Imagine the coastline disappears behind you.
There is no GPS. No radio beacon. No map app showing a blue dot.
You have the horizon, the Sun, the stars, a clock, and a chart.
How do you know where you are?
Quick Answer
Sailors had to solve two different problems.
Latitude tells how far north or south you are. It could often be estimated from the altitude of the Sun or a known star above the horizon.
Longitude tells how far east or west you are. That was much harder because it required a reliable way to compare your local time with a reference time.[1]
Latitude was largely an angle problem. Longitude became a time problem.
Latitude: Measure the Sky
The simplest idea is familiar from our earlier articles.
Measure an angle between the horizon and a celestial object whose position is known.
In the Northern Hemisphere, the altitude of Polaris gives a useful approximation to latitude. NOAA notes that this kind of celestial-angle method made latitude practical centuries before equally reliable longitude at sea.[2]
The Sun can also be used, but the calculation depends on the date and the Sun's changing declination.
So the mental model is not simply “look at one star.” It is:
measure an angle → compare with known celestial geometry → infer latitude
Longitude Was the Hard Part
Earth turns once in about 24 hours.
That gives a wonderfully useful conversion:
360° / 24 h = 15° per hour
If you know the time at a reference meridian and the local solar time on your ship, their difference tells you how far Earth has rotated between those two longitudes.
But there was a brutal engineering problem: the clock had to keep accurate time on a moving ship for weeks or months.
Figure 1. A useful simplification: angles help with latitude; accurate time makes longitude possible.
A Two-Hour Difference Means 30 Degrees
Suppose it is local solar noon on your ship.
Your reference chronometer, kept on Greenwich time, reads 14:00.
Local noon is two hours behind Greenwich noon.
2 h × 15°/h = 30°
In this simplified example, the ship is about 30° west of Greenwich.
Real celestial navigation adds corrections, astronomical tables, and careful observations. But the underlying connection between time and longitude is this simple.
John Harrison Made Time Portable
By the early eighteenth century, the longitude problem had become urgent enough for the British Parliament to offer major rewards through the Longitude Act of 1714.
John Harrison, a self-taught clockmaker, spent decades developing marine timekeepers that could keep useful reference time at sea. His H1 appeared in 1735, and his later H4 performed strongly in an Atlantic trial beginning in 1761.[3]
Harrison's story is important, but it should not be told as if clocks were the only serious solution.
Astronomers also developed the lunar-distance method, using the Moon's changing angular position relative to stars and carefully prepared tables. By the 1760s, Harrison's timekeeper and astronomical methods were being tested side by side.[4]
The longitude problem was not only a mathematics problem. It was also an instrument, data, and accuracy problem.
Python — Turn Time Difference into Longitude
Here is the simplified local-noon calculation. East is positive; west is negative.
def longitude_at_local_noon(reference_time_hour):
local_solar_noon = 12.0
time_difference = local_solar_noon - reference_time_hour
return 15.0 * time_difference
longitude = longitude_at_local_noon(14.0)
print(longitude, "degrees")The result is:
-30°
Negative means west in this convention.
Predict first.
At your local noon, suppose Greenwich time is 16:00.
How many degrees west should the simplified calculation give?
The Surprising Modern Connection: GPS Still Needs Time
Modern GPS does not navigate the way an eighteenth-century sailor did.
GPS receivers determine position from signal travel times and distances to satellites. But that makes precise time even more important, not less.
NIST notes that GPS satellites carry atomic clocks and that precise time is fundamental to modern positioning.[5]
The instruments changed from a sextant and marine chronometer to radio signals and atomic clocks.
The deeper engineering pattern survived:
measure carefully → compare with a reference → compute position
Words to Keep
latitude
North-south angular position on Earth.
longitude
East-west angular position relative to a chosen reference meridian.
sextant
An instrument used to measure angles between celestial objects and the horizon.
marine chronometer
A precise timekeeper designed to maintain reference time at sea.
celestial navigation
Navigation using observations of the Sun, Moon, stars, planets, and time.
One Sentence to Keep
Before GPS, sailors turned celestial angles and precise time into latitude and longitude.
What Should We Ask Next?
By now, we have watched people measure circles, Earth, shadows, stars, positions, maps, images, and ocean voyages.
Why did so many practical problems keep producing new mathematics?
Next: Why Did Maps, Ships, and Stars Push Mathematics Forward?
Previous: How Did Renaissance Artists Put 3D Space on a Flat Page?
Sources & Further Reading
- Royal Museums Greenwich, “Time and Longitude” — why latitude was practical earlier and longitude remained difficult at sea.
- NOAA Ocean Service, “What is latitude?” — celestial-angle methods for approximate latitude.
- Royal Museums Greenwich, “Longitude found — Harrison's timekeepers” — Harrison, H1–H4, and sea trials.
- Royal Museums Greenwich, “Longitude found: Nevil Maskelyne and the lunar method” — astronomical alternative and competing longitude methods.
- NIST, “Knowing Where We Are” — timekeeping from Harrison to GPS atomic clocks.
Teaching note: the time-to-longitude example is deliberately simplified. Historical navigators needed astronomical corrections, tables, instrument calibration, and careful observation.