Maritime Maths
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The aspects touched are:
The tragedy on October 22nd, 1707
Admiral Sir Clowdisley Shovell
Computing your position from
bearing
s
Using
bearing
s from North
Including error allowances
Using relative
bearing
s 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 Eclipse
s 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 Number
s
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 /
Knot
s
7
fathom
s in 30
second
s = 5040ft/hour
47'3" in 28
second
s = 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
Eclipse
s of
moons of Jupiter
Galilean Moon
s
1728
James Bradley
Stellar Aberration
(1/200 degrees)
Other pages:
Newtons Cannon
Orbital Velocity
Orbital Period
CategoryMaths
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