# Sun Angle

(glossary entry)

## Description

```The angle of the Sun above (positive) or below (negative) the local horizontal as viewed from a lunar surface feature.
```

• Sun angle is determined by the Sun's position as viewed from the Moon, and does not depend on the direction from which the Moon is being viewed.
• Sun angle conventionally refers to the elevation of the Sun's center. Since the Sun's angular size as seen in the lunar sky is about 0.5° (essentially the same as its size as seen from Earth), the Sun's upper limb will typically be above the sun angle by about 0.25°, while the lower limb will be below it by the same amount.
• In addition to the sun angle a second parameter is required to completely describe the direction of the incident sunlight: this is the Sun's azimuth, which is defined as the angular direction of the rays as observed from directly over the feature of interest, usually expressed as the angle measured clockwise relative to a line drawn from the feature towards the Moon's north pole.
• The "local horizontal" mentioned in the definition is the plane perpendicular to a radial line drawn from the Moon's center through the point of interest. The actual horizon will be above or below this plane by an amount that varies with azimuth. Local sunrise or sunset occurs when the Sun's upper limb is coincident with the actual horizon. Hence sunrise and sunset occur when the sun angle is positive or negative by an amount depending on the Sun's azimuth, sometimes by several degrees.
• The appearance of lunar surface features can change drastically with sun angle, and, usually to a much lesser extent, as seen from different viewing angles. At a given sun angle, the Sun's azimuth can also be important, especially for features like rilles, which can become invisible when the Sun's azimuth is along the direction of the channel.
• The sun angle can be determined by using the rules of spherical trigonometry or vector math applied to radial lines drawn from the Moon's center through the subsolar point and the feature of interest. The angle between these lines is the Sun's distance from the local zenith, and subtracting this from 90° gives the sun angle.
• Programs like LTVT automatically calculate and display the sun angle (and azimuth) based on the stated date/time and feature of interest.

## A Sun Angle Calculator

• The following Excel spreadsheet can be used to compute the sun angle at any longitude and latitude on the Moon given the coordinates of the subsolar point at the moment of interest. The coordinates of the subsolar point can be determined using JPL Horizons.

• The spreadsheet also gives the great circle arc length between the sub-solar point and the feature of interest both in degrees and kilometers. This angle is an intermediate result used for calculating the sun angle. By entering the coordinates of a second feature of interest as an artificial "sub-solar" point, this can be used for calculating the length and direction of the arcs connecting any two points of interest.