There are several ways to detetime the latitude and longitude of your location using celestial observations. Ofcourse, these methods will not provide accurate angles of the latitude and longitude compared to a GPS but still, it helps.
Find longitude using time
In order to determine your longitude, first, you have to find the time difference between the local meantime and the Greenwich meantime. We know that the meridian passing through Greenwich is universally adopted as the prime or zero meridian.
A prime meridian is a meridian (a line of longitude) in a geographic coordinate system at which longitude is defined to be 0°. For example, if you are in Greenwich, UK, then your angle of longitude is 0°.
We know that a day has 24 hours and the angle for one full rotation of Earth is 360°. Now, divide 360°/24 hours = 15°/hour. One hour of time difference corresponds to 15° of longitude.
For example, let’s say that the local mean time at your place is 5:00 p.m. And the Greenwich mean time is 12:00 p.m. The time difference here is 5 hours. Multiply 5 hours x 15°/hour = 75°. Your angle of longitude is 75°.
For example, if you are in Melbourne, which is 10 hours away from Greenwich meantime, then your angle of longitude is (10 hours x 15°/hour) approximately 150° E.
If you are in New York, which is 5 hours behind the Greenwich mean time, then your angle of longitude is (5 hours x 15°/hour) approximately 75° W.
Similarly, you can calculate the time if you know the longitude. For example, If you are near Mumbai at a longitude of 73.5° E, then, 73.5°/(15°hour) = 4.90, which is 5 hours and 30 minutes. So, time at Mumbai is GMT+5:30 hours.
Find latitude using pole star
You can find latitude using the angle between the pole star and your horizon. A pole star is a star that is aligned to the axis of rotation of Earth. We have a northern pole star called Polaris (Alpha Ursae Minoris), which is closely aligned to the north pole. And we also have a southern pole star called Sigma Octantis (Polaris Australis). These stars are helpful in celestial-based navigation.
Find latitude in the northern hemisphere.
If you are located in the northern hemisphere, the latitude of your exact position can be determined using the pole star Polaris. Polaris is a bright star with a magnitude of 2 and can be easily seen with your naked eye.
To determine your latitude, you will have to measure the angle between Polaris and your horizon. For example, if you are located exactly at the north pole, then Polaris will be right above your head. So, it’s angle will be 90°. Latitude will be 90° too.
Similarly, if you are located at the equator, Polaris will be at your horizon, which is a 0° angle, i.e., the equator. Measuring that angle between Polaris and the horizon from your position will give you the angle of latitude.
Find latitude in the southern hemisphere
If you are located below the equator, i.e., in the southern hemisphere, then Sigma Octantis is your pole star. It is a fainter star with a magnitude of around 5.47 which varies about 0.03 every 2 hours and 33 minutes. Just follow the same procedure as stated above but with Sigma Octantis as your reference star.