<p>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.</p>

<p><li><b>Why is the path of the sun a part of a circle?</b></p>

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

<p><li><b>Why is this path in a plane?</b></p>

<p>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. </p>

<p><li><b>Why is this plane tilted?</b></p>

<p>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</p>

<p><li><b>How to get this "tilt-angle"?</b></p>

<p>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.</p>

<p>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.</p>

<p><li><b>Why does this motion seem to be uniformly from a equatorial point of view.</b></p>

<p>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.</p>

CC BY-SA 3.0
2016-04-21T12:07:00.903Z
If you were sitting in a chair in the middle of a room, and that chair revolved once every hour - from your perspective you'd be fixed in space, but the walls would revolve around you once per hour.

The stars are "fixed" in the sky and as we rotate ata constant velocity about our axis, they appear to move at precisely 15 degrees per hour, or 15 arc minutes per minute, or 15 arc seconds per second.

As for the sundial - if it's not equatorial, the suns motion will experience "drift" much like a poorly aligned equatorial telescope will.  The drift rate + rotation rate = non-uniform shadow rate
EastOfJupiter
CC BY-SA 3.0
2016-04-21T12:13:00.217Z
The shadow cast by a horizontal sundial can be precisely predicted at any moment in time using trigonometry:  tan(Hh) = sin(L)  tan(15t).  Because it can be modeled at any moment in time and the only changing variables are the time variable and the angle of the North Line and Current Hour Line (Hh), then the rate of change is constant, too.

https://en.wikipedia.org/wiki/Sundial#Horizontal_sundials
EastOfJupiter
CC BY-SA 3.0
2015-09-28T18:29:13.523Z
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: http://www.cs.technion.ac.il/~gershon/irit/user_man/compose.gif, http://www.aristidesatelier.com/sites/default/files/images/Exercise-1-Juliette-17.jpg) So I want to know why it must be a plane curve.
re1
CC BY-SA 3.0
2015-09-28T18:31:19.730Z
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
CC BY-SA 3.0
2015-09-28T18:36:10.137Z
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
CC BY-SA 3.0
2015-09-28T18:39:59.923Z
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.
James K
CC BY-SA 3.0
2015-09-28T18:41:43.433Z
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.
James K
CC BY-SA 3.0
2015-09-28T18:58:44.913Z
I tried this with a camera. This works if you point the camera upwards and not exaclty below the spot but a bit translated to one side. Hoever this seems to be the wrong rotation axis, if one sees the relation of the earth and the sun: https://www.classzone.com/books/earth_science/terc/content/visualizations/es0408/es0408page01.cfm?chapter_no=visualization I think  a more correct model would be to lie on the floor and roll over the floor... I tried this also with a camera but this doesn't work.
re1
CC BY-SA 3.0
2015-09-28T19:05:16.310Z
For the last point: I accept that the earth is spinning uniformly. But why does this translate in a uniformly changing hour angle. For example in a horizontal sundial the shadow doesn't move uniformly, but in a equatorial one it does.
re1
CC BY-SA 3.0
2015-09-28T18:09:31.997Z
2015-09-28T18:37:23.637Z
2015-09-28T18:37:23.637Z
James K
<p>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:</p>

<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="https://i.sstatic.net/uc0u6.gif" alt="enter image description here"></p>

<p>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? </p>

<p>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:</p>

<ul>
<li>Why is the path of the Sun a part of a circle? </li>
<li>Why is this path in a plane?</li>
<li>Why is this plane tilted?</li>
<li>How to get this "tilt-angle"?</li>
</ul>

<p>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?</p>

<p>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.</p>

<orbit><the-sun><earth><apparent-motion><frame-of-reference>
How can one explain the apparent motion of the Sun from a heliocentric point of view?
re1
# How can one explain the apparent motion of the Sun from a heliocentric point of view?

(Asked by: username_0 on 2015-09-28)

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:

![enter image description here](https://i.sstatic.net/uc0u6.gif)

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.

**Tags:** orbit, the-sun, earth, apparent-motion, frame-of-reference

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## 1 answers

### Answer by username_1 on 2015-09-28. Score: 3

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.

> **Comments:**
> **username_0**: 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: http://www.cs.technion.ac.il/~gershon/irit/user_man/compose.gif, http://www.aristidesatelier.com/sites/default/files/images/Exercise-1-Juliette-17.jpg) So I want to know why it must be a plane curve.  
> **username_0**: 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?  
> **username_0**: 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.  
> **username_1**: 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.  
> **username_1**: 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.  
> **username_0**: I tried this with a camera. This works if you point the camera upwards and not exaclty below the spot but a bit translated to one side. Hoever this seems to be the wrong rotation axis, if one sees the relation of the earth and the sun: https://www.classzone.com/books/earth_science/terc/content/visualizations/es0408/es0408page01.cfm?chapter_no=visualization I think  a more correct model would be to lie on the floor and roll over the floor... I tried this also with a camera but this doesn't work.  
> **username_0**: For the last point: I accept that the earth is spinning uniformly. But why does this translate in a uniformly changing hour angle. For example in a horizontal sundial the shadow doesn't move uniformly, but in a equatorial one it does.  
> **username_2**: If you were sitting in a chair in the middle of a room, and that chair revolved once every hour - from your perspective you'd be fixed in space, but the walls would revolve around you once per hour.  The stars are "fixed" in the sky and as we rotate ata constant velocity about our axis, they appear to move at precisely 15 degrees per hour, or 15 arc minutes per minute, or 15 arc seconds per second.  As for the sundial - if it's not equatorial, the suns motion will experience "drift" much like a poorly aligned equatorial telescope will.  The drift rate + rotation rate = non-uniform shadow rate  
> **username_2**: The shadow cast by a horizontal sundial can be precisely predicted at any moment in time using trigonometry:  tan(Hh) = sin(L)  tan(15t).  Because it can be modeled at any moment in time and the only changing variables are the time variable and the angle of the North Line and Current Hour Line (Hh), then the rate of change is constant, too.  https://en.wikipedia.org/wiki/Sundial#Horizontal_sundials  

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