What time of the year is Neptune closest to the earth?

Answer 1

It happens at the time of opposition, when the Earth overtakes Neptune in its orbit. The Earth goes round the Sun 164 times while Neptune goes round only once, so each year Neptune is at opposition 1/164 of a year later, which means that opposition is only 2.2 days earlier each year, and its position is only 2.2 degress further east on the ecliptic.

At opposition Neptune crosses the meridian at midnight. This year (2014) opposition occurs on August 29 when Neptune is in Aquarius (position RA 22 hr 33 min, declination -9 degrees 56 min).