Earth’s orbit.

(b) Give a polar coordinate equation for Earth’s orbit, assuming that the sun is the focus of the elliptical orbit.

Part (a) The cartesian equation is x2(1.00000011)2+y2(0.9998606552)2=1.

Part (b) The polar equation is r=1.000000111+0.0167cosθ.

See the step by step solution

Step by Step Solution

Part (a) Step 1. Given information.

The eccentricity is 0.0167 .

The semi-major axis is role="math" localid="1649526544989" 1.00000011 astronomical units.

Part (a) Step 2. Explanation.


e=A2-B2AA=1.00000011, e=0.01670.0167=(1.00000011)2-B21.000000110.0167(1.00000011)=(1.00000011)2-B20.0167000018=1.00000022-B2(0.0167000018)2=(1.00000022)-B220.00027889006=(1.00000022)-B2B2=0.99972133A2=(1.00000011)2=1.00000022Therefore,x21.00000022+y20.99972133=1 or x2(1.00000011)2+y2(0.9998606552)2=1

Part (b) Step 1. Explanation.

Now, the standard form,


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