When will perihelion coincide with the June solstice? When this happens, will the average global temperature rise, fall, or stay the same?
Earth's perihelion with coincide with the June solstice in about 10,000 years time.
Currently the Earth is at perihelion around the 3rd of January. The actual date and time vary by up to about 3 days due to perturbations of the Earth's orbit caused by other planets' gravitational effects.
Perihelion actually gets later each year due to precession. It is on average a day later every 58 years.
In about 10,000 years perihelion will be around the time of the June solstice.
Curiously the Earth is warmest around aphelion in July. The reason for this is that in July the northern hemisphere, which is mainly land, is in summer. The southern hemisphere, which is mainly water, gets warmer summers due to being closer to the sun, but water loses heat less rapidly than land.
When perihelion is around the June solstice the northern hemisphere will get warmer summers and colder winters. Conversely for the southern hemisphere.
After 139 centuries, from now.
My answer is for the prediction part only.
2017 June Solstice will be by June 21.
2017 perihelion date will be about Jan 4.
The in-between time interval is 168 days.
The equinoxes/solstices retrograde motion is at the rate of
(Earth year/Great Year)/Earth year
For the coincidence of perihelion with June solstice. the retrograde
motion has to cover
(365.26-168)/365.26) of a year
So, the event might take place after
#=139 centuries, nearly.
I have made 3-sd approximation, on par with 3-sd Great Year = 258