## Latitude

Earth can be divided into two half by taking a plane and divide as transverse. When we divide the Earth in 2 half, they are called as North and South hemisphere, as they contains North and South poles, and dividing line is called as Equator. As parallel to equator there many lines which are called as parallels and they are measured in Latitudes.

Parallel to Equator there is another line which is 23.5 degree north is called as Tropic of Cancer, and 23.5 degree south is called as tropic of Capricorn.

In the same way there are many parallel lines and each of those lines are invisibly divided in degrees. Difference in one degree is approximately 69 miles or 111 kilometers.

And again it is divided in minute and seconds.

1 minute difference of latitude is usually 9 kilometres.

## Longitude

The Earth is almost spherical in shape and it keeps revolving around its axis. The axis on which it rotates divides the earth longitudinally in 2 half. The zero degree Meridian is called as prime meridian which crosses the London Greenwich Observatory. One half of Earth goes towards east and other half goes towards west. So quite naturally the total angles of a circle which is 360 degree will be divided in 2 half and each half East and West will vary from 0 degree to 180 degree. These degrees of East and West are called as longitudes, and all those lines are called as Meridians.

Longitudes are also measured in degree, minutes and seconds however difference between longitudes is not always same as latitude, because it varies from equator to the pole. On equator difference is highest and at pole difference is zero.

At equator difference between each degree in longitude is equal to 111.32 kilometers, however at tropic of cancer and Capricorn which is at 23.5 degree of latitudes, difference between each minutes of longitude would be 103.8 kilometers, and as we move towards pole it would further reduce and gradually will become zero.

There is a video I found which is pretty good to understand quickly, you can watch it here.

https://www.youtube.com/watch?v=swKBi6hHHMA

## Polar Co-ordinate System

To understand this latitude and longitude mathematically, let’s take a reference of Geometrical co-ordinate system.

There are 3 major co-ordinate systems, which are being used a lot in our practical life.

- Cartesian (X, Y, Z)
- Polar (R, Phi, Lambda)
- Cylindrical (Row, Phi, Z)

Polar co-ordinate system is exactly same concept which is used to locate any point on Earth and they are called geographical coordinates.

- R is nothing but Elevation, mostly same as radius of earth which is almost constant
- Phi is Latitude
- Lambda is Longitude

So if we are only talking about Surface of Earth which is at constant radial distance from center of Earth then we can easily locate any point on Earth surface using only two variables, Phi and Lambda or Latitude and Longitude. I believe that is a reason we have chosen Polar co-ordinate system to locate any point on Earth, because in Cartesian system, we’ll have work with 3 variables.

Conversion of co-ordinate system from Cartesian to Polar and vice versa is very simple, below picture will bring good understanding.

## Conversion of latitude and longitude to distance

In a common understanding, how to translate degree of latitude and longitude to distance? Latitudes are parallels so they are usually same, and each degree of latitude would be approximately same as 111 km, but in longitude it depends on what latitude we are asking this question. However, the earth is slightly elliptical in shape and that creates a small variation between the degrees as we work our way from the equator to the north and south poles.

### How much of 1 degree of latitude difference at different points on Earth?

- At the equator, 1 degree of difference will result in distance as 110.567 kilometers
- At the Tropic of Cancer and Tropic of Capricorn (23.5° north and south), the distance is 110.948 kilometers
- At each of the poles, the distance is 111.699 kilometers

### How much is distance on Earth when latitude changes by 1 degree, 1 minute and 1 second?

- 1 degree = 111 kilometers
- 1 minutes = 1.85 kilometers
- 1 seconds = 31 meters

Unlike latitude, the distance between degrees of longitude varies greatly. They are farthest apart at the equator and converge at the poles.

### How much of 1 degree of longitude difference at different points on Earth?

- At the equator difference in 1 degree of longitude will result in distance of 111.321 kilometers
- The distance gradually reduces to zero as they meet at the poles
- At 23.5° north or south(tropic of Cancer Capricorn) the distance between a degree of longitude is 103.8 kilometers

### How do I calculate distance when longitude degrees varies?

Formula is simple, **Longitudinal distance = Cosine (latitude at that point) x Longitudinal distance at Equator (which is 111.32 kms)**

For example, 1 degree of longitude in New Zealand is how much distance?

New Zealand is at 40 degree of latitude of south, so longitudinal distance = Cos(40)x111.32 = 0.76×111.32 = 85 kms

In India, latitude is varies from 7 degree, which is almost Kanyakumari to 35 degree, 34 degree latitude is Leg/Laddakh, and Mumbai is at 19 degree, so different parts in India longitudinal distance will vary.

At Leh/Laddakah

- 1 degree of longitude = 111.32 x Cos(34) = 111.32×0.82 = 91.28 kms
- 1 minutes of longitude = 91.28 kms/60 = 1.5 kms (where as equator it 1.8 kms)
- 1 seconds of longitude = 1.5 kms/60 = 25.35 meters (where as equator its 31 meters)

I hope you’ve learnt out of this articles, please write your comments and provide feedback

Thank you.