Delta T and Eclipses

On this site and others, you will read about something called “Delta T”. Because of its extreme importance in eclipse calculations, it’s something every eclipse fanatic is concerned with. If you’re into the technical details of eclipses, it will be of interest to you as well!

Rotation of the Earth

It’s common knowledge that the Earth rotates on its axis once per day, and that there are 24 hours in a day. That equates to 1440 minutes, or 86,400 seconds per day – every day, just like clockwork.

But it hasn’t always been like that. The early Earth rotated much faster, as we can tell by extrapolating the current rate of rotational slowing that we observe today.

“Rotational slowing?” As in, the Earth’s rotation is slowing down? How can that be?

Well, the proof is there, so the facts aren’t up for debate – the day is in fact getting longer – but not to worry, you won’t notice anything in a period of time as short as a human lifetime! We’re talking about a second or so of slowing in maybe 75,000 years!

How do we know this? Well, we have atomic clocks now, and atomic vibrations don’t rely at all on the spinning of the Earth. They aren’t affected by tidal friction, and so they serve as a perfect baseline for comparison between what we THINK a day should look like, and what we actually observe it to be on a regular basis. The day is in fact getting longer.

The reasons for the slowing are several, but it mainly comes down to this: The same forces that cause the tides (namely, the gravitational pull of the Moon on the Earth as it spins), and the movement of the water around the earth as it sloshes over all the beaches on the planet, create a slight amount of friction that causes the Earth to rotate slightly slower over time. Just like any moving system that has friction injected into it, the system will slow down and ultimately stop altogether. (That is going to take longer than the Earth will even be around, though – so again no cause for worry any time soon!)

Just in case you’re wondering, some other factors involved in the rotational slowing involve the distribution of the Earth’s mass around its center of gravity. Any shift of mass with relation to that mass’s distance from Earth’s center will result in a change in spin speed due to the Conservation of Angular Momentum principle from physics. But what could cause the Earth’s mass to shift? Here are a few reasons:

• Cosmic dust that falls to Earth (estimates range from a few to a few hundred tons per day!)
• Shifting of magma and liquid rock in the Earth’s core and inner mantle
• Crust rebound from the melting of ice following the last Ice Age
• Melting polar ice due to climate change

These are all relatively small with respect to the overall mass of the Earth, but small pieces can add up to big effects over long periods of time.

In any case, this slight lengthening of the day causes a huge problem for scientists, who need to have a constant unit of time – the second – firmly established. Let’s take a look at that all-important unit for just a minute (pun intended!…):

Definition of the second

Originally, the second was defined as 1/86,400th of a Solar Day – which is the amount of time needed for the Earth to rotate so that the Sun is in the same relative position in the sky as the day before. This makes a lot of sense, because there are that many seconds in a 24-hour day. But what was not known before the advent of atomic clocks was that the length of a day is not constant over time, as we described above.

Many SI units rely on the second for their definitions; these include such fundamental units as the Newton, Pascal, Joule, Watt, Coulomb, Volt, Ohm, Henry, and Farad. Therefore, any variation in the second caused by basing it on something that isn’t exactly constant will create havoc in the results of any calculation or experiment which relies on any of these basic units – meaning, most of Physics.

In 1967, the second was therefore dispassionately redefined as:

While not something that can be as easily measured as the position of the Sun in the sky, this definition has the great advantage of being based on something that does not rely on the variable rotation of the Earth! This is indeed a fair trade from the perspective of Science. Predictability and constancy were once again imposed on physics, with an accompanying sigh of relief offered by scientists everywhere.

What is Delta-T?

So the Earth is slowing down slightly, and we’d like to be able to predict what the exact length of the day will be for any point in the future. Simple, right? We just extrapolate the current rate of slowing that we observe now, and that’ll give us the exact number. But since you’re reading this, you probably realize that it’s not at all that simple!

Because of all the variability in the factors that allow us to realize that the Earth is slowing down in the first place, we cannot EXACTLY predict how much slowing there is going to be in the future. We can observe the amount of slowing any time we want, and plot those observations over time to come up with a graph, and then develop a model to extrapolate that out – but because we’re dealing with a constantly changing system, we can’t be 100% certain that the slowing trends we’ve seen historically will continue at the same rate in the future. Again, we can predict what we think it will be, but until we measure it we can’t be exactly sure.

We’re simplifying a lot here, but this is a basic "normal English" explanation: Delta-T is the difference between what we think the slowing of the Earth is going to be, and what we actually measure it to be.

(And let’s call it "ΔT" for short from now on! And say it again…)

It’s not the actual slowdown of the Earth that ΔT measures – it’s the difference between how much we’ve predicted that it will slow down (based on years of observations), and what we actually observe. We can only predict what ΔT is going to be; we then have to measure ΔT every so often and look to see how what it actually is.

Leap Seconds

In real life, none of this makes even the slightest bit of difference. (Has your life been affected in any way by any of it? Thought so.) But there is one thing you can see, every few years or so, that happens not only because of the slowing of the Earth, but by the way that the UTC time measurement system was originally created. Some of these factors contribute greatly to the need we have to synch up our time system to the Earth, and so every few years the IAU needs to add a leap second to bring things in line. (Please note, the need for a leap second is not created ONLY from the slowdown of the Earth! If that were the case, we’d only need to add one every 75,000 years or so.)

Whenever this happens, we find the news media generally will make jokes about what wonderful things you might be able to accomplish during that extra second! But we’re guessing you’ll never even notice it. Here is what the official display at time.gov shows for the one second that is added. This particular minute in question actually had 61 seconds in it, by official definition. That 61st second looked like this:

After which, with the next second the time became 19:00:00.

What does ΔT have to do with eclipses?

