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From Wiki[1] the aphelion and perihelion for Mars are 1.381 and 1.666 so I think assuming that Mars orbit is circular is just wrong. The eccentricity is 9%. Th

From Wiki[1] the aphelion and perihelion for Mars are 1.381 and 1.666 so I think assuming that Mars orbit is circular is just wrong. The eccentricity is 9%. The inclination of Mar's orbit is also 1.8 degrees which makes a difference as well. Wiki also lists a closest approach to Earth of 0.372 AU and a furthest distance of 2.675. The graphs on that link do not come close to those figures. They are off by 25%. Basically I do not understand why someone would take an orbital problem, simplify all the interesting bits out of it and then put it up on a blog. Maybe he was more interested in the maths than the physics. (1) - https://en.wikipedia.org/wiki/Orbit_of_Mars#Table_of_orbital_parameters https://en.wikipedia.org/wiki/Orbit_of_Mars#Table_of_orbital...

adaml_623 11y ago
Looks at the graph on here: http://www.wolframalpha.com/input/?i=distance+from+earth+to+mars+over+time http://www.wolframalpha.com/input/?i=distance+from+earth+to+... (expand the time period to +/- 10 years) It's wonderful.
johndcook 11y ago
The results in the blog post wouldn't do to launch a probe, but they do give you a good idea of how the distance varies over time. It's a little surprising that such a simple calculation works as well as it does. More accurate calculations would be interesting, much more complicated.
yaks_hairbrush 11y ago
The interesting thing here is that he used only algebra. This model therefore occupies a sort of sweet spot, insofar as adding to the accuracy of the model requires machinery a level above what was used to get this model. To wit: If you want to take into account eccentricity (which I think would be the biggest source of error), the steps needed are fairly involved. For one way to do it, see [0]. [0] https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Position_as_a_function_of_time https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_m...

adaml_623 11y ago

Looks at the graph on here: http://www.wolframalpha.com/input/?i=distance+from+earth+to+mars+over+time http://www.wolframalpha.com/input/?i=distance+from+earth+to+... (expand the time period to +/- 10 years) It's wonderful.

johndcook 11y ago

The results in the blog post wouldn't do to launch a probe, but they do give you a good idea of how the distance varies over time. It's a little surprising that such a simple calculation works as well as it does. More accurate calculations would be interesting, much more complicated.

yaks_hairbrush 11y ago

The interesting thing here is that he used only algebra. This model therefore occupies a sort of sweet spot, insofar as adding to the accuracy of the model requires machinery a level above what was used to get this model. To wit: If you want to take into account eccentricity (which I think would be the biggest source of error), the steps needed are fairly involved. For one way to do it, see [0]. [0] https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Position_as_a_function_of_time https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_m...