The distances vary. To get the distances between a pair of planets, look up their distances from the Sun (for example: Venus, 0.72 AU, Earth: 1.00 AU). Subtract these distances to get the closest distance (0.28 AU), and add them to get the farthest distance (1.72 AU), since they are farthest when they are on opposite sides of the Sun. This makes the simplifying assumption that the planets have circular orbits, so it is not entirely accurate, but close enough to get a general idea.
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Another contributor approached the matter this way:
Nearest that two of the solar system's planets can approach each other:
Mercury and Venus in line on the same side of the sun . . . 31.2 million miles.
Farthest apart for any two of the solar system's planets:
Neptune and Pluto in line on opposite sides of the sun . . . 6.463 billion miles.
In a rough ballpark, those two figures are the extremes. As the planets perform all of their
orbital revolutions, the distances between them are constantly changing, and are
always somewhere in this range. No two can ever be closer than 31.2 million miles,
nor farther apart than 6.463 billion miles.
Of course these numbers are completely incomprehensible, which of in turn means
that some people will see these numbers and worry about planets getting too close
together and having some sort of messy and catastrophic accident.
So we took that minimum distance between planets ... 31.2 million miles ... and found
a few things to compare it to, for the relief and comfort of visitors to this page:
The closest together that any two planets can ever be . . . 31.2 million miles, which is:
-- 87% of the distance from the sun to its nearest planet (Mercury)
-- 36 times the diameter of the sun
-- 131 times the distance between the earth and moon
-- 351 times the diameter of the largest planet (Jupiter)
-- a distance that takes a beam of light 2minutes 47seconds to cross it
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