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The position of a planet that a closest to and farthest from the sun are called its  perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 108 km and the aphelion distance of 1.52 x 108 km.  Find the Cartesian equation of the elliptical orbit.

The position of a planet that a closest to and farthest from the sun are called its  perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 108 km and the aphelion distance of 1.52 x 108 km.  Find the Cartesian equation of the elliptical orbit.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The position of a planet that a closest to and farthest from the sun are called its 
perihelion and aphelion respectively. We know that the Earth orbits around the Sun (as one focus) in an elliptical orbit with the perihelion distance of 1.47 x 108 km and the aphelion distance of 1.52 x 108 km. 
Find the Cartesian equation of the elliptical orbit.

The diagram illustrates the elliptical orbit of the Earth around the Sun, highlighting key points: Aphelion and Perihelion. - **Sun**: Positioned at one of the two foci of the ellipse. - **Earth**: Shown at a point in its orbit. - **Aphelion**: The point in Earth's orbit where it is farthest from the Sun. - **Perihelion**: The point in Earth's orbit where it is closest to the Sun. This diagram effectively demonstrates the elliptical nature of Earth's orbit, in accordance with Kepler's First Law of Planetary Motion.
Transcribed Image Text:The diagram illustrates the elliptical orbit of the Earth around the Sun, highlighting key points: Aphelion and Perihelion. - **Sun**: Positioned at one of the two foci of the ellipse. - **Earth**: Shown at a point in its orbit. - **Aphelion**: The point in Earth's orbit where it is farthest from the Sun. - **Perihelion**: The point in Earth's orbit where it is closest to the Sun. This diagram effectively demonstrates the elliptical nature of Earth's orbit, in accordance with Kepler's First Law of Planetary Motion.
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