Why doesn't Earth's axis change during the year?

My understanding is that the Earth's axis points in the same direction in space during its entire orbit around the sun. And this is what causes our seasons.

My question is why doesn't the axis follow the orbital path (kind of like a car driving around a circle)?

I imagine the Moon plays a part in this.

As a secondary question, do the other planets in our solar system orbit the same as Earth (its axis points in the same direction in space for its entire orbit)?

• Why would you expect it to change? Changing the direction of the Earth's axis would require a huge change of angular momentum. It does change over thousands of years, but there's no mechanism to change it over a single year. – Keith Thompson Jan 2 '15 at 20:24
• It's not that I expect it to change. It's simply that I don't know why it works one way and not the other. I'm a computer programmer, not a math/physics whiz. :) – rmaddy Jan 2 '15 at 20:27
• I think the answer boils down to conservation of angular momentum, but I'll leave it to someone else who knows the physics better than I do to post an answer. – Keith Thompson Jan 2 '15 at 20:29
• My advice: get one of those little toy gyroscopes or a bicyle wheel on an axle, get it spinning quickly, and try walking (or driving) it around a light bulb such that the axis points the way you expect it should. You'll very quickly discover that you have to apply a huge force to make the axis change direction as you orbit the light bulb; there is no corresponding force on the earth, so the axis doesn't change direction. More generally, the answer to "why doesn't this happen?" in physics is usually "because nothing made it happen". The axis doesn't change because no force changes it. – Eric Lippert Jan 3 '15 at 13:10
• Gyro-top to stop: Maker closing shop: "Feb 22, 2015 - Nagoya-based toy maker Tiger & Co. has decided to close its 94-year-old business, possibly at the end of April, bringing an end to production ..." google.com/… – Wayfaring Stranger Apr 3 '15 at 12:05

My understanding is that the Earth's axis points in the same direction in space during its entire orbit around the sun. And this is what causes our seasons.

The second statement is correct. The axial tilt is the primary driver of the seasons.

The first statement is not exactly correct. There is a small but persistent change in the orientation of the Earth's axis. The change over the course of a year is small. The change over the course of 13,000 years is large. In 13,000 years the Earth's axis will be tilted by about 47 degrees compared to the current orientation. In yet another 13,000 years the Earth will be oriented very similarly to how it is oriented now. I'll write more about this later.

My question is why doesn't the axis follow the orbital path (kind of like a car driving around a circle)?

That is not a good mental model. The only contact between your car and the ground are the bottoms of the four wheels on your car. The forces at these four small contact areas are what change your car's orientation and change your car's velocity vector. This means that the torque on your car as you turn the steering wheel and the centripetal force on your car that makes your care negotiate a turn are intimately connected. Turn the steering wheel gently and the heavy front end of your car follows suit. Assuming a gentle turn, the light rear end of you car soon follows suit. If you turn too hard, your car starts to skid instead of turn. Turn even harder yet and you risk having your car flip and roll. The motion of your car depends on that intimate coupling between force and torque.

Gravitation doesn't work like that. It instead acts on each and every bit of the Earth, all together, all at once, all the time. There is a slight variation in the gravitationally-induced acceleration across the Earth due to variations in distance to the Moon (or Sun), but these variations are small. The net gravitational force on the Earth is very much decoupled from the small net gravity gradient torque on the Earth.

The principal result of the gravity gradient torque exerted by the Moon and the Sun on the Earth is a very slow but large precession of the Earth's rotation axis (for more, read this wikipedia article on axial precession). This precession makes the Earth's rotation axis rotate about the normal to the ecliptic at a rate of one revolution per 25772 years. There are lesser effects collectively called nutations and polar motion that result from gravity gradient torque. These lesser effects are much, much smaller in magnitude but have much, much shorter periods. The largest of these lesser effects results from the 18.61 year cyclical variations in the lunar node. Even this largest component of nutation is small, two orders of magnitude smaller than the large but slow precession.

