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The closest planet to the Earth is sometimes Venus and sometimes Mars depending on their positions. 
When Venus is in the middle of the Sun and Earth, it is at its closest point to Earth. During this period, Venus would be the closest planet to Earth. However, there are times when Mars is actually the closest planet.
Venus is about 23.6 million miles away from Earth when it's at its closest, though it can be as far as 162 million miles away.