- #1

DaveC426913

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- TL;DR Summary
- distances of planets, converting AU to inches and plotting logarithmically

I'm designing a growth chart for my granddaughter with the planets on it. I wanted them to be proportional* as far as distance goes - with the sun at the floor and Pluto at, say, six feet, but obviously that's impossible since all the inner planets would be in the first inch or two from the floor.

So the next best thing is to do it logarithmically. Unfortunately, I never studied logs.

Instead of putting the sun at 0", I'll put it at 19" (her height at birth)

and I'll set 40AU at, say, 72"** from the floor.

So that's a span of 53" with an offset of 19".

Now I want to spread the planets logarithmically from zero to 53.

These are the distances in AUs, rounded to about 2 decimals.

Not sure how to calculate logs for these. I can probably do some of it in Excel, but I'm not sure how to set the fractional log so that 40AU=53"* Is it overkill? She's too young, of course, but ideally she'll be using this into her tweens. How old were you before you realized that the planets are not all close-by and evenly spaced? It's the kind of entrenched illusion that results in long lists of "Today I Learned". IMO, there's no harm in starting children off with accurate images.

** How likely is it she'll exceed six feet before she gives up on her childhood growth chart? Pretty unlikely. But one's reach should exceed one's grasp.

So the next best thing is to do it logarithmically. Unfortunately, I never studied logs.

Instead of putting the sun at 0", I'll put it at 19" (her height at birth)

and I'll set 40AU at, say, 72"** from the floor.

So that's a span of 53" with an offset of 19".

Now I want to spread the planets logarithmically from zero to 53.

These are the distances in AUs, rounded to about 2 decimals.

Body | Distance (AU) | Height (Inches) |

S | 0 | 0 |

M | .4 | |

V | .7 | |

E | 1 | |

M | 1.5 | |

AB | 3 | |

J | 5.2 | |

S | 9.6 | |

U | 19 | |

N | 30 | |

P | 40 | 53 |

** How likely is it she'll exceed six feet before she gives up on her childhood growth chart? Pretty unlikely. But one's reach should exceed one's grasp.