• My car analogy was only meant to indicate one concept - the front of the car is always pointing in the direction of travel, as opposed to say, always facing north. That's all. I meant no comparison to forces of any kind. – rmaddy Jan 3 '15 at 17:03
• @rmaddy: Right but you have to constantly apply energy (by keeping the steering wheel turned â€” it'll be fighting against you) in order to make that happen. A car on the ground is not at all the same as a planet in space. Your imagined model is not the "default" state at all. – Lightness Races in Orbit Jan 3 '15 at 17:49
• @LightnessRacesinOrbit Again, that's not at all what I was implying with the car analogy. I was simply trying to describe the direction, that's all. – rmaddy Jan 3 '15 at 17:51
• This is the scientifically correct answer, but it's not well-explained for someone not coming from either a physics or an astronomy/astrophysics background. You should consider simpler language, at least for the basics (i.e. everything up to the discussion on precession). – MandisaW Jan 4 '15 at 3:45

Picture the Earth as a small ball suspended in midair, not moving, although it's rotating on its axis. Unless forces are applied to it, absolutely nothing will happen. That's conservation of energy (or momentum; you can work with it either way). Earth will not spontaneously start moving in one direction because that would violate conservation of translational energy and conservation of linear momentum. If that did happen, energy would be gained out of nowhere.

For the same reason, Earth will not start tilting to one side. This is conservation of rotational kinetic energy and conservation of angular momentum at work. Savvy?

So, yep, Keith is spot-on. You'd need some sort of torque to turn the Earth's axis like that.

So why does the Earth's axis move over 26,000 years (it does, by the way, just not one cycle per year)? Just like with the tides, as well as how Earth's rotation is slowing down, it's primarily the tidal forces of the Moon and the Sun at work, although the other planets do make some contributions to the overall changes.

I can add in some math if you want, but be warned, I'm learning it myself, so it won't be explained as well as you might like.

The other planets obey the same laws as the Earth, so their axes should point in the same direction throughout the year, ignoring the effects of axial precession.

• I wish I had a picture but I guess I'm still not sure why the Sun's gravity (which keeps Earth in orbit) isn't causing, for example, the north pole to roughly point toward the sun all year. I get how a spinning ball, as you describe, points in one direction. But the Earth is orbiting the Sun and the Sun's gravity is a force acting on the Earth. – rmaddy Jan 3 '15 at 0:10
• @rmaddy That's because there's really nothing special about the poles, in terms of gravity. The poles aren't any more massive than any other location on Earth - in fact, they might be less massive, because a line segment drawn from a pole to the center of the Earth is shorter than a line drawn from, say, the equator to the center of Earth. There's no extra mass at the poles, so there's nothing extra for the Sun to pull. Does that help a bit? – HDE 226868 Jan 3 '15 at 0:15
• I get that there is nothing special about the pole. That was probably a misleading description. It just seems like the Earth's tilt should remain constant relative to its orbital path, not constant relative to space. Why doesn't the Earth's orbit and the Sun's gravity cause the tilt to be constant with the orbital path? – rmaddy Jan 3 '15 at 0:23
• The Sun's gravity doesn't attract the pole any more than it attracts any other part of Earth. For the pole to continuously point towards the Sun, the Sun would have to be attracting the pole more than any other part of Earth - which it doesn't. – HDE 226868 Jan 3 '15 at 0:25
• @rmaddy because the only thing that could cause it to do that is gravity, and gravity doesn't do that. Gravity doesn't make the Earth drive in a circle around the Sun like a car; it just pulls the Earth "sideways" towards the Sun at all times. In space, the direction something is pointing and the direction it's moving are unrelated. – hobbs Jan 3 '15 at 0:47

The changing angle between sun and moon does cause some slight nutation in the earth's axis of rotation over an 18.6 year period.

In the case of the Earth, the principal sources of tidal force are the Sun and Moon, which continuously change location relative to each other and thus cause nutation in Earth's axis. The largest component of Earth's nutation has a period of 18.6 years, the same as that of the precession of the Moon's orbital nodes.1 However, there are other significant periodical terms that must be calculated depending on the desired accuracy of the result.

The principal term of nutation is due to the regression of the moon's nodal line and has the same period of 6798 days (18.61 years). It reaches plus or minus 17â€³ in longitude and 9â€³ in obliquity. All other terms are much smaller; the next-largest, with a period of 183 days (0.5 year), has amplitudes 1.3â€³ and 0.6â€³ respectively.

