# Seasons are due to the tilt of the Earth. Really?

1. Mar 26, 2009

### Smatter

OK, the prevailing wisdom says that the tilt of the Earth relative to the plane of the ecliptic is the main reason for the Earth's seasons. This is caused by, among other things, the variation in angle at which the sun's light hits the Earth, the day length and distribution of land/sea masses etc.

Now, I'm Ok with this but I don't understand why the distance from the Sun doesn't have a noticeable effect on the seasons. If you look at the figures the Earth is 91,405,436 miles from Sun at perihelion and 94,511,989 miles from Sun at aphelion, so that's a difference of approximately 3,000,000 miles. But, the diameter of the Earth is approximately 8000 miles and therefore no matter how large the Earth's tilt, it is an insignificant change in distance from the Sun in comparison to the 3,000,000 mile change in distance due to the eccentricity of the Earth's orbit.

The obvious conclusion is that the effects of the angle at which the Sun's rays hit the Earth and day length etc. are orders of magnitude greater than the effect of distance from the Sun.

So if what I've written is correct, all well and good, but I'd like to see some simple figures proving it. Can anyone do the maths or point me to a page that demonstrates (proves) that the distance from the sun is insignificant when compared to other factors in determining the Earth's seasons please?

2. Mar 26, 2009

### D H

Staff Emeritus
Orbital eccentricity does have an effect on the seasons, but it is a rather minor effect. If eccentricity was much greater obliquity was much smaller than they currently are, eccentricity rather than obliquity would be the driving factor in determining the seasons. The seasons would be the same world-wide.

As it is, the seasons in the Northern and Southern hemispheres run 180 degrees out of phase. It is currently early fall in the Southern hemisphere, early spring in the Northern hemisphere.

3. Mar 26, 2009

### mgb_phys

The difference in distance summer-winter is about 3% and because of the inverse square law the solar flux changes by about 6%. But in radiative equilibrium, Earth receives more heat, Earth heats up, Earth radiates more - the change in overall average temperature is much smaller.

The summer winter effects due to the tilt are due to weather. The difference in heating between two latitudes drives a huge mass movement of air, which carries a lot more energy than the simple difference in solar flux.

For example the southern hemisphere is closest to the sun in it's summer - so overall it gets the most solar energy. But Antartica is much colder than the North pole - due to the much greater effects of ocean currents, land vs. water etc.

4. Mar 26, 2009

### Smatter

Thanks DH but that really only restates what I've already said. What I'm looking for is numbers (preferably simple or simplified) that prove that the distance from the Sun is a relatively insignificant factor in the equation.

5. Mar 26, 2009

### rcgldr

It is significant. Generally winters are colder and summers hotter once significantly south of the equator compared to locations equi-distant from the equator north of the equator.

6. Mar 26, 2009

Staff Emeritus
If this were dominant, both hemispheres would have summer in January. We don't. As Jeff points out, there is an effect, but it's subdominant.

7. Mar 26, 2009

### Janus

Staff Emeritus
As already stated, the difference in radiant heating due to eccentricity is about 6% (94% at aphelion vs. 100% at perihelion)

Now consider a point on the Earth's surface at a lattitude of 23 degrees. During the summer the sun is directly overhead and in winter it is 46 degrees from vertical. The comparaitve radiant heating of a horizontzl surface can be found by taking the cosinse of the angle from vertical. In Summer it is 1 and in Winter it is 0.6946. IOW, at the Winter angle, the Sun is only 70% as effective at heating the surface, compounded by the fact that in winter there are fewer daylight hours.

8. Mar 26, 2009

### uart

It was calculated above at about 6% (due to distance variations). That's not an insignificant variation, however depending on your latitude then you might for instance get an asymmetry of 14 hr daylight versus 8 hour night (and opposite in Winter). Also, in addition to this time asymmetry, factor in the sun at a lower zenith angle (angle from directly overhead) in summer and it really shouldn’t be too hard to believe that the effect due to tilt has more than a 6% effect on the insolation! (though how much more is very much latitude dependant).

9. Mar 26, 2009

### Subductionzon

The effect that Janus gave of angle of incidence is magnified as you go north. By the time you get to 77 degrees or more north latitude you will have no sun at all for a period of time to a low angled sun that is constantly heating the Earth in the summer.

10. Mar 26, 2009

### Smatter

Thanks everyone for your helpful replies, and particularly to Janus for putting a few more numbers to it.

What I'm thinking now, which is what started me asking the question in the first place, is that the 6% variation due to distance from the Sun is not exactly insignificant compared to the example Janus gave of a 70% variation due to angle of incidence (although I accept that, as requested, Janus may have oversimplified the analysis for me).

So it looks to me that the Earth-Sun distance is anything but insignificant in its effect on the Earth's seasons. Is this true? Are all the references I've read oversimplifying the matter?

11. Mar 26, 2009

### Cantab Morgan

So would it seem that the hemisphere that is in winter while the Earth is closest to the sun would have slightly milder seasons than the other hemisphere? Does anybody know which hemisphere that would be?

12. Mar 26, 2009

### mgb_phys

Perihelion is around 3/4th January

13. Mar 26, 2009

### D H

Staff Emeritus
For now, that is. Perihelion advances about 1 day every 58 years due to precession of the equinoxes. Perihelion will occur at the spring equinox in 5000 years or so and at summer solstice in another 5000 years or so.

Eccentricity does play a role in the seasons, but a secondary one. So does the fact that the southern hemisphere is mostly water and the northern hemisphere is mostly land.

14. Mar 26, 2009

### Staff: Mentor

Well as said, the effect of the tilt gets more pronounced the further north you go. You could repeat Janus's calculation for a latitude of 40 degrees and find the difference for yourself (23 degrees is pretty far south, south of anything in the US besides Hawaii)...

The difference in hours of daylight is also more pronounced the further north you get, and that's not part of the calculation Janus did.

Btw, the difference Janus calculated was 30%, not 70%.

15. Mar 26, 2009

### Gnosis

The telltale proof that you’re seeking is revealed by the following realization:

If Earth’s proximity to the Sun were the major cause of summer when closest, and the major cause of winter when farthest, then both hemispheres (northern & southern) would have to experience their summers at the same time just as they would have to experience their winters at the same time.

In reality however, while the northern hemisphere is experiencing its dead of winter (while the Earth is closest to the Sun), the southern hemisphere is experiencing its dead of summer (and vice versa 6 months later). This factor alone proves that the major cause of the change of seasons cannot be attributed to Earth’s distance from the Sun due to its 3% eccentric orbit. The major cause of the change of seasons is in fact due to the 23 degree tilt that the Earth maintains as it orbits the Sun.