Imagine this! You are on a solo camping or fishing trip and stumbling on your way to the river in the dark, both your watch and cell phone fall into the river. You can’t retrieve either, since you can’t see, but you need to know what the time is. Doesn’t matter why you need to know, but it is imperative that you know how long it is before sunrise. What to do?
Well, if you know same basic astronomy, you can use the North Star and the Plough (Big Dipper) asterism to tell the time to within about 30 minutes or so. Here is how, but if you don’t know some basic astronomy and are a beginner to using stargazing equipment, refer to the image below before you leave on a camping or fishing trip.
This image shows the relationship between the Plough and Polaris, the North Star. Note that the distance between the star and the asterism never changes. The only thing that changes is the position of the Plough relative to the star, since the asterism completes one complete orbit around the star in the course of each 24-hour period. Thus, the asterism will return to the same position relative to the star on the same date every year.
It is worth noting that the rate at which the Plough revolves around the North Star also does not change, meaning that the time it takes the asterism to compete a part of its rotation around the star, say 15 degrees, will always be the same, regardless of where in the rotational circle each subsequent 15- degree segment falls.
So referring to the image again, we can see that it is possible to divide the circle traced out by the Plough’s anti-clockwise rotation around the North Star into equally-sized segments- 24 in this case since the Plough takes 24 hours to complete one revolution around the North Star in an anti-clockwise direction. For our purposes, one segment represents 15 degrees, or one hour of time.
Telling the time
Before you can actually use our Big Dipper clock, you need to remember that the relative positions of the Plough and the North Star as they are represented on Fig. 1 indicate the correct time, but only on the night of March 7/8, but this happens every year, so the clock is reasonably accurate from one year to the next.
So on March 7/8, the clock will show the correct time, midnight, but as the year wears on, you need to correct for the passage of time. There are various ways of doing this, one being the addition or subtraction of one hour per month before or after March 7/8, but there is an easier way. Here’s how:
- Bear in mind that the Plough takes 24 hours to complete one revolution. Therefore, and regardless of where in its rotation the Plough is, the passage of four hours will equal an angle of 60 degrees.
- So, remembering that midnight is represented by the Plough being at the top of the imaginary clock, it becomes a simple matter to gauge the angle between the pointer stars and the North Star from the perpendicular to where it is now. Every 60 degrees of movement translates into four hours of elapsed time. Subdividing each 60 degree segment yields a more accurate guesstimate of the actual time, but remember that the actual time read off the celestial clock will be accurate only on March 7/8. Thus, on this date, follow the rule below-
- Midnight (24:00): The Plough is directly over the North Star.
- 6AM (06:00): The Plough is due west of the North Star.
- Noon (12:00): The Plough is due south of the Pole Star.
- 6PM (18:00): The Plough is due east of the North Star.
Correcting for the date
Since a circle only has 360 degrees, and the Earth takes roughly 365 days to complete an orbit around the Sun, the celestial clock runs fast at the rate of 4 minutes per day, which translates into around two hours per month.
To correct for this deviation, you must subtract 30 minutes for each week after March 7/8. Thus, if you read a time of say, midnight on May 7, (3 months, or 12 weeks later), you get a value of 360 minutes, or three hours that must be taken into account. This would make the time on May 7 not midnight, but 9 PM, since you must subtract the time that the celestial clock had been running fast over the 12 weeks from March 7, to May 7. To correct for Daylight Saving Time (when DST is in effect), add one hour to the calculated time to get a reasonably accurate time.