# How can one explain the apparent motion of the Sun from a heliocentric point of view?

From a horizontal frame of reference, the path of the Sun looks like a part of a circle in a tilted plane, as shown in this picture:

If you go to a heliocentric system, one would say that this is because the Earth is rotating around it's axis. Is there any more detailed explanation of this change of reference?

So how can one explain in detail the following facts (seen from a geocentric point of view - horizontal reference system) starting from a heliocentric system and the fact that the Earth is rotating around it's axis:

• Why is the path of the Sun a part of a circle?
• Why is this path in a plane?
• Why is this plane tilted?
• How to get this "tilt-angle"?

Why does this motion seem to be uniform from an equatorial point of view, and can I neglect the ecliptic to understand the points above?

I tried to model it using a ball as Earth, attached a camera to it and used another ball as the Sun, but I didn't succeed in reproducing the effect of the apparent motion in this model. Perhaps there is any animation which makes the points above clear.

The picture shows 3 paths of the sun over a single day, plotted on three particular days: Midsummer, midwinter, and an equinox. The apparent motion of the sun is due to the rotation of the Earth, not the motion of the Earth around the sun.

• Why is the path of the sun a part of a circle?

Because the Earth is spinning, so you are moving in a circle around an axis that passes through the poles of the Earth

• Why is this path in a plane?

The local surface of the Earth is modelled as a plane tangent to the sphere of the Earth. As the Earth spins, this plane rotates, and so relative to this plane, the sun appears to move. Because the plane is rotating in a single axis and at a uniform rate, the sun appears to move in a circle, across the sky. As it is a circle, it is in a plane.

• Why is this plane tilted?

It is tilted because you are not at the poles, the surface of the Earth on which you stand is tilted with respect to the axis of the Earth

• How to get this "tilt-angle"?

It is your latitude, or more exactly 90 - latitude. If you are at the poles the sun would travel in a horizontal plane. If you are at the equator the sun travels in a vertical plane.

The different paths (red green and blue in the picture) are due to the tilt of the Earth at 23.4 degrees, and so in Summer (in the north) the sun is higher at midday and further North at rise and set.

• Why does this motion seem to be uniformly from a equatorial point of view.

The image appears to show the path of the sun from a location about 45 degrees North, for example Northern USA. Again, I may be misunderstanding the question.

• Yes, a circle is in a plane. But it might also be a curve (similar to a circle) which doesn't lie in a plane (here are some examples of curves not lying in a plane: cs.technion.ac.il/~gershon/irit/user_man/compose.gif, aristidesatelier.com/sites/default/files/images/…) So I want to know why it must be a plane curve.
– re1
Sep 28 '15 at 18:29
• You say: "Because the Earth is spinning, so you are moving in a circle around an axis that passes through the poles of the Earth" thats one point I don't understand (see my original question). It is clear that this implies that I will see the sun on some curve but why is it exactly a part of a circle?
– re1
Sep 28 '15 at 18:31
• The last point "Why does this motion seem to be uniformly from a equatorial point of view" is only indirectly about the linked picture. I may rephrase it as: "Why does the hour angle change univormly with time?" Ony may answer "Because the earth is spinning uniformly around it's axis", but I am not satisfied with this answer. It's too sloopy.
– re1
Sep 28 '15 at 18:36
• Stand in a room, with a light on the ceiling. Rotate yourself by pirouetting on the spot. You can observe that the light appears to move in a circle. Sep 28 '15 at 18:39
• For the last point. It is because the rotation of the Earth constant. It is unchanging to an accuracy of less than one second per year. There is nothing sloppy about that. The rotation of the Earth is very precisely measured. Sep 28 '15 at 18:41