All About Rise and Set Times (2024)

Radiant Drift includes a dedicated web service end point that calculates details of the rise, transit, and set of the Sun, Moon, or Galactic Center. This article discussed some of the subtleties of calculating rise and set times related to the effects of the elevation of the observer.

The photo above shows the moments just after the moonrise over the plains of eastern Colorado, as viewed from a location near Boulder. The chimneys silhouetted by the Moon at around 25 miles away.

What’s interesting about this particular setup is that the Moon appears around 3 minutes before the standard rising time. Why? Because the observer (me, the photographer) was at a location elevated above the local horizon as viewed in the direction of the moonrise.

Colorado is known to be the ‘highest’ state in the lower 48 in terms of average elevation above sea level. The lights in the photograph lie at around 1,534m above sea level. But the spot from which the photograph was taken is even higher: 1,807m, a difference of some +275m — the observer is elevated above the local horizon.

The resulting ‘dip of the horizon’ — you’re looking ever so slightly downwards by around 0.6° to view the horizon — means that the Moon rises earlier than the standard time and at a slightly different azimuth than the ‘standard time’.

Standard rising and setting times are calculated assuming an unobstructed view of the ideal horizon, 0°, i.e. a zenith angle of 90°. If you construct a line from the center of the Earth, out through the top of the observers head and off into space, that is the zenith. The ideal horizon lies at right angles to the zenith.

Practically, this means that if your view to the horizon is blocked by a building, a tree, or a mountain or ridge line, then you won’t be able to observe the moment when the Sun rises.

This sometimes causes people consternation — they’ll say “but the Moon rose 20 minutes later and much farther south”. More correctly, the Moon came into view for that particular observer 20 minutes after moonrise, and at an azimuth and altitude particular to that location — a very different thing than standard rise.

Imagine if we defined the time of sunrise to be when it is first visible to the observer? You’re walking through Manhattan early one morning. “Look, there’s the Sun! Oh, but I walked into the shadow of the Chrysler Building — the Sun has set again. But now, there it is again, rising for the second time!” etc. It doesn’t really work very well.

The same issues arise with trying to account for terrain. Look at this photo from Monument Valley. If you define sunrise as dependent on local terrain, then walking 10 feet to the right could change the time of sunrise by minutes:

By default, Radiant Drift will return the standard time of rise/set. You can call the API as shown in this example:

curl -L \
 'https://api.radiantdrift.com/rise-transit-set/2024-01-28T00:00:00.000Z/2024-01-29T00:00:00.000Z/?body=moon&obs=40.0061,-105.2926,1850'

Ensure you include your API key or token in the request. The response, in all its gory detail, is shown below. I’ve omitted the transit and set details for brevity:

{
 "query": {
 "name": "rise-transit-set",
 "startDate": "2024-01-28T00:00:00.000Z",
 "endDate": "2024-01-29T00:00:00.000Z",
 "observer": {
 "lat": 40.0061,
 "lng": -105.2926,
 "height": 1807
 },
 "body": [
 "moon"
 ],
 "hah": 0,
 "cost": 9
 },
 "response": {
 "2024-01-28T00:00:00.000Z": [
 {
 "key": "moonrise",
 "date": "2024-01-28T02:15:08.728Z",
 "dateTD": "2024-01-28T02:16:17.835Z",
 "jde": 2460337.59465087,
 "eclipticCoordinates": {
 "λ": 153.5062489,
 "β": 3.54044789
 },
 "geocentricSphericalCoordinates": {
 "λ": 153.5062489,
 "β": 3.54044789,
 "Δ": 405108.39310982
 },
 "apparentCoordinates": {
 "ra": 156.73995273,
 "decl": 13.51907589
 },
 "apparentLongitude": 153.50512365,
 "obliquityOfEcliptic": 23.43852938,
 "radiusVector": 405108.39310982,
 "nutationInLongitude": -0.00112524,
 "nutationInObliquity": 0.00236835,
 "equatorialHorizontalParallax": 0.90211765,
 "meanElongation": 206.16553599,
 "meanAnomalySun": 23.5128655,
 "meanAnomalyMoon": 170.15103059,
 "argOfLatitude": 133.58603969,
 "azAlt": {
 "true": {
 "azimuth": 72.3922427,
 "altitude": -0.7169722
 },
 "apparent": {
 "azimuth": 72.3922427,
 "altitude": -0.21541116
 },
 "parallax": {
 "azimuth": 0,
 "altitude": 0.90086901
 },
 "refraction": 0.50156105
 }
 },
...
}

The response includes a number of astronomical values, but date property tells us the time of moonrise: 2024–01–28T02:15:08.728Z. You should treat this as accurate to within 1 minute — the unpredictable variation in atmospheric refraction, which ‘lifts’ the Sun or Moon higher above the horizon, mean that the actual time of moonrise will vary a little.

