As a better way to understand my post about James Croll’s work, and Milankovitch cycles, consider a world with zero tilt. The equator would still be as hot as today, averaging about 90°F between day and night. That’s 32°C or 305°K. The polar caps would still be snow covered, but since there would be no summers at the poles, the snow would never melt. It would just build up, and build up. As for the middle latitudes, at some point there would be no snow at all. As a first estimate of how far down the ice would range, consider that the heat into a spot always equals the heat out, and that the heat out is proportional to the temperature to the fourth because of grey body radiation.

Q_in = Q_out = A(T⁴) with Temperature in degrees K.

If the temperature at the equator averages 305K, we can say that A_equator = Q_equator/305⁴.

Now consider what happens further north; at any random latitude,

Heat in = Q_equator *cos φ*α

where φ is the latitude and α is albedo (a whiteness factor), an equation I’ve explained elsewhere.

Heat out = A_equator T⁴ α = Heat in.

We use the same value for albedo for absorption as for radiation. Substituting fo A_equator above we find that

Q_equator/305⁴ * T⁴ α = Q_equator*cos φ*α.

(T/305)⁴ = cos φ.

If we now solve for cos φ* such that T = 273 K, the freezing temperature for water, we find that φ= 50.1°. Permanent ice will extend that far south, at least 300 miles south of Paris. While this is happening the oceans will slowly dry up as ice piles up, miles deep on the land. You’ll be able to walk from France to England, and that’s just the effect of tilt. Be glad there is a tilt to the earth. Sorry to say, the tilt has been decreasing for the last 5000 years or so. The decreasing tilt of the earth is one reason to expect another ice age beginning in the next 1000 years.

Eccentricity of the rocky planets. The black line is earth. As you can see eccentricity is decreasing fast. Interaction between the planets causes the change in eccentricity, as well as the change in tilt and precession. 

An even stronger effect comes from eccentricity, and the part of eccentricity that’s most important, according to Croll, is the minor axis. When there is a large eccentricity and a large tilt towards the sun at the long and short end, you have warming. The sun shines very warm at the pole at one end of the major axis, but only for a brief time; though it shines less brightly on the other side, it’s for a longer time. Thus, the two ends of the ellipse have no more or less heating than for a circular orbit, but a long ellipse brings in the earth at the point of the minor axis and this adds heat to the planet in general. When the orbit is less eccentric the earth is further away at the minor axis and the earth cools. We are heading to an increasingly circular orbit and bit by bit we can expect that icebergs will flow down from up north and cool the lower latitudes too. Interaction between the planets, particularly with Jupiter and Venus, is the cause of all these cyclic variations. Here’s a link to Croll’s book.

Dr. Robert E. Buxbaum, November 16, 2018