<p>I'll start at the end and walk your question backwards to provide a partial answer. <em>However I too am looking forward to find out if there is any <em>independent testing</em> of the DEs using phenomenon not used in the process of their fitting!</em></p>
<hr />
<blockquote>
<p>Additionally, are there any algorithms more accurate than DE441?</p>
</blockquote>
<p>If I remember correctly, there is a similar European numerically generated ephemeris of the same caliber as the <a href="https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris" rel="nofollow noreferrer">JPL Developmet Ephemerides</a><sup>1,2</sup> but if I'm not mistaken JPL DE's have now become the gold standard worldwide.</p>
<p>You can read the documentation for DE441 to see how JPL compares its accuracy to the other JPL DEs. They are all going to be (in my opinion) remarkably close<sup>3</sup> to each other, but they are refined differently for different uses, for different numbers of parameters, and for different spans of time. Download and read the PDF from</p>
<ul>
<li><a href="https://ssd.jpl.nasa.gov/doc/de440_de441.html" rel="nofollow noreferrer">https://ssd.jpl.nasa.gov/doc/de440_de441.html</a></li>
</ul>
<p>The abstract alone is enough to suggest that currently <strong>this is as good as it gets!</strong></p>
<blockquote>
<p>Is there a website where I can retrieve documentation for eclipse observations, such as when an eclipse starts and ends?</p>
</blockquote>
<p>Any website that's worth its salt (i.e. you put in your exact latitude, longitude and elevation above the <a href="https://en.wikipedia.org/wiki/World_Geodetic_System#WGS_84" rel="nofollow noreferrer">WGS84</a> ellipsoid (i.e. &quot;GPS coordinates&quot;) and it gives you millisecond or microsecond timing information by correcting for all kinds of things (GR or general relativistic effects (due to your speed and local gravity), atmospheric effects, astronomical aberration, etc.) and it's going to be using one of the JPL DE's to give you the predictions.</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/54110/7982">What is the difference between SPICE kernels and JPL Development Ephemerides? Is a DE just a bunch of kernels on a string?</a></li>
</ul>
<blockquote>
<p>How to test accuracy of DE441?</p>
</blockquote>
<p>Since the DEs are generated by fitting every available <em>accurate</em> measurement of astronomical measurement, primarily those that involve both space and time (like an eclipse of a moon or a start by a planet or asteroid) and radar and spacecraft delay-doppler measurements via coherent transponders (to name a few) it really has testing built in.</p>
<h3>However - that's no excuse for not doing independent testing!</h3>
<p>Therefore I think your question is a good one! I'd phrase it more like &quot;Do JPL or other astronomers ever <em>test and/or validate</em> the JPL DEs using independent measurements?&quot; DE generation is a pretty elaborate software endeavor and for anything that software touches (or humans touch for that mater) independent testing is always essential.</p>
<h3>Okay, but for amateurs <em><strong>How to test accuracy of DE441?</strong></em></h3>
<p>Timing solar and lunar eclipses is a bit fuzzy, but <strong>lunar occultations</strong> of planets and stars can be nailed down pretty nicely.</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/40532/7982">Does a lunar occultation of Mars happen twice a year?</a></li>
<li><a href="https://in-the-sky.org//newsindex.php?feed=occultations" rel="nofollow noreferrer">https://in-the-sky.org//newsindex.php?feed=occultations</a></li>
<li><a href="https://in-the-sky.org/article.php?term=lunar_occultation" rel="nofollow noreferrer">https://in-the-sky.org/article.php?term=lunar_occultation</a></li>
<li><a href="http://www.lunar-occultations.com/iota/planets/planets.htm" rel="nofollow noreferrer">http://www.lunar-occultations.com/iota/planets/planets.htm</a></li>
<li><a href="https://iota-es.de/moon/moon_occ_plan.html" rel="nofollow noreferrer">https://iota-es.de/moon/moon_occ_plan.html</a></li>
</ul>
<p>With binoculars or small telescope and a good sky, You can also watch the eclipses of Jupiter's moons by Jupiter. This is actually how the speed of light was first measured!</p>
<p>And every ~5.9 years you can watch (and time) Jupiters moons eclipse each other! Now that's a real cool test</p>
<ul>
<li><a href="https://astronomy.stackexchange.com/q/23477/7982">When will the next series of mutual eclipses of Jupiter&#39;s moons begin?</a></li>
</ul>
<p>The best way to be absolutely sure you are using DE441 is to use a package like <a href="https://rhodesmill.org/skyfield/" rel="nofollow noreferrer">Skyfield</a> and predict the occultation times for your lat/lon/alt using the the tools at <a href="https://rhodesmill.org/skyfield/searches.html" rel="nofollow noreferrer">Searching for the dates of astronomical events</a></p>
<hr />
<ul>
<li><sup>1</sup> <a href="https://english.stackexchange.com/q/370655/217285">How to pronounce &quot;Ephemerides&quot;?</a></li>
<li><sup>2</sup> and I don't mean semi-analytic planetary theory-based <a href="https://en.wikipedia.org/wiki/VSOP_model" rel="nofollow noreferrer">VSOP</a> (cf. <a href="https://stackoverflow.com/q/34487170/3904031">PyEphem under the hood - how does it calculate position of planets?</a>)</li>
<li><sup>3</sup> DE-to-DE-variations like a few meters for the Earth-Moon system for recent times, maybe a few tens of meters for Mars, and a few hundreds of meters for the outerest outer planets. Basically if a modern spacecraft has spent some time there, then delay-Doppler information will nail it down really quite well. <strong>Of course if you need any one body's position to the utmost accuracy, those are done with more specialized ephemerides</strong> that are not global fits to the whole solar system but instead heavily weight measured data related to the body in question!</li>
</ul>
<hr />
<p>From the link to DE440/DE441:</p>
<blockquote>
<p>Abstract:</p>
<p>The planetary and lunar ephemerides called DE440 and DE441 have been generated by fitting numerically integrated orbits to ground-based and space-based observations. Compared to the previous general-purpose ephemerides DE430, seven years of new data have been added to compute DE440 and DE441, with improved dynamical models and data calibration. The orbit of Jupiter has improved substantially by fitting to the Juno radio range and Very Long Baseline Array (VLBA) data of the Juno spacecraft. The orbit of Saturn has been improved by radio range and VLBA data of the Cassini spacecraft, with improved estimation of the spacecraft orbit. The orbit of Pluto has been improved from use of stellar occultation data reduced against the Gaia star catalog. The ephemerides DE440 and DE441 are fit to the same data set, but DE441 assumes no damping between the lunar liquid core and the solid mantle, which avoids a divergence when integrated backward in time. Therefore, DE441 is less accurate than DE440 for the current century, but covers a much longer duration of years -13,200 to +17,191, compared to DE440 covering years 1550-2650.</p>
</blockquote>

