## Most recent change of MaritimeMaths

Edit made on July 16, 2008 by RiderOfGiraffes at 22:15:06

Deleted text in red / Inserted text in green

WW
This is one of the talks that Colin does.

The aspects touched are:
* The tragedy on October 22nd, 1707
* Computing your position from bearings
** Using bearings from North
*** Including error allowances
** Using relative bearings between multiple points
*** Generalisation of Thales' Theorem
* 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
* Out of sight of land
** Measure Latitude with a Sextant or an Octant
*** How does that work?
*** 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?
***** Value 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 hist firstm 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-????) (1643-1727)
** RoyalMint Royal Mint / Royal Society
** Inverse square law of gravity
*** Acceleration due to gravity
** Reflecting telescope
* GPS / Global Positioning System
** Speedoflight Speed of light
*** 1638 Galileo Galilei
**** Lanterns
*** 1676 OleRoemer Ole Roemer
**** Eclipses of moons of Jupiter
***** Galilean Moons