How far is it from Cape Town to London

1
How far is it from Cape Town to London ?

• Professor Alan Beardon
• University of Cambridge
• SA and UK schools

2
(No Transcript)
3
(No Transcript)
4
Basic calculation

• We need the distance on the surface, l, between A
  and B
• We will use R, the radius of the Earth, and the
  angle ?
• We can find ? if we first calculate the distance
  d

5
Calculating d

• First, we need to find the coordinates of A
• and B.
• If a point has
• (lat, long) (p,q), then
• Lets find d in a
• straightforward example

6
How far is it from A (lat, long) (0, 0) to
B (lat, long) (0, 90) ?

• Since this is a quarter of a great circle (why?)
  start by finding the distance using R 6380 km

7
How far is it from A (lat, long) (p, q)
(0, 0) to B (lat, long) (p, q) (0, 90) ?

• Calculate the coordinates for A and B

8
Calculating ?

• If l is the length of the arc we are trying to
  find

9
If A (R, 0, 0) and B (0, R, 0), what is the
distance between them on the surface ?

• Find 2 d using Pythagoras Theorem, and then d.
• Find sin ? from d and R ( 6380 km), and then ?.
• From ? and R, find l.

10
Calculating d

• The distance 2d can be found using Pythagoras
  Theorem in 3 dimensions