We consider a body in an elliptical orbit around the sun. The following table gives eccentricity, the ratio of distances between aphelion and perihelion, and the ratio of sunlight received between perihelion and aphelion.

Eccentricity | Distance ratio | Power ratio |
---|---|---|

0.000 | 1.000 | 1.000 |

0.001 | 1.002 | 1.004 |

0.002 | 1.004 | 1.008 |

0.005 | 1.010 | 1.020 |

0.010 | 1.020 | 1.041 |

0.020 | 1.041 | 1.083 |

0.050 | 1.105 | 1.222 |

0.100 | 1.222 | 1.494 |

0.200 | 1.500 | 2.250 |

0.300 | 1.857 | 3.449 |

0.400 | 2.333 | 5.444 |

0.500 | 3.000 | 9.000 |

0.600 | 4.000 | 16.000 |

0.700 | 5.667 | 32.111 |

0.800 | 9.000 | 81.000 |

0.900 | 19.000 | 361.000 |

0.950 | 39.000 | 1521.000 |

An eccentricity of (sqrt(1.1)-1)/(sqrt(1.1+1)) = 0.0238 is the eccentricity that sees 10% additional power from the sun at perihelion. Perhaps that is the threshold eccentricity beyond which an orbit ought not be called "roughly circular", because 10% is (subjectively) a significant difference in power. Currently, only Venus, Neptune, and Earth have roughly circular orbits around the sun. (Eccentricities change over time, because Jupiter.)

Mercury's eccentricity is 0.21. Other planets.

At e = 0.172, the power ratio is 2.

At e = 1/3, the distance ratio is 2.

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