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I want to create a planet where there are extreme winters (3 months with temperatures up to -40°C) at around 50° latitude. The summers are just slightly hotter (a day of 30°C in the summer would not be unusual).
The size of the planet is the same as earth. What would the orbit and axial tilt be like to make this seasonal pattern possible?
(x 1,000,000,000m)
So as L.Dutch beat me to saying, you need to make the orbit more eccentric. To show it visually; the earth is the orange ring currently. Move it to the green ring or maybe the blue ring.
if 0 is a perfectly circular orbit, and 1 is an escape orbit, earth is currently 0.0167, with min and max distances of 147gm (gigameters) and 152gm, and an average of 149.5gm
50 degrees north seems to get winter max temps of 5-7 degrees, to get winter maxes of -40, you need to take 45 degrees off the winter temp. From about 278 Kelvin to 233 Kelvin, a 16% decrease in temperature.
As a simplification, we can just approximate that at ~9% further increase in distance will give a ~16% decrease in temperature.
So you want an orbit that gives 146gm (slightly closer as you want slightly hotter summers) and 166gm, using this calculator I calculate you need an eccentricity of 0.064103 and an average distance of 156.
This would also cool the Australian summer and shorten and warm the Australian winter - that sounds quite nice.
You need to make the orbit more eccentric, so that the winter in the North emisphere corresponds to the period of maximum distance from the sun, while the minimum distance happens at a distance comparable with the one of our planet to the sun.
Summers will be shorter, because the closest the planet to the star, the faster the orbital velocity.
