The piece I did with Mark Thompson was broadcast on BBC Stargazing Live on BBC2 last night. It will be available on iPlayer for a for a short time. Inevitably TV is short of time, so it ended up being a very brief introduction to some ideas. For those who are interested, below is a much more detailed explanation of the nuts and bolts of what happened on that boat that night.
The following piece was first published in Navigation News:
Astronavigating with the BBC
It was cold in Weymouth when they put the blindfolds on. And it was a lot colder than the Mauritius beach I had been standing on six weeks earlier when the phone rang.
“This is the BBC and we understand you can navigate by using the stars?”
“Yes.” I replied and looked up at the small coincidence. Mauritius is twenty degrees south of the equator and I had been enjoying a feast of southern stars when the mobile started buzzing.
“If we were to blindfold you, put you on a boat, take you out into the sea somewhere and then take off the blindfold… could you work out where you are using the stars?”
“If we then revealed a secret destination to you, could you find your way to it using only the stars?”
“Yes.” I replied, then added for good measure, “This is what I do.” I did not add that sometimes I used waves, birds, clouds or a hundred other things too. “Who is this exactly?”
“I’m calling from BBC Stargazing Live.”
“I see.” And so it began.
The BBC informed me that if I accepted this challenge I would need to be on standby for 9 days, but I would only get paid for the time I worked and that would only be if we went to sea. Since we needed a perfectly clear night in winter, it started to look like a long slow way to earn nothing.
Then, in the midst of seven days of solid cloud cover, all available forecasts – from shipping to satellite photos – predicted a perfect window for the evening of Saturday 30th November. I filled the boot of my Land Rover with oilskins, boots, lifejacket, celestial sphere, astrolabe and a pair of sextants. One sextant I had faith in and one which had been dropped a couple of times during my courses. I have learned over the years that it is a good idea to have a second sextant that you don’t care too much for – it is the one to be generous with when GPS navigators get excited and want to play.
The fishing boat, Supernova II, was moored at the quayside in Weymouth. I met the regular presenter of Stargazing Live, Mark Thompson, and both crews: boat and filming. Tom, the director, blindfolded Mark and me and then Supernova slipped out of Weymouth. There was little ceremony. An hour and a half later, the cameras were rolling as Mark and I took our blindfolds off and surveyed our surroundings. I knew that the boat was unlikely to have exceeded 15 knots and we had travelled for less than 90 minutes, so we could not possibly be more than 23 nautical miles from Weymouth, but that wasn’t the point.
The challenge wasn’t to work out roughly where I was, but to pinpoint my position as precisely as possible using only the stars. We could see the sun setting and I explained to Mark that sunset is a golden opportunity for us to get our bearings, it’s a compass in itself. I knew that the sun would set close to 235 degrees that day. I also explained that things were about to get busy. Many people think of astronavigation as a romantic and leisurely business. At the sharp end, it’s not. To be specific, finding direction using the stars can be a laid-back process – it really is very simple – but fixing your position is not leisurely. There is a fairly narrow time window to get the sights you need and when it’s gone, it’s gone for another thirteen hours in winter. You need enough light to see the horizon and enough darkness to see your stars – twilight is a vague notion to some, but an exact one when it comes to celestial navigation.
I got us warmed up with some sights of Venus. I called, ‘Time… Now!’ And Mark noted down the GMT time to the second. I then gave him the degrees and minutes reading off the sextant. By the time true twilight came we were well drilled as a team and ready.
The director and I had held long conversations by phone in the weeks leading up this moment. Our chats hinged around the method I would use. We settled on a slightly unorthodox approach for a good reason. The usual approach is to take sights of at least three stars, sometimes as many as six. For a programme like this it was very important that the viewer was able to follow the logic of what I was doing and to achieve this I was happy to simplify things. I suggested we sacrifice a little accuracy (and redundancy) by only using a two-star sighting and fix. I would get my latitude from the North Star, Polaris, and use a star in the west or east to work out my longitude. It was fortunate that at the times we were considering, one of the brightest stars of the night sky would be very close to due west.
I pointed out this bright western star, Vega, and everyone on board was pleasantly surprised that a star was visible when it still appeared to most on board to be late in the day – not early in the night. That is something that surprises many: you can spot stars much earlier than most imagine, if you know where to look. In fact you can use this approach to find Venus during the day too. It’s worth trying if you haven’t before. At sunset or sunrise, at a time when Venus is clear (ie. reasonably far from the sun), look at where Venus is relative to the sun. Then the following day, if the sky is clear in the middle of the day, look to the same spot relative to the sun (shield the sun from your eyes with one hand) and you may well find it again.
We took three sights of Vega, then scanned the sky for Polaris. Capella was easy to find in the northeast and then the North Star appeared, very faintly at first. Another three sights and it was time for me to do some arithmetic. In truth, the few astronavigators that remain in the world will normally lean on microchips at this point. I did have that option with an app on my iPhone; it contains data up to 2500AD and would fill enough books to sink our boat. But both Tom and I felt that this would rob the viewer at home of both the logic of what happens next and the romance.
With the help of the Nautical Almanac and my sight reduction tables, I began compiling the information with pencil and paper. I explained to Mark that once we had averaged our sights for each star, we would have two key pieces of information for each one. The first was the time of the sighting and the second was a good measure of the angle of each star above our horizon. The first of these, time, was ready for use, because we had used a watch that I had synchronized to GMT earlier that day. But the second, the angle, was not yet fit for purpose. The sums that needed doing before our angles were useful were simple, but essential.
