Finding the distance between two points on the Earth

The next part is a little technical. You need to be able to find the distance between two points on the Earth, given their longitudes and latitudes. This will allow you to find the closest Weather Station to you.

If you’re not particularly interested in how this works, then rather than write the code, you can download the file you need from here. Just make sure it’s saved as haversine.py and stored in the same directory as the rest of your code.

As discussed earlier, we use longitude and latitude to work out the exact position of places on the Earth. Finding distances between these points is quite tricky, as the distance is over the surface of a sphere, and therefore not in a straight line. To do this calculation, you need a clever bit of maths called the haversine formula.

Without getting too technical, the haversine formula can provide the distance between two points on a sphere using longitudes and latitudes.

Create a new program by clicking on File > New File in the Python script.
Click on File > Save As and call your file haversine.py.
To begin with, you’re going to need a few functions from the maths library. Start off your file by importing the following:
```
from math import radians, cos, sin, asin, sqrt
```
Now you can define a new function, which we’ll call haversine. It’s going to take 4 arguments, which will be the longitude and latitude of the two points whose distance we need to find.
```
def haversine(lon1, lat1, lon2, lat2):
```
Most mathematical formulae require us to work in radians rather than degrees when dealing with angles, so the first thing to do is to convert each of the latitudes and longitudes passed into the function as arguments into radians.
```
def haversine(lon1, lat1, lon2, lat2):
    #convert degrees to radians
    lon1 = radians(lon1)
    lat1 = radians(lat1)
    lon2 = radians(lon2)
    lat2 = radians(lat2)
```
Now we want to find the difference between the two longitudes and latitudes, so add this into your function:
```
dlon = lon2 - lon1
dlat = lat2 - lat1
```
Now comes the tricky bit. If you want to know more about the haversine formula then you can have a read of the Wikipedia article linked above. Otherwise, you can just take it at face value that the following lines of code will calculate the distance between the two points:
```
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
distance = 2 * asin(sqrt(a)) * 6371 #6371 is the radius of the Earth
return distance
```

The number 6371 in the code above is the radius of the Earth

Save your file and run your program to test it.

In the Python shell type the following:

haversine(74.0059, 40.7128, 0.1278, 51.5074)

run the haversine function

You should get an answer of 5570. This is the distance from London to New York. You can check the answer online if you like, although the values will be slightly different as the Earth is not an exact sphere. It’s good enough for our purposes, though.

Try a few more longitudes and latitudes from Google Maps.

CoderDojo Kinsale

Fetching the weather

Finding the distance between two points on the Earth