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If it were possible to replace the Moon with Mars, how distant would it have to be to essentially create the same oceanic tides as the Moon currently does? Mars seems to be roughly 3 times the mass of the Moon, so does that mean it should be 300% the distance?

Furthermore, would the increased distance cause any issues with Earth's orbit around the Sun or potentially cause some sort of situation like Charon and Pluto where the centre of mass is between them?

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What do you mean by "same tides"? Any two bodies orbiting each other are going to cause "tidal effects", so the answer might be doesn't matter, all orbiting bodies will cause tidal effects like the moon. But if you are looking for a system that causes the same amplitude, or the same time frequency, or the same distribution of diurnal/semi-diurnal tides; or if you you asking about tidal effects on just oceans or other systems — or all of the above — working out the orbital mechanics becomes a bigger challenge. What is it you are trying to solve for? –  Robert Cartaino Jun 5 at 14:12
    
Sorry, I did mean oceanic tides, I fixed it. I'm not trying to solve for anything in particular, just my own curiosity. –  simontemplar Jun 5 at 17:27

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The Tidal acceleration between 2 bodies is calculated with this formula:

$$ a_T = \frac{2GM_MR_1}{Dm^3} $$

Where $M_M$ is Mar's mass, $R_1$ Earth Radius and $D_m$ the distance to the Moon. If you equal this to Moon's Tidal acceleration you will get $D_M$ as distance to Mars to get the same Tidal acceleration having $\frac{M_M}{M_m}=8.73328184501$:

$$ D_M = \sqrt[3]{8.73}D_m\simeq2.06Dm $$

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...went that far, should finish with cube-root-of-3 is about 1.44. Or about 1.5 times the current moon's distance. –  Craig Constantine Jun 5 at 14:55

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