When I did my first ever celestial position fix, I was extremely happy to get within 20 miles of my GPS position. Since then, I have been able to improve somewhat, but it got me wondering: how accurate can you be with a celestial fix compared to a GPS?
The theoretical accuracy of celestial position fix is within 0.1 mile of your true position. In comparison, a modern GPS should be able to give you an accuracy of less than 1 meter. A GPS fix is at least 100 times more accurate than a celestial fix.
While the theoretical maximum accuracy of a celestial fix is 0.1 miles, in reality you will probably never achieve closer than 1 mile.
How Accurate is a Celestial Position Fix?
The theoretical accuracy of a celestial position fix is based on the accuracy of a sextant. Most sextants let you measure angles to within 0.1 minutes of a degree. 0.1 minutes on the altitude of a celestial body translates to 0.1 nautical miles on the surface of the earth.
In reality, however, it is almost impossible to actually achieve an accuracy of 0.1 minutes with a sextant.
You are taking your measurements from a moving boat, which is floating on a moving ocean. The horizon needs to be clear, and the celestial body needs to be a perfect, bright speck.
It is far more realistic to get an accuracy of 1 minute with a sextant in day-to-day conditions.
An accuracy of 1 minute with the sextant implies a final position fix accuracy of 1 mile.
Of course, getting that sort of accuracy relies on minimising every other source of error. Unfortunately, in celestial navigation, there are plenty of potential sources of error:
- Errors reading the measurement from the sextant
- Errors identifying a celestial body
- Potential inaccuracies in your chronometer
- Errors in identifying prevailing atmospheric conditions
- Errors in your calculations
- Rounding errors
- Errors plotting the final fix
Fortunately though, practise and precision can be used to reduce or eliminate most of these errors.
We can therefore say that an experienced navigator can realistically expect an accuracy of around 1 mile when completing a celestial position fix.
Beginners, on the other hand, will be lucky to achieve an accuracy of 10 miles the majority of the time.
How Accurate does a Celestial Fix need to be?
Not very accurate at all.
Celestial navigation is used when you are far out at sea, when no other methods of position fixing are available.
If you are hundreds of miles from the nearest land, 10 miles of error in your position is not too significant.
Remember, in the middle of an ocean, you will be using a small scale chart. The chart probably covers most of the ocean.
Your position only needs to be accurate enough for you to make landfall in roughly the right place. After that, visual navigational techniques can take over.
What Affects the Accuracy of a Celestial Fix?
There are many different things that can affect the final accuracy of a celestial position fix. Some will have far more of an impact that others. Let’s take a look at a few of the main ones.
How your Sextant Affects the Accuracy of a Celestial Fix
The sextant is a precise scientific instrument that needs to be set up correctly to minimise sources of error.
If you get an incorrect measurement of the altitude of a celestial body with your sextant, the accuracy of your celestial position fix will be reduced.
1/60th of a degree of altitude moves the corresponding line of position by 1 nautical mile.
You can watch this video to see all the different errors and methods for correcting each one.
How your Chronometer Affects the Accuracy of a Celestial Fix
When you take a sight with a sextant, you need to record the precise time of that sight. That’s fine if your chronometer is precisely calibrated. If it is out, even by a couple of seconds, it can have quite a significant impact.
The earth is spinning at roughly 15 degrees per hour. If your timepiece was 1 hour wrong, your position line could be 900 miles out. That is the same as ¼ of a mile out for every second that your timepiece is incorrect.
A precisely calibrated digital clock should be accurate to within a second.
Ironically nowadays, most ships get the time from their GPS. To do a true celestial fix they would need to use a completely independent chronometer.
How the Atmosphere Affects the Accuracy of a Celestial Fix
Atmospheric conditions affect the path that the light from a celestial body takes before it reaches your eye. In physics, it is called refraction.
Within a nautical almanac, you have a correction called ARC, or “Additional Refractive Correction”. This is the correction that you need to apply to counter the different refractive effects at different atmospheric pressures and temperatures.
The other way that the atmosphere affects the accuracy of a celestial fix is at the horizon. If the conditions make the horizon hazy, or hard to discern, it becomes harder to get an accurate measurement.
How your Calculations Affect the Accuracy of a Celestial Fix
The calculations themselves can have a massive impact on the accuracy of your final position.
If you physically type the wrong numbers into the calculator, it could give impossible answers. Similarly, if you read the wrong numbers out of your almanac, the final result would be completely incorrect.
More of a realistic proposition is making small errors with your rounding. If you round some of your numbers too early, or to too few decimal places, you will get a less accurate final fix.
Pro Tip: I keep all my numbers at 5 decimal places throughout my calculations.
How can I Improve the Accuracy of a Celestial Fix?
You can improve the accuracy of a celestial fix by taking great care with your sextant. The altitude reading that you get from your sextant is the most significant number you can really control.
Make sure you watch my youtube video on correcting your sextant and compensating for any residual errors.
You should also ensure that your chronometer is as accurate as possible. This can be done by synchronizing it with the most accurate clock you can find. Your GPS is probably the most accurate clock you have onboard, so just make sure all other clocks are synchronised in case the GPS stops working.
How Accurate is a GPS?
According to this US Government website, “GPS enabled smartphones are accurate to within a 4.9m radius”.
In the marine environment, we do use additional features through a system called “differential GPS”, or DGPS.
DGPS attempts to calculate some of the errors of GPS by comparing the known position of an object to its GPS position. The difference between the two, or the error, is then broadcast to other units in the area. They can then take the local error into account and produce a more accurate position themselves.
DGPS can give users an accuracy of 10cm in ideal conditions. You can read more about Global GDPS from NASA’s JPL by visiting gdgps.net.
Pro Tip: You can see how reliable your GPS thinks your position is by checking its HDOP value. A HDOP of 1 is accurate. Then the higher the value, the less accurate the position.
Do Professional Sailors Need to Learn how to use a Sextant?
Yes. Learning to use the sextant is part of the syllabus and examination process for gaining your international Officer of the Watch Certificate of Competency.
Even within the US Navy, use of the sextant has returned to the curriculum. You can read an article about it from NPR in this article: US Navy Brings Back Navigation By The Stars For Officers.