When will perihelion coincide with the June solstice? When this happens, will the average global temperature rise, fall, or stay the same?

I only have an answer for the prediction portion.

The June Solstice of 2017 falls on June 21.

The date of 2017 perihelion is roughly January 4.

There are 168 days between each of the two times.

The retrograde motion of the equinoxes and solstices is at the rate of

(Great Year/Earth Year)/Great Year

Because the June solstice and perihelion coincide, the retrograde

Motion must encompass

of a year is (365.26-168)/365.26.

= 0.540 of a year.

Thus, the event may occur subsequent to

1.2540 years / 0.540 years

#=139 centuries, nearly.

I have estimated the 3-sd, which is comparable to the 3-sd Great Year = 258.

centuries.

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.

Around the year 11700 AD, perihelion, or the June solstice, will occur. Since the Earth is at its closest point to the Sun during this time, an increase in the average global temperature is anticipated.