<p>If you had your longitude/latitude, and the time/date, how could I go about working out the angle between your normal and the sun?</p>

<p>At first I was doing a simplistic approach of assuming elliptical orbit in only two dimensions and that the earth is a perfect sphere,</p>

<p>Can I get a more accurate method /formula than this that can be evaluated in one step without any iterative methods?</p>

<p><a href="https://i.sstatic.net/ONqDJ.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/ONqDJ.png" alt="enter image description here"></a></p>

<p>Here is rough example of what I mean, say the green plane is the point on the surface of the earth I want.</p>

<p>The angle I seek is between the black line perpendicular to the green plane and the black line between the plane and the sun.</p>

<p>There are 2 problems involved here, knowing how the normal changes as the non spherical earth rotates and knowing the relative position between the earth and the sun.
Any help appreciated.</p>

CC BY-SA 4.0
2020-01-05T07:02:21.313Z
Do you want the Sun's zenith angle, or the complement of its declination?
Mike G
CC BY-SA 4.0
2020-01-05T07:39:48.300Z
edited the question with a 3D example of what I'm looking for
BinkyNichols
CC BY-SA 4.0
2020-01-05T12:56:05.967Z
What do you mean "your normal"? There are several possible definitions, depending on if it's a mathematical surface like a reference ellipsoid, or if it takes into account local gravity and/or centrifugal acceleration (e.g. a plumb line), or maybe you mean radially away from the geocenter? See https://space.stackexchange.com/a/31723/12102 and https://en.wikipedia.org/wiki/Geoid and https://en.wikipedia.org/wiki/Earth_Gravitational_Model and https://en.wikipedia.org/wiki/World_Geodetic_System#WGS84
uhoh
CC BY-SA 4.0
2020-01-05T19:24:45.877Z
thanks for taking the time for the links,though I meant mathematical surface,
BinkyNichols
<the-sun><coordinate>
Calculating angle between the sun and a perpendicular to earth given lon/lat & time
BinkyNichols
# Calculating angle between the sun and a perpendicular to earth given lon/lat & time

(Asked by: username_0 on 2020-01-05)

If you had your longitude/latitude, and the time/date, how could I go about working out the angle between your normal and the sun?

At first I was doing a simplistic approach of assuming elliptical orbit in only two dimensions and that the earth is a perfect sphere,

Can I get a more accurate method /formula than this that can be evaluated in one step without any iterative methods?

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

Here is rough example of what I mean, say the green plane is the point on the surface of the earth I want.

The angle I seek is between the black line perpendicular to the green plane and the black line between the plane and the sun.

There are 2 problems involved here, knowing how the normal changes as the non spherical earth rotates and knowing the relative position between the earth and the sun.
Any help appreciated.

**Tags:** the-sun, coordinate

> **Comments:**
> **username_1**: Do you want the Sun's zenith angle, or the complement of its declination?  
> **username_0**: edited the question with a 3D example of what I'm looking for  
> **username_2**: What do you mean "your normal"? There are several possible definitions, depending on if it's a mathematical surface like a reference ellipsoid, or if it takes into account local gravity and/or centrifugal acceleration (e.g. a plumb line), or maybe you mean radially away from the geocenter? See https://space.stackexchange.com/a/31723/12102 and https://en.wikipedia.org/wiki/Geoid and https://en.wikipedia.org/wiki/Earth_Gravitational_Model and https://en.wikipedia.org/wiki/World_Geodetic_System#WGS84  
> **username_0**: thanks for taking the time for the links,though I meant mathematical surface,  

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