Editing MaritimeMaths
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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? ***** 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 pages: * Newtons Cannon * Orbital Velocity * Orbital Period ---- CategoryMaths