### Abstract

Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. This paper demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyse the angular velocity or the reciprocal of the distance - for the Earth's orbit around the Sun - and can be defined as a periodic function by analysing the available data, which help explain the law of ellipses for the Earth.

Original language | English |
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Pages (from-to) | 1405-1412 |

Number of pages | 8 |

Journal | European Journal of Physics |

Volume | 32 |

Issue number | 5 |

DOIs | |

Publication status | Published - 2011 Sep 1 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*European Journal of Physics*,

*32*(5), 1405-1412. https://doi.org/10.1088/0143-0807/32/5/028

**An alternative way to achieve Kepler's laws of equal areas and ellipses for the Earth.** / Hsiang, W. Y.; Chang, H. C.; Yao, Herng; Chen, P. J.

Research output: Contribution to journal › Article

*European Journal of Physics*, vol. 32, no. 5, pp. 1405-1412. https://doi.org/10.1088/0143-0807/32/5/028

}

TY - JOUR

T1 - An alternative way to achieve Kepler's laws of equal areas and ellipses for the Earth

AU - Hsiang, W. Y.

AU - Chang, H. C.

AU - Yao, Herng

AU - Chen, P. J.

PY - 2011/9/1

Y1 - 2011/9/1

N2 - Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. This paper demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyse the angular velocity or the reciprocal of the distance - for the Earth's orbit around the Sun - and can be defined as a periodic function by analysing the available data, which help explain the law of ellipses for the Earth.

AB - Kepler's laws of planetary motion are acknowledged as highly significant to the construction of universal gravitation. This paper demonstrates different ways to derive the law of equal areas for the Earth by general geometrical and trigonometric methods, which are much simpler than the original derivation depicted by Kepler. The established law of equal area for the Earth was applied to analyse the angular velocity or the reciprocal of the distance - for the Earth's orbit around the Sun - and can be defined as a periodic function by analysing the available data, which help explain the law of ellipses for the Earth.

UR - http://www.scopus.com/inward/record.url?scp=80051921087&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051921087&partnerID=8YFLogxK

U2 - 10.1088/0143-0807/32/5/028

DO - 10.1088/0143-0807/32/5/028

M3 - Article

AN - SCOPUS:80051921087

VL - 32

SP - 1405

EP - 1412

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 5

ER -