CC BY-SA 4.0
2023-09-10T08:07:55.677Z
Wow, your answer is so detailed! I was thinking I can test DE441's accuration (for moon and sun) with compare it to the actual observation of eclipse (when it start, when it end). What's your opinion?
Ath Genube
CC BY-SA 4.0
2023-09-10T08:47:02.950Z
@AthGenube ya it's always frustrating when someone forgets to actually answer YOUR question! I've added a section titled "Okay, but for amateurs *How to test accuracy of DE441?*" Perhaps that's at least a little more helpful? Let me know, thanks!
uhoh
CC BY-SA 4.0
2023-09-10T10:16:59.240Z
Thanks, @uhoh! The answer is very insightful!
Ath Genube
CC BY-SA 4.0
2023-09-10T11:55:51.743Z
@AthGenube sure, happy to hear it! :-)
uhoh
CC BY-SA 4.0
2023-09-10T13:17:50.630Z
Incidentally, as well as his outstanding work producing the JPL DEs, Dr Ryan Park is heavily involved in the Juno, Psyche, and Europa Clipper missions https://solarsystem.nasa.gov/people/514/ryan-park/ So he has an active role in gathering that data that the DEs are fitted to.
PM 2Ring
CC BY-SA 4.0
2023-09-10T13:29:18.640Z
The Observatoire de Paris also provides an ephemeris produced by numerical integration, INPOP: https://www.imcce.fr/services/ephemerides/
PM 2Ring
CC BY-SA 4.0
2023-09-10T13:52:18.737Z
@PM2Ring yes I'll bet that's what I was thinking of, *thanks!*
uhoh
CC BY-SA 4.0
2023-09-10T06:49:18.663Z
2023-09-12T11:04:55.140Z
2023-09-12T11:04:55.140Z
uhoh
<p>I want to write about processing DE441 data for Moon and Sun and include a section about the validation and accuracy testing of the algorithm. Is there a website where I can retrieve documentation for eclipse observations, such as when an eclipse starts and ends? Additionally, are there any algorithms more accurate than DE441?</p>

