### Abstract

In this we design a simple and insightful way to achieve Kepler's first two laws for planets. The approach is quite different from what we have done for the Earth before. It is because the planet-Sun distance can be determined only through the Earth-Sun distance in the analysis. By applying the law of equal areas for the Earth and the observed angular speeds of a planet over the Sun, the law of equal areas for planets can be re-constructed. Furthermore, for the periodicity of a planet to the Sun, the distance from each planet to the Sun may be expressed as an angular periodic function. By coordinating with the observed data, this periodic distance function depicts an exact elliptical path. Here, we apply relatively easy mathematical skills to illustrate the invariant forms of planetary motions and indicate the key factors used to analyse the motions in complicated planetary systems.

Original language | English |
---|---|

Article number | 045006 |

Journal | European Journal of Physics |

Volume | 36 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2015 Jul 1 |

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### Keywords

- Kepler
- law of ellipses
- law of equal areas
- planet

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*European Journal of Physics*,

*36*(4), [045006]. https://doi.org/10.1088/0143-0807/36/4/045006

**Re-establishing Kepler's first two laws for planets in a concise way through the non-stationary Earth.** / Hsiang, W. Y.; Chang, H. C.; Yao, Herng; Lee, P. S.

Research output: Contribution to journal › Article

*European Journal of Physics*, vol. 36, no. 4, 045006. https://doi.org/10.1088/0143-0807/36/4/045006

}

TY - JOUR

T1 - Re-establishing Kepler's first two laws for planets in a concise way through the non-stationary Earth

AU - Hsiang, W. Y.

AU - Chang, H. C.

AU - Yao, Herng

AU - Lee, P. S.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - In this we design a simple and insightful way to achieve Kepler's first two laws for planets. The approach is quite different from what we have done for the Earth before. It is because the planet-Sun distance can be determined only through the Earth-Sun distance in the analysis. By applying the law of equal areas for the Earth and the observed angular speeds of a planet over the Sun, the law of equal areas for planets can be re-constructed. Furthermore, for the periodicity of a planet to the Sun, the distance from each planet to the Sun may be expressed as an angular periodic function. By coordinating with the observed data, this periodic distance function depicts an exact elliptical path. Here, we apply relatively easy mathematical skills to illustrate the invariant forms of planetary motions and indicate the key factors used to analyse the motions in complicated planetary systems.

AB - In this we design a simple and insightful way to achieve Kepler's first two laws for planets. The approach is quite different from what we have done for the Earth before. It is because the planet-Sun distance can be determined only through the Earth-Sun distance in the analysis. By applying the law of equal areas for the Earth and the observed angular speeds of a planet over the Sun, the law of equal areas for planets can be re-constructed. Furthermore, for the periodicity of a planet to the Sun, the distance from each planet to the Sun may be expressed as an angular periodic function. By coordinating with the observed data, this periodic distance function depicts an exact elliptical path. Here, we apply relatively easy mathematical skills to illustrate the invariant forms of planetary motions and indicate the key factors used to analyse the motions in complicated planetary systems.

KW - Kepler

KW - law of ellipses

KW - law of equal areas

KW - planet

UR - http://www.scopus.com/inward/record.url?scp=84934969041&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84934969041&partnerID=8YFLogxK

U2 - 10.1088/0143-0807/36/4/045006

DO - 10.1088/0143-0807/36/4/045006

M3 - Article

VL - 36

JO - European Journal of Physics

JF - European Journal of Physics

SN - 0143-0807

IS - 4

M1 - 045006

ER -