<p>I suspect this is fundamentally a question of error propagation.  My personal favorite reference is "Data Reduction and Error Analysis" by Philip Bevington.  Basically,  once you have the formulas in place,  such as  </p>

<p>eclipse_time = f(sun_ephem, moon_ephem) </p>

<p>You take all the partial derivatives and "stuff" them into the error propagator formulas along with the known or estimated standard deviations (error/uncertainty) of your input variables.  The uncertainty in the output  just pops right out.   </p>

CC BY-SA 4.0
2020-04-01T18:27:09.770Z
2020-04-01T18:27:09.770Z
Carl Witthoft
<p>I am writing a program to simulate eclipses for about -2000 to 6000. My question is, how accurate does my ephemeris for the sun and moon have to be to get a decent accuracy for eclipses? I currently have an accuracy of about 1'' for the Sun and an accuracy of about 12'' for the moon. Is this good enough, or should I find a more accurate system?</p>

<p><strong>Edit:</strong>
I'm still rather new to calculating eclipses, though I have some experience with calculating ephemerises. I'd like to calculate several things: when they occur, the duration, the path of the shadow on the earth for a solar eclipse, and perhaps the percent covered. I suppose I'd like the accuracy on these to be about <span class="math-container">$\pm 0.005$</span> or better. I have access to several resources that should help me do this, but I need to know how accurate to get the ephemeris.</p>

CC BY-SA 4.0
2020-04-01T13:25:27.587Z
*for a good period of time* - you need to give at least an order of magnitude for the timescale to get a useful answer.  That expression is totally vague.  "Decent accuracy" could also do with some values - what's your idea of acceptable error ranges ?
StephenG - Help Ukraine
CC BY-SA 4.0
2020-04-01T13:27:09.233Z
Diameter of both bodies is about 30'. Given your accuracy in positioning you can probably do the math yourself - and the answer to 'good enough' depends on what you define as 'good enough'
planetmaker
CC BY-SA 4.0
2020-04-01T13:34:17.437Z
You should also mention exactly what you want to predict. Do you just want to predict when eclipses will happen? Or do you also want to predict the duration of the eclipse, and if it's partial what percentage of the Sun or Moon is maximally covered? And for solar eclipses, do you want to calculate the path on the ground of the Moon's shadow?
PM 2Ring
CC BY-SA 4.0
2020-04-01T13:35:14.647Z
Thank you all for your comments. I'll add to my question.
John Dumancic
<the-sun><the-moon><solar-eclipse><lunar-eclipse><ephemeris>
How accurate should sun\moon ephemeris be for calculating eclipses?
John Dumancic
# How accurate should sun\moon ephemeris be for calculating eclipses?

(Asked by: username_0 on 2020-04-01)

I am writing a program to simulate eclipses for about -2000 to 6000. My question is, how accurate does my ephemeris for the sun and moon have to be to get a decent accuracy for eclipses? I currently have an accuracy of about 1'' for the Sun and an accuracy of about 12'' for the moon. Is this good enough, or should I find a more accurate system?

**Edit:**
I'm still rather new to calculating eclipses, though I have some experience with calculating ephemerises. I'd like to calculate several things: when they occur, the duration, the path of the shadow on the earth for a solar eclipse, and perhaps the percent covered. I suppose I'd like the accuracy on these to be about $\pm 0.005$ or better. I have access to several resources that should help me do this, but I need to know how accurate to get the ephemeris.

**Tags:** the-sun, the-moon, solar-eclipse, lunar-eclipse, ephemeris
> **Comments:**
> **username_1**: *for a good period of time* - you need to give at least an order of magnitude for the timescale to get a useful answer.  That expression is totally vague.  "Decent accuracy" could also do with some values - what's your idea of acceptable error ranges ?  
> **username_2**: Diameter of both bodies is about 30'. Given your accuracy in positioning you can probably do the math yourself - and the answer to 'good enough' depends on what you define as 'good enough'  
> **username_3**: You should also mention exactly what you want to predict. Do you just want to predict when eclipses will happen? Or do you also want to predict the duration of the eclipse, and if it's partial what percentage of the Sun or Moon is maximally covered? And for solar eclipses, do you want to calculate the path on the ground of the Moon's shadow?  
> **username_0**: Thank you all for your comments. I'll add to my question.  

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## 1 answers

### Answer by username_4 on 2020-04-01. Score: 1

I suspect this is fundamentally a question of error propagation. My personal favorite reference is "Data Reduction and Error Analysis" by Philip Bevington. Basically, once you have the formulas in place, such as

eclipse\_time = f(sun\_ephem, moon\_ephem)

You take all the partial derivatives and "stuff" them into the error propagator formulas along with the known or estimated standard deviations (error/uncertainty) of your input variables. The uncertainty in the output just pops right out.


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