CC BY-SA 4.0
2023-09-10T21:22:16.773Z
The ultimate resource for eclipse info is the https://www.eclipsewise.com/ site of Fred Espenak, aka Mr Eclipse.
PM 2Ring
CC BY-SA 4.0
2023-09-12T19:55:51.860Z
Eclipses (and lunar occultations) are a poor choice for evaluating DE441 as it is based on the center of mass of the Moon, not the geometric center.
Greg Miller
CC BY-SA 4.0
2023-09-16T04:15:01.590Z
Hi @GregMiller, I get DE441 data via [web Horizons app](https://ssd.jpl.nasa.gov/horizons/app.html#/). Is it also use geometric center? If not, is there any configuration should I set to get Moon's geometric center?
Ath Genube
<ephemeris>
How to test accuracy of DE441?
Ath Genube
# How to test accuracy of DE441?

(Asked by: username_0 on 2023-09-10)

I want to write about processing DE441 data for Moon and Sun and include a section about the validation and accuracy testing of the algorithm. Is there a website where I can retrieve documentation for eclipse observations, such as when an eclipse starts and ends? Additionally, are there any algorithms more accurate than DE441?

**Tags:** ephemeris
> **Comments:**
> **username_1**: The ultimate resource for eclipse info is the https://www.eclipsewise.com/ site of Fred Espenak, aka Mr Eclipse.  
> **username_2**: Eclipses (and lunar occultations) are a poor choice for evaluating DE441 as it is based on the center of mass of the Moon, not the geometric center.  
> **username_0**: Hi @GregMiller, I get DE441 data via [web Horizons app](https://ssd.jpl.nasa.gov/horizons/app.html#/). Is it also use geometric center? If not, is there any configuration should I set to get Moon's geometric center?  

---

## 1 answers

### Answer by username_3 on 2023-09-10. Score: 7

I'll start at the end and walk your question backwards to provide a partial answer. *However I too am looking forward to find out if there is any *independent testing* of the DEs using phenomenon not used in the process of their fitting!*

---

> Additionally, are there any algorithms more accurate than DE441?

If I remember correctly, there is a similar European numerically generated ephemeris of the same caliber as the [JPL Developmet Ephemerides](https://en.wikipedia.org/wiki/Jet_Propulsion_Laboratory_Development_Ephemeris)1,2 but if I'm not mistaken JPL DE's have now become the gold standard worldwide.

You can read the documentation for DE441 to see how JPL compares its accuracy to the other JPL DEs. They are all going to be (in my opinion) remarkably close3 to each other, but they are refined differently for different uses, for different numbers of parameters, and for different spans of time. Download and read the PDF from

* <https://ssd.jpl.nasa.gov/doc/de440_de441.html>

The abstract alone is enough to suggest that currently **this is as good as it gets!**

> Is there a website where I can retrieve documentation for eclipse observations, such as when an eclipse starts and ends?

Any website that's worth its salt (i.e. you put in your exact latitude, longitude and elevation above the [WGS84](https://en.wikipedia.org/wiki/World_Geodetic_System#WGS_84) ellipsoid (i.e. "GPS coordinates") and it gives you millisecond or microsecond timing information by correcting for all kinds of things (GR or general relativistic effects (due to your speed and local gravity), atmospheric effects, astronomical aberration, etc.) and it's going to be using one of the JPL DE's to give you the predictions.

* [What is the difference between SPICE kernels and JPL Development Ephemerides? Is a DE just a bunch of kernels on a string?](https://astronomy.stackexchange.com/q/54110/7982)

> How to test accuracy of DE441?

Since the DEs are generated by fitting every available *accurate* measurement of astronomical measurement, primarily those that involve both space and time (like an eclipse of a moon or a start by a planet or asteroid) and radar and spacecraft delay-doppler measurements via coherent transponders (to name a few) it really has testing built in.

### However - that's no excuse for not doing independent testing!

Therefore I think your question is a good one! I'd phrase it more like "Do JPL or other astronomers ever *test and/or validate* the JPL DEs using independent measurements?" DE generation is a pretty elaborate software endeavor and for anything that software touches (or humans touch for that mater) independent testing is always essential.

