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This is one of the talks that Colin does.

The aspects touched are:

* 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 EQN: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

**** That means from 5m high, distance to the horizon is that

**** 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?

*****

****** 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

* 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

**

** Inverse square law of gravity

*** Acceleration due to gravity

** Reflecting telescope

* GPS / Global Positioning System

**

*** 1638 Galileo Galilei

**** Lanterns

*** 1676

**** Eclipses of moons of Jupiter

***** Galilean Moons

***

**** Stellar Aberration (1/200 degrees)

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CategoryMaths