It's not a large effect (from link):

• Thanks but this really has nothing to do with my question. – rmaddy Jan 3 '15 at 0:04
• Actually, it has EVERYTHING to do with your question. – Dawood ibn Kareem Jan 4 '15 at 2:10
• @DavidWallace No. It described why the Earth's tilt wobbles a bit over time. It makes no attempt to explain why the tilt points in one general direction in space during a year instead of following the Earth's orbit. – rmaddy Jan 4 '15 at 20:03
• Well, your question amounts to "why doesn't the angular momentum of the earth vary" - because for some reason, you expected it to vary a lot. And this answer is saying, "well, it does actually vary a little bit" and explains why. – Dawood ibn Kareem Jan 4 '15 at 20:09
• @DavidWallace 1) I didn't expect anything. I know what actually happens. I was curious why something different doesn't happen. 2) I know the axis wobbles over time. Again, not at all what I was asking about. Which is why I don't believe this answer addresses my question. – rmaddy Jan 5 '15 at 18:27

The Earth acts like a massive gyroscope. A tremendous force would be required to change the orientation of the axis. While forces are certainly exerted, they are not large enough to cause appreciable change in the orientation of the axis as the Earth falls/orbits about the Sun. As you indicate, the orientation of the axis is responsible for the change in season. The areas that receive the most direct exposure to sunlight are in summer; areas receiving glancing sunlight are in winter.

The Earths rotation about the Sun is not circular but elliptical. During its orbit the Earths distance from the Sun changes. Many sources report that while this is true, it has little effect on the season. These sources indicate that the orientation of the Earths axis combined with the "tilt" of the Earths orbit above or below the Suns equator determines the seasons.

• Thanks but only the 1st half of your first paragraph is related to my question. I'm not asking anything about seasons. – rmaddy Jan 3 '15 at 3:51

Lets Keep things simple. Below is a picture of the orbit of the Earth.

I take the question to mean why the axis doesn't point toward the Sun all the time. The answer comparing the Earth to a Gyroscope is the easiest to use. The spinning effect on the axis does cause a force that helps keep the Earth's axis at a 23.5Â° angle (Approx) there is a slight wobble of a few meters in the earths axis. Try looking from above might make it clearer. There is a red circle of rotation at the pole if you look closely.

The Earth is not driving around the Sun it is in effect being pulled to the Sun but is going fast enough around it to counteract gravity and not get closer, the same way satellites stay orbiting in space. The car would be more like a spaceship as it would have a force/thrust pushing it around the Sun.

As for the second question the other planets do the same but at different angles.

• Simplified, but IMO this is the most appropriate answer for the OP. Get the basic "what's happening" from here, then go to David Hammen's answer for "why is it happening". Also, this is the only one that addressed the second part of the question. – MandisaW Jan 4 '15 at 3:47

Because the Sun's gravitational pull on Earth is (nearly) uniform, it doesn't tilt the Earth, it only pulls it as a whole, without affecting the Earth's spinning around its own axis.

The Earth's radius is ~ 6,400 km, the distance to the Sun is ~ 150,000,000 km, and the gravitational force diminishes as a square of a distance, so the ratio in the pull on some two small volumes of Earth, the closest and the farthest from the Sun at a given moment, is

$$\frac{(150000+6.4)^2}{(150000-6.4)^2} = 1.00017068$$

so the tilting force is very small.

Were the variation exactly 0 (i.e. the ratio exactly 1) the tilting force would be exactly 0 and the Earth's spinning wouldn't have been affected, at all. To get that, remove the Sun from the picture.

And by the general theory of relativity, if Earth were moving in a uniform force, it would be as if there was no force at all, from Earth's point of view.

If the Earth's axis is always pointing toward Polaris then the Earth's axis has to continually change throughout year over a 186,000,000 mile orbit distance change.

If the tilt in December is 23.4 degrees then, March would be less tilt and an added tilt toward the sun, June would be the smallest Earth tilt, October would be less tilt and and added tilt toward the sun. Without this Earth tilt change Polaris would only be aligned one day a year in December.

You can easily prove this yourself.

• You seem to have no idea of how far away Polaris is. – Rob Jeffries Mar 28 '16 at 13:15