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Comment by imglorp | Hacker News Reader

So they seem to be implying a gravitational interaction between Earth and Mars. Out of curiosity I wanted to see roughly what kind of forces we're talking about at closest approach. (Edit: including feedback below, thanks)

    r   1e11 m
    Me  6e24 kg
    Mm  6e23 kg
    G = 6e-11 m^3 kg^-1 s^-2

    F ~~ GMeMm/r^2 = 6e-11 * 6e24 * 6e23 / (1e11)^2 
      ~~ 2e16 N

http://www.wolframalpha.com/input/?i=G+*+6e24+kg+*+6e23kg+%2...

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Your distance is off by quite a bit (should be ~1e11 m at closest approach).

The actual force is closer to 10^16 N. Which is big, but 10^7 weaker than the earth-sun interaction. But the sun has to move the earth by a couple AU per year whereas Mars has had a couple billion years to move it by the same amount.

Only thing that might be off is the radius there, as it'll vary based on the phase that each planet is in it's orbit, which will make it go even lower at points.

Also WFA will do the units too, http://www.wolframalpha.com/input/?i=G+*+6e24+kg+*+6e23kg+%2...

You got the distance wrong. The minimum distance the two planets can have on their orbits is 55 million km. The force between the two is of the order 1e15 N.

The value `r` above is off by a factor of 10^9. It should be 0.5 AU or 7.48x10^10 meters:

http://www.wolframalpha.com/input/?i=distance+between+Mars+a...

The current gravitational force between Mars and Earth is 2.832x10^15 N:

http://www.wolframalpha.com/input/?i=(gravitational+constant...

For comparison, the current gravitational force between the Sun and Earth is 3.614x10^22 N:

https://www.wolframalpha.com/input/?i=(gravitational+constan...

P.S. My favorite Wolfram Alpha feature is being able to use natural language descriptions of various quantities!

> What am I missing?

Resonance over a few million years.

Okay, so does that mean the resonance has damped over the years or built? Even if I'm off by 3 oom, it's still less force than 1kN between planets, hardly enough to influence our geology.

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