First, I needed to account for ‘index error’ – this error stems from the fact that no sextant is perfect and nearly all misread by a touch. So long as you know what this error is, you just factor it in at this stage and it does no harm. Next there was ‘Dip’. The Dip stage came as a surprise to all on board. Dip takes account of the fact that you are not taking your sight from sea level, but slightly above it. In our case we stood six foot above a deck that itself was four feet above the sea. It doesn’t sound like much, but it means our sights would all be 3 minutes (1/20th of degree) larger than they would have been from sea level and this needed subtracting. A small adjustment, but a vital one as without it we would be out by 3 miles.
Then there was the ‘apparent altitude correction’ or what I prefer to call the ‘stick in the pond effect’. Whenever you see a star (or the sun, moon or planets) it is not exactly where it appears to be, because its light gets bent slightly by our atmosphere. The lower a star is, the greater this effect and sights below 10 degrees are not recommended for this reason. (If you do happen to find a star directly overhead, its light hits our atmosphere perpendicularly and there is no refraction – it is exactly where it appears to be – but that is very rare.)
The final calculations are the real business of celestial navigation. They are not at all complex, but their full intricacies can fill a 5-day indoor course. I have never seen the logic of this process explained clearly and I may fail here, but I would like to try.
A Small Detour into the Logic of Celestial Navigation
I would like you to find a lamppost and to stand underneath it. What angle is this light above the street? Answer: 90 degrees. Which means that if you called me and told me that you had taken a ‘sight’ of this light and it was 90 degrees, I could tell you with certainty that you were standing exactly underneath that light. Next, if you took five steps away from the light and gauged its angle above the street, you might come up with something like 70 degrees. The light appears lower, the further you are from it. And that in a nutshell is almost all you need to know about how celestial navigation works. Let me demonstrate with a strange thought experiment.
Imagine I called you on your mobile and asked you to stand somewhere on the street and tell me the angle that a streetlight we both know is above the ground. Whatever your answer, I would then be able to gauge roughly how far you were from that light. If you said the light was 50 degrees above the pavement I would say that I think you are 12 paces from the light (it’s not magic, just trigonometry).
But – and it is a very big but – although I would be able to tell you roughly how far you were from the light, I would not be able to tell you exactly where in the street you were. I would have what is called a ‘position line’, that is I know the line you are standing on, but it is not an exact point, it stretches in a circle all the way around your light, at an equal distance from it. This is because there is only one set of places in the street where the light appears that angle above the ground and it forms a circle around the light, with its centre at the light.
A single position line is a big clue to where you are, but not definitive enough to be really useful. I would need at least one other piece of the jigsaw to fix your position precisely. If you told me that when you looked in another direction you could see a second streetlight and it was at an angle of 30 degrees above the ground, I would then be able to pinpoint where you are standing. There can only be one place in the street where light A appears 50 degrees above the ground and light B is 30 degrees above it. Each angle creates a line of possible spots where you could be standing and the precise point where these two lines intersect is the only place in the street where you could possibly have observed these precise angles.
This is how celestial navigation works. The single only thing that makes it a little more challenging under the night sky is that the streetlights move – the stars are not stationary relative to our horizon. They rise, set or rotate because the Earth spins. So we need some way of relating their position to time: hence the tables and chronometers of old and the digital watches and apps of new.
Back out on the English Channel, the angle of Polaris above the horizon told me my latitude, which is after all just a long position line that stretches around the globe. If Polaris is 50 degrees above your horizon then your latitude is approximately 50 degrees north; you might be in the English Channel, but you might equally be in Ukraine, or Kazakhstan for that matter. Fortunately, my sight of Vega gave me my longitude, which narrowed things down to a precise spot southeast of Weymouth.
It transpired that I was between 3 and 4 NM off our position by GPS (we probably drifted about a mile during the time it took to take and plot the sights). Which is fair enough and about as good as can be hoped for from a sighting of two stars on a deck that was rolling considerably.
Mark prized open the sealed envelope in his hands. He pulled out a white card, with the word ALDERNEY printed clearly on it. Using a chart we then worked out that Alderney was due south of our position.
Next, all we needed to do was to work out how to head south, which was nice and straightforward. We used Polaris, the North Star, to find north and then used the stars opposite it to hold a course south. As the voyage progressed and the southern stars wheeled clockwise from southeast to southwest, we updated these target stars. This is very similar to the process used by the Pacific navigators and is referred to as following a ‘star path’. The bright star, Fomalhaut, was ditched early on and then both Markab and Algenib in Pegasus helped us on our way.
Orion rose in the east and Jupiter shone very brightly under the Gemini twins. Hours passed and then lights began appearing over our southern horizon. There was a general glow and many vague splashes of brighter light. There were also three bright and intermittent bursts of distinct light, much clearer than anything else. I pointed up at the southern stars and recapped with Mark. We knew that the southern stars wheel from left to right and we knew how fast they moved.
“So which stars would be a good bet for a southerly course now?” I asked Mark.
“This group, Cetus.” Mark replied and pointed at the constellation.
“I agree. Now lower your eyes and look at the horizon directly below them.”
Mark had spotted the four flashes in fifteen seconds that identified Alderney’s lighthouse. We’d made it due south to within sight of our destination.
Paper, pencil, sextant and stars were used to shape our short voyage, but at no point did we turn anything on.
© Tristan Gooley 2013
If you enjoyed this programme, you might also like to join Clare Balding and me on our walk on the South Downs when we did some navigating by stars in 2010 for Radio 4.