Here is an outline of some of the aspects touched on:

• The tragedy on October 22nd, 1707
  • Admiral Sir Clowdisley Shovell
• Computing your position from bearings
  • Using bearings from North
    • Including error allowances
  • Using relative bearings between multiple points
    • Generalisation of Thales' Theorem
      • Thales was about 600BC
• Doesn't work over the horizon
  • What shape is the Earth?
    • Shadows during Lunar Eclipses show it's a sphere
    • Eratosthenes of Cyrene measured the circumference of the Earth
      • Summer Solstice (not necessary)
      • Reflected in a deep well => Sun overhead - no shadow
      • 7.2 degree shadow in Alexandria, some distance north
      • Divide by 2*pi to get the Radius of the Earth
    • Eratosthenes also invented Latitude and Longitude
  • How far is the horizon?
    • "Mountain" 5 metres high
      • How far to get to that point?
        • Uses Pythagoras - about 550BC
          • Pythagoras of Samos - student of Thales
            • Wouldn't accept Irrational Numbers
      • Add answers for total distance
• Out of sight of land
  • Measure Latitude with a Sextant or an Octant
    • How does that work?
  • Dead reckoning
    • Log / Knots
      • 7 fathoms in 30 seconds = 5040ft/hour
      • 47'3" in 28 seconds = 6075ft/hour
  • How do we measure Longitude?
    • That is the £6m question
• Prize offered in 1714 - 6 million pounds in today's money
  • Many methods suggested
    • wounded dogs
    • Anchored ships with flares and cannons
    • Measuring the Moon against a fixed star map
      • Parallax
      • Distance to the Moon?
        • Acceleration due to gravity - value of g?
          • Regular dropping - two ticks per second
          • Pendulum timing
    • Clocks
      • Existing clocks were out by minutes per day
        • Robert Hooke had a clock in the late 1600s
        • Required sub-second error
      • John Harrison, 1693-1776
        • H1 - still can be seen in the Worshipful company of Clockmakers Guild Museum
        • H4 - Met the requirement
          • Never given the prize
        • K1 carried by James Cook on his second and third voyages
          • not on his first to Tahiti for the transit of Venus
• Galileo Galilei
  • Acceleration is a time squared thingy
  • Analysed the pendulum
    • Or was that Isaac Newton?
• CPA / Closest Point Of Approach
• Intercept Problem
• Isaac Newton (1643-1727)
  • Royal Mint / Royal Society
  • Inverse square law of gravity
    • Acceleration due to gravity
  • Reflecting telescope
• GPS / Global Positioning System
  • Speed of light
    • 1638 Galileo Galilei
      • Lanterns
    • 1676 Ole Roemer
      • Eclipses of moons of Jupiter
        • Galilean Moons
    • 1728 James Bradley
      • Stellar Aberration (1/200 degrees)

• Newtons Cannon
• Orbital Velocity
• Orbital Period

Quotation from Tim Berners-Lee