What’s Wrong Here? Wolfram Alpha and Roche Limits

June 25th, 2013

Blog reader Iljitsch van Beijnum, inspired by images an an artist made of planets as seen from Earth if they were as far away as our moon, sent me an email about a calculation from Wolfram Alpha:

It occurred to me that we would then be within Jupiter’s Roche limit. So I went to Wolfram Alpha to investigate. But strangely, it reports 709000 km for Jupiter and 880000 for Saturn. And 441200 km for Earth:


That can’t be right, we wouldn’t have a moon…

I love checking these things out quantitatively, and for checking to see if the answers make sense!  That’s thinking like a scientist and a good hard science fiction writer!  If you haven’t come across the term “roche limit” before, it’s the location where tidal forces from a primary body (like a central star, or a planet with moons around it) match the gravitational force from the orbiting body’s own gravity.  Inside that limit, rings would be expected, outside it moons.  It’s a little more complicated than that, but not a lot more complicated.  More more information see my reply:

I saw those pictures a few months back and enjoyed them very much.

You’re correct, Wolfram Alpha is wrong.  Wikipedia has the right expressions you need to do the calculations and some examples:


I don’t use Wolfram Alpha.  I’m not sure where it’s getting this number from, but it’s totally wrong.  Is there a way to see its sources?  I hate black box stuff — it’s hard to trust, especially when it isn’t giving the right answer.  I wonder if it’s answering a different question?

Well, I poked around for a few minutes to satisfy myself Wolfram Alpha is giving wrong answers.  I don’t see how to figure out where it’s getting its information.  Anyone reading who knows the answer?



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