(Fiction) How would a time traveler locate himself with 1962 technology?

Question

I'm a writer doing research for a time travel story; my character's origin is in 1962 and his contraption has been built into a DC-3 No fancy mechanical clock dials or precision digital readouts; when the contraption is activated he "flies" back and forth through the time dimensions in a manner similar to navigating through the air.

Eventually I plan to have him recognize that an alternating band of dark and light represents a 24 hour day and that there's a more subtle pattern as the sun traces its way through the analemma which lets him count years, and by varying the "field intensity" he'll be able to progress more quickly or slowly. But for the very first time jump, with no experience and nothing calibrated, I want to have him badly overshoot his mark and end up in the year 1519.

When he lands the DC-3 he has no idea of when in time he is, and the only instruments he has are those which he brought with him from 1962. I'm writing the character as a physicist, the dean of the science department at a fictional university in Western Australia. So, with that as the setup...

• How might he recognize when he is? Western Australia in the 16th century was a mighty lonely place, especially when you're looking for a newspaper or a petrol station...
• What instruments and reference books should a putative time traveler have been prudent enough to bring on board before departing? (By The Way, I'd like to write in a US Navy Mark V aviation sextant with chronometric averager...since I have one. I'm leery of posting links my first time out, but more data is available on the web site of a company called Celestaire.)
• What are some of the calculations which might be necessary to work out his chronological position?

Help me get my character back to 1962...in time to get involved in the Cuban Missile Crisis!

Edit To Add: It's been autosuggested that I edit my question. What I'm looking for are patterns in the night sky which might predictably change over long periods and which a physicist knowledgeable of astronomy could recognize and interpret. Aside from the Mark V sextant (which does have an internal, radium-illuminated bubble level/horizon), what other tools, instruments, and reference works would be helpful? Again, I'm not suggesting that he focus down to a specific day or even year; if he can chronologically locate himself within a twenty- or even fifty-year window it will work for the purposes of my story.

Second edit: It has been suggested that an observation of Uranus and Neptune would be helpful. I'm pretty sure that Neptune is out, but the Mark V sextant has a 2x telescopic optical path. Is it possible to take an accurate sighting of Uranus with a 2 power telescopic sextant after you have located the position of the planet with a larger, portable tripod-mounted telescope? If so, or if an sufficiently accurate sighting could be taken with the larger telescope, how would one work out the calculations from there?

Answer 1

Your semi-intuitive thought that there must be a pattern of the planet locations that would show the date is correct, I think. You won't need any special equipment but a sextant which will measure angles between stars and planets - can't be a bubble sextant. You will also need data: (1) The sidereal hour angles (SHAs) of Jupiter and Saturn on your departure day or any day within a few weeks of it. (2) Eccentricity, aphelion, perihelion, semi-major axis, and date of the perihelion closest to the departure day for both planets and Earth. Siderial orbit period for Jupiter and Saturn. (3) Trig tables. (4) Navigational star chart.

At the time the plane lands Jupiter and Saturn will have traveled some number of complete orbits around the sun and a partial orbit. The number of complete orbits will be different for the two planets, as will the sizes of their two partial orbits.

The first task is to find Jupiter and Saturn. They're bright and their positions will change from day to day. They'll also be within a couple of degrees of the ecliptic, which is plotted on the star chart. There's a chance that one or both won't be visible - above the horizon - at night, and you might have to wait as much as a month until it's back. There might be a food problem IRL. Fortunately, it's not IRL so you can pick a time of year when both are in the night sky.

All eight planets are very close to the ecliptic, so you'll need to sort. The best way to do that is to calculate their orbital periods. Brightness will help but it's partly subjective, and varies a lot. To get an orbital period, start by finding the planet's celestial coordinates on the star chart. You can get to one degree, best case, by seeing how close it is to nearby stars. Then you'll have to convert the geocentric coordinates to heliocentric. You do that by solving the plane triangle whose vertices are Sun, Earth and planet. The triangle isn't solvable by the law of cosines, but it's one of the types that can be solved by the law of sines. You know the length of two sides and one angle. That angle is the difference in SHAs of planet and Sun as seen from Earth. You brought the distances planet to Sun and Earth to Sun, as well as corrections for their elliptical orbits, in the data package. Those distances are the triangle's two known sides. To determine the corrections for elliptical orbits you'll need to know the time of year, which you'll be finding in a parallel task. Think of finding the planets your night job and finding the time of year as your day job.

The best way to do the day job is to observe the maximum altitude of the Sun over several days with a sextant. You'll see that the Sun reaches its maximum altitude and seems to stay there for a few minutes. The middle of those minutes is local apparent noon. Pick the most likely middle.

Continuing, you'll use the observed altitude to find the time of year. You know where you are. Most of the Western Australia airports in 1962 should have been near Perth. If that's so, the Sun will always be in your north sky. You can calculate a pair of days when the Sun would be at the altitudes you observed with the formula D = 365.25 arcsin(a/23.44), where D is the number of days since the vernal equinox, and a is the observed altitude of the Sun at local apparent noon, corrected for latitude, in degrees. Use 16.2 arc minutes for the semidiameter correction. Take readings for several days, long enough to see whether the trend is increasing or decreasing altitude. If it's decreasing the day is in summer or fall - increasing, winter or spring, using Australian naming of the seasons. Considering that the arcsine function is double valued you'll have two values for D. You can pick the right one knowing the season.

Getting back to finding orbital period: solve the triangle for the angle at the Sun. Knowing that angle, and your heliocentric SHA (180 degrees minus the Sun's geocentric SHA) you can find the heliocentric SHA of the planet. Whew! Accumulate the changes in SHA until you have a handle on degrees per day. Compare it to about 12 days per degree for Saturn and 84 days per degree for Saturn. Obviously, if you don't plan on staying for a few months, you'll need to observe the planet's position with a sextant, watching the trends in separation from nearby stars.

At this point you'll know where Jupiter and Saturn are. To get to those positions they both made a number of complete orbits and one part orbit around the Sun. Find the part orbit by converting the departure SHA and the current SHA to heliocentric values. the difference in those values is the angular size of the part orbit. Convert it to years by dividing it by 360 and multiplying by the orbital period. Make a list of the possible times since departure: part orbit duration, part orbit duration plus orbital period, etc., for each planet. Look through the lists for two durations that are very close. Done.