The azAlt property, and specifically the apparent property of that object, give us the azimuth and altitude of the moon at the moment of moonrise, that is, when the upper limb is first visible above the unobstructed ideal horizon.

In the example request above, we set the obs property to 40.0061,-105.2926,1850 which is the lat/lng/elevation, with elevation above sea level given in meters. Note — this is the elevation of the observer location above sea level, it is unrelated to the local horizon — more on that below. If you don’t know the elevation of the observer, it’s ok to use zero. If you specify zero, the results will vary a little — the date is now 2024–01–28T02:14:36.882Z, a few second earlier.

This is because at sea level, the higher atmospheric pressure results in a larger ‘lift’ due to refraction, making moonrise a little earlier.

A separate concept to observer elevation above sea level is the observer height above the horizon.

If you take off from an airport at the moment of sunset, if the aircraft climbs quickly enough and you have the right window seat, you might see the Sun reappear. This is due to your elevation above the local horizon — as you climb higher the ‘dip of the horizon’ increases.

You can account for the effect of the dip of the horizon on the timing of rise and set by specifying a height above the horizon in your API request. Using the +275m value we calculated earlier, we can add the hah parameter to the request:

curl -L \
 'https://api.radiantdrift.com/rise-transit-set/2024-01-28T00:00:00.000Z/2024-01-29T00:00:00.000Z/?body=moon&obs=40.0061,-105.2926,1850&hah=275'

It makes a significant difference to the result:

{
 "query": {
 "name": "rise-transit-set",
 "startDate": "2024-01-28T00:00:00.000Z",
 "endDate": "2024-01-29T00:00:00.000Z",
 "observer": {
 "lat": 40.0061,
 "lng": -105.2926,
 "height": 1850
 },
 "body": [
 "moon"
 ],
 "hah": 275,
 "cost": 9
 },
 "response": {
 "2024-01-28T00:00:00.000Z": [
 {
 "key": "moonrise",
 "date": "2024-01-28T02:11:48.336Z",
 "dateTD": "2024-01-28T02:12:57.443Z",
 "jde": 2460337.59233152,
 "eclipticCoordinates": {
 "λ": 153.47867111,
 "β": 3.54217111
 },
 "geocentricSphericalCoordinates": {
 "λ": 153.47867111,
 "β": 3.54217111,
 "Δ": 405105.99802149
 },
 "apparentCoordinates": {
 "ra": 156.71425681,
 "decl": 13.53075639
 },
 "apparentLongitude": 153.4775459,
 "obliquityOfEcliptic": 23.43852934,
 "radiusVector": 405105.99802149,
 "nutationInLongitude": -0.00112521,
 "nutationInObliquity": 0.00236831,
 "equatorialHorizontalParallax": 0.90212298,
 "meanElongation": 206.13726135,
 "meanAnomalySun": 23.51057955,
 "meanAnomalyMoon": 170.12072827,
 "argOfLatitude": 133.55535617,
 "azAlt": {
 "true": {
 "azimuth": 71.86139474,
 "altitude": -1.30086204
 },
 "apparent": {
 "azimuth": 71.86139474,
 "altitude": -0.72150995
 },
 "parallax": {
 "azimuth": 0,
 "altitude": 0.90085702
 },
 "refraction": 0.57935209
 }
 },
...
}

The time of moonrise is now given as 2024–01–28T02:11:48.336Z, some 3 minutes and 20 seconds earlier. The azimuth has also changed from 72.39° to 71.86°, about one moon width. For some applications, e.g. alignment of the Moon with a building in a photograph, that’s a highly significant difference.

However, with the observer height above the horizon specified, we’re no longer talking about the standard rise and set times.

Determining the observer’s height above the horizon

It’s rare to find these adjusted rise/set times quoted anywhere online.

One exception is the website of the Mauna Kea observatory in Hawaii. Located high on a summit and overlooking the ocean, their quoted rise and set times differ from the standard times by some 10 minutes, due the observatory elevation above the local horizon.

In this case, the observer’s height above the horizon is easy to determine: it’s simply the observer’s own elevation above sea level (4,114m), because the horizon lies over the ocean.

In other circ*mstances, it can be trickier to decide — you need to estimate the value based on the local terrain. It’s a somewhat iterative process as the distance to the horizon depends on the elevation above the horizon. You can read more about the process here.

That said, usually, an approximate value is just fine — don’t stress about false precision. Rise and set times vary due to atmospheric conditions anyway and when the path through the atmosphere to the horizon is longer, as it is for an observer elevated above the horizon, there’s even more scope for uncertainty.

If you have any questions about using the Rise/Transit/Set API, don’t hesitate to email us — we’re happy to help!