Sky & Telescope - March 2020 - 60

p VOYAGES OF EXPLORATION Cook's first, second, and third voyages
are shown in brown, green, and blue, respectively. The dotted blue line
shows his ship's voyage home after Cook was killed in Hawaii.

Magellan's ﬂeet between 1519 and 1522, his estimate of the
longitude of the Philippines was off by 53 degrees, or approximately 3,500 miles.
In 1612, two years after he discovered Jupiter's four
bright satellites, Galileo realized that their regular motions
could serve as a "universal clock" for determining longitude. In 1668 the great Italian-French astronomer Giovanni
Domenico Cassini published accurate tables of the positions
of Jupiter's satellites, which were used to improve maps of
Europe. The timing of other predictable astronomical events
such as solar eclipses, lunar eclipses, and occultations of
bright stars by the Moon could also be used, but they aren't
frequent enough to be practical.
Observing Jupiter's satellites is problematic because it
requires a stably mounted telescope. That's ﬁne when observ-

ing from land but problematic aboard a ship. What was
needed was a predictable astronomical event that happened
frequently and could be observed accurately at sea. In 1514
the German mathematician Johannes Werner suggested
using the distance between the Moon and the Sun or other
reference star for determining longitude. The Moon's orbital
motion causes it to move through the background stars at
13.2° per day, or 33′ per hour. So if the distance between the
Moon and a known star can be measured accurate to, say,
3.3′, that determines the time - and hence the longitude -
within six minutes, which is six nautical miles at the equator.
Unfortunately, unlike Jupiter's satellites, which are far
from the Sun and strongly bound to their massive planet, the
Moon is attracted roughly equally by Earth and the Sun, making its motion very complex. Only in 1755 did the German
astronomer Tobias Mayer come up with a way to compute the
Moon's orbit sufﬁciently accurately to be useful for the lunar
distance method.
The other alternative was to use a mechanical clock set to
Greenwich Time. By the mid-1700s the best pendulum clocks
had achieved an accuracy of a few minutes per year, but only
if mounted on a stable platform. At the time of Cook's ﬁrst
voyage (1768 to 1771), the only clock that could keep accurate
time at sea was John Harrison's H4 chronometer, which was
unavailable because it was being evaluated for the Longitude
Prize set up by the British Parliament in 1714.
But Harrison's H4 clock was only expected to provide
accurate time during the two-month trip from Britain to the
West Indies; its cumulative error would have made it almost
useless for Cook's multiyear voyages.
For his ﬁrst voyage Cook used lunar distances as his primary method for determining Greenwich Time. He measured
the angular distance between the Moon and the Sun or
reference star with a sextant, and recorded the local time. He
consulted the British Nautical Almanac to determine at what
time the angular distance would be the same if observed from
Greenwich.
Although the lunar distance method is simple in concept,
other factors make it more complex in practice. Atmospheric
refraction causes the Moon and the star to appear higher
than they actually are. The Moon is also close enough to
Earth that its apparent position must be adjusted for parallax. So in addition to obtaining the angular distance between
the Moon and the star, it's necessary to measure the altitudes
of the two objects above the horizon, as shown on page 62.
Applying the corrections for refraction and parallax (called
clearing) requires the use of spherical trigonometry. To simplify the computations, mathematicians developed a clever
method using logarithms. This operation didn't require the
t THE ONCE AND FUTURE SEXTANT Sextants use mirrors to superpose the images of two distinct objects, much as rangefinders in
old-fashioned cameras do. The angle between the objects can then be
read off a finely calibrated scale. In 2016 the U.S. Navy reemphasized
training with sextants, because they are immune to antisatellite weapons,
electromagnetic pulses, and hacking.

MARCH 2 02 0 * SK Y & TELESCOPE

M A P: JON PL ATEK / CC BY-SA 3.0; SE X TA N T: FOTOK A NN A N / CC BY 3.0

Celestial Navigation

Sky & Telescope - March 2020

Table of Contents for the Digital Edition of Sky & Telescope - March 2020