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File: MaritimeMaths [[[> A MathematicsTalk given _ by ColinWright _ _ TaggedAsTalkDescription ]]] "Maritime Maths" introduces the audience to what was the major practical problem of the early 18th Century - safe navigation at sea. 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) Other topics: * Newtons Cannon * Orbital Velocity * Orbital Period ----