The Minimum Distance from Earth to Mars

This is another question where you're just gonna have to have a guess. You would have to be a real specialist to know this to within one million miles (let alone one million kilometres!)

To work out the answer, I began from the premise that Mars is about half as far again from the Sun as Earth is. That would put it at about 140 million miles from the Sun. When Earth and Mars are at the same point in their orbits (I reckoned) they should be about 47 million miles from each other (140 million minus 93 million).

So I was out by a factor of about 38% (and about 13 times as far out as the leeway allowed!).

Turns out that my estimate of how far Mars is from the Sun was actually pretty close to its semi-major axis (which is pretty close to the mid-point between the maximum and minimum values). What I hadn't realised was that Mars's orbit is actually a lot more eccentric (i.e. less circular and more elliptical) than Earth's. While Earth's orbit only varies between 91.4 and 94.5 million miles, Mars's varies between 128.4 million and 154.8 million.

The answer to the question is the difference between Earth's maximum distance from the Sun (94.5 million miles) and Mars's minimum distance (128.4 million). Which is 33.9 million miles.

Well done if you managed to work that out in twenty seconds!

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