Why do we care about any of this? Well, if you read the section on eclipse calculations, you’ll see that once we determine the position of the Moon’s shadow on the fundamental plane, we then have to project that shadow outline up to the actual Earth’s surface using an iteration technique. Remember that we will need to convert that position to a latitude and longitude, in order to tell people where on Earth they have be to see totality. The latitude for this shadow position is not affected by the rotational speed of the Earth, but the longitude is! We need to know how far the Earth will have rotated from some standard reference point, for each of the eclipse times we are predicting, in order to know what part of it will be in the exact spot we’ve projected the shadow up to from the fundamental plane. That means we need to know how fast the Earth is rotating, so we can apply a correction factor to longitude based on the actual value of ΔT.

If ΔT turns out to be LESS than what we thought, then the Earth will have rotated MORE than predicted, and the position of the eclipse shadow on its surface will be shifted to the WEST. Similarly, if ΔT is MORE than predicted, then the path gets shifted to the EAST:

Since the Earth rotates about half a kilometer per second at the equator, and about a third of a kilometer per second at 45° latitude (N or S), a change in ΔT of a few seconds can be significant when it comes to defining the edge of the eclipse path! (The centerline would be shifted as well, but at the edges the difference impacts whether an observer actually sees totality or not! For example, cities that used to be on the edge of the path might now get a minute or so of totality! Folks formerly on the other edge would then not be seeing totality at all.)

What do we do about it?

We predict what ΔT is going to be, and give all our eclipse timings with respect to that value of ΔT. We do the predications as close to the eclipse as possible, and then if necessary we refine them again, as close to eclipse day as possible. We encourage folks who are seeing their first eclipse to be as close to the centerline as possible, so that updates to ΔT will not affect whether they see totality or not. We warn people that edge effects and variations in ΔT will cause all those really accurate predictions not to be as accurate as they think. They will be good to within a few seconds, but for people who need tenth-of-a-second accuracy, those people already know they have to recalculate using the latest obtainable value of ΔT.

(Note that all eclipse times you see on eclipse2024.org are based on a value of ΔT=74.0s. This appeared to be accurate as of January 2019, and was the value used by leading eclipse calculator Xavier Jubier in his 2024 eclipse map as of that date. As we get closer to eclipse day, it is looking more and more like ΔT will be closer to 72s or so. This means we should prepare for a slight westward shift of the path at all locations.)

UPDATE as of 8 Aug 2019: All the eclipse circumstance calculations on Eclipse2024.org have been updated! The predictions of ΔT have been refined, and astronomers now believe ΔT will have a value of 71.2s by the time of eclipse day 2024. Therefore, we’ve updated our tables and eclipse simulator accordingly.

UPDATE as of 4 Mar 2021: All the eclipse circumstance calculations on Eclipse2024.org have been updated! The predictions of ΔT have been refined, and astronomers now believe ΔT will have a value of 69.6s by the time of eclipse day 2024. Therefore, we’ve updated our city pages for the 2024 eclipse and our 2024 eclipse simulator accordingly.

UPDATE as of 28 Oct 2021: The Earth's rotation has shown some marked accelerations during the previous several months, and it is apparent that ΔT will now be slightly less than previously expected by eclipse day (maybe a half second or so).

UPDATE as of 15 Aug 2022: The Earth has indeed been accelerating, and even the news media has begun reporting on this fact! We are getting close enough to eclipse day that Eclipse2024.org is comfortable updating ΔT once again. The models are predicting that these updates will hold, and it will not be necessary to adjust again. (But we'll still continue to track it!)

UPDATE as of 4 Sep 2023: We are making a new prediction for the 2023 eclipse:

We have updated our city pages for the 2023 annular eclipse and the eclipse simulator. We are now using values of 69.2s for the 2023 annular eclipse. We are staying with 69.0s for the 2024 total eclipse for now, though that will almost definitely be updated again.

UPDATE as of 20 Dec 2023: We are making a new prediction for the 2024 eclipse:

We have updated our city pages for the 2024 total eclipse and the eclipse simulator. We are now using a value of 69.18s for the 2024 total eclipse for now, though we will continue to monitor the situation.

Remember, this update is due to a very slight change of the Earth's rotation, measured against the astronomers' predictions of what that rotation speed would be. The Moon's shadow isn't going to do anything differently, but the Earth will have rotated to a VERY slightly more eastward position by the time the umbra passes by. Not to worry, though - this change has only resulted in a movement of the eclipse path by only a few dozen meters. The eclipse timings have changed from our last update by maybe a tenth of a second or so. It's not enough for the general public to worry about, but it is certainly important for astronomers!

We will continue to monitor the situation regularly, and if any more updates are required, we'll make them! As always, it’s all about bringing you the MOST ACCURATE information possible, as you prepare for eclipse day!

What time zone am I in?

How do you know what time zone you’re in? Well, the vast majority of places (except for Saskatchewan, most of Mexico, Central America, the Caribbean and Arizona) will be observing daylight time on eclipse day. You should know if you’re in a location that doesn’t. And if you get stuck, just do a web search for “Current Universal Time” and compare what it says to the time you see on your phone. If the UT is 4 hours ahead of your local time, then you know you’re in the EDT or AST zone! (Or if you want, download a UT clock app, and you won’t even have to do any conversions – though you may tend to be really early for appointments if you look at the UT clock by mistake!)

If you intend to observe the eclipse from the edge of the path, you must keep up to date with the value of ΔT, and plan accordingly. Fortunately, you will be assisted in this effort by world-class sites such as our eclipse simulator, Xavier Jubier’s Interactive Map – and eclipse2024.org!)

An excellent synopsis

Here is an excellent summary of the various astronomical time standards (in English).