### Okay, but for amateurs ***How to test accuracy of DE441?***

Timing solar and lunar eclipses is a bit fuzzy, but **lunar occultations** of planets and stars can be nailed down pretty nicely.

* [Does a lunar occultation of Mars happen twice a year?](https://astronomy.stackexchange.com/q/40532/7982)
* <https://in-the-sky.org//newsindex.php?feed=occultations>
* <https://in-the-sky.org/article.php?term=lunar_occultation>
* <http://www.lunar-occultations.com/iota/planets/planets.htm>
* <https://iota-es.de/moon/moon_occ_plan.html>

With binoculars or small telescope and a good sky, You can also watch the eclipses of Jupiter's moons by Jupiter. This is actually how the speed of light was first measured!

And every ~5.9 years you can watch (and time) Jupiters moons eclipse each other! Now that's a real cool test

* [When will the next series of mutual eclipses of Jupiter's moons begin?](https://astronomy.stackexchange.com/q/23477/7982)

The best way to be absolutely sure you are using DE441 is to use a package like [Skyfield](https://rhodesmill.org/skyfield/) and predict the occultation times for your lat/lon/alt using the the tools at [Searching for the dates of astronomical events](https://rhodesmill.org/skyfield/searches.html)

---

* 1 [How to pronounce "Ephemerides"?](https://english.stackexchange.com/q/370655/217285)
* 2 and I don't mean semi-analytic planetary theory-based [VSOP](https://en.wikipedia.org/wiki/VSOP_model) (cf. [PyEphem under the hood - how does it calculate position of planets?](https://stackoverflow.com/q/34487170/3904031))
* 3 DE-to-DE-variations like a few meters for the Earth-Moon system for recent times, maybe a few tens of meters for Mars, and a few hundreds of meters for the outerest outer planets. Basically if a modern spacecraft has spent some time there, then delay-Doppler information will nail it down really quite well. **Of course if you need any one body's position to the utmost accuracy, those are done with more specialized ephemerides** that are not global fits to the whole solar system but instead heavily weight measured data related to the body in question!

---

From the link to DE440/DE441:

> Abstract:
>
> The planetary and lunar ephemerides called DE440 and DE441 have been generated by fitting numerically integrated orbits to ground-based and space-based observations. Compared to the previous general-purpose ephemerides DE430, seven years of new data have been added to compute DE440 and DE441, with improved dynamical models and data calibration. The orbit of Jupiter has improved substantially by fitting to the Juno radio range and Very Long Baseline Array (VLBA) data of the Juno spacecraft. The orbit of Saturn has been improved by radio range and VLBA data of the Cassini spacecraft, with improved estimation of the spacecraft orbit. The orbit of Pluto has been improved from use of stellar occultation data reduced against the Gaia star catalog. The ephemerides DE440 and DE441 are fit to the same data set, but DE441 assumes no damping between the lunar liquid core and the solid mantle, which avoids a divergence when integrated backward in time. Therefore, DE441 is less accurate than DE440 for the current century, but covers a much longer duration of years -13,200 to +17,191, compared to DE440 covering years 1550-2650.

> **Comments:**
> **username_0**: Wow, your answer is so detailed! I was thinking I can test DE441's accuration (for moon and sun) with compare it to the actual observation of eclipse (when it start, when it end). What's your opinion?  
> **username_3**: @AthGenube ya it's always frustrating when someone forgets to actually answer YOUR question! I've added a section titled "Okay, but for amateurs *How to test accuracy of DE441?*" Perhaps that's at least a little more helpful? Let me know, thanks!  
> **username_0**: Thanks, @uhoh! The answer is very insightful!  
> **username_3**: @AthGenube sure, happy to hear it! :-)  
> **username_1**: Incidentally, as well as his outstanding work producing the JPL DEs, Dr Ryan Park is heavily involved in the Juno, Psyche, and Europa Clipper missions https://solarsystem.nasa.gov/people/514/ryan-park/ So he has an active role in gathering that data that the DEs are fitted to.  
> **username_1**: The Observatoire de Paris also provides an ephemeris produced by numerical integration, INPOP: https://www.imcce.fr/services/ephemerides/  
> **username_3**: @PM2Ring yes I'll bet that's what I was thinking of, *thanks!*  

---

