Post on 16-Jan-2016
Announcements• Next exam is scheduled for Monday March 31. Due to the ice week, it will be delayed one week to Monday April 7. Tentatively will cover the rest of Chapter 5 (from Kepler) and all of Chapter 6 and some of Chapter 7. Sample questions will be posted tomorrow.
• Dark Sky Observing Night tonight! Forecast looks good: clear but cold. Set-up starts at 7:30pm.
The problem of Longitude
Finding your latitude is easy, just measure the altitude of Polaris to get close. To be precise you need to know how far Polaris is from the NCP
Measuring longitude requires
determining your angle
from a reference
line on Earth
The Longitude Act of 1714 offered a £20,000 prize for an
accurate method of determining longitude at sea
The matter was brought to a head after a particularly disastrous shipwreck in 1707 in which four large ships and over 1400 sailors of the Royal Navy perished
Early methods involved measuring the moons of Jupiter
Once their orbits were determined, ephemeredes could be generated to show their location at any time in the future. Then all you have to do is accurately measure your local time.
Accurate ephemeredes of Jupiter’s moons became available in 1668
Gian Domenico Cassini
The problem was it isn’t possible to accurately
measure the moons of
Jupiter from the deck of a rolling ship
If you could accurately measure the difference between true north and magnetic north, that might work
Problem was the magnetic pole isn’t stable, it moves over time
Next came attempts to use the Moon to measure time
An eclipse is seen by everyone on Earth at the same time
The location of the Moon with respect to the background stars
could be used if…
Nevil Maskelyne, Astronomer Royal, published his first Nautical
Almanac in 1766
Again, the problem is
making astronomical observations from the deck
of a rolling ship at sea
John Harrison
came up with the solution:
make an accurate and stable clock
Harrisons 1st attempt
in 1735 used a double
pendulum design
He continues with several other models
H3 front and back H4 tested in 1764
H4 passes several sea trials and meets all the requirements but isn’t awarded the prize due to “land trials” at Greenwich
His final model, H5 built in 1770, has better than the required accuracy
James Cook took one of the copies on a voyage to the Pacific
It took many years and a
Royal Decree before
Harrison was finally awarded £8,750 by act of Parliament
in 1773
Chaos in the Solar System
At its very inception, Newton knew that it would be impossible to get a “closed solution” to the three body problem
The orbits of all the planets are known to have long-term variations
The biggest problems were with the orbits of Jupiter and Saturn
Their interactions led to periodic variations and what appeared to be non-periodic changes
Lagrange and Laplace showed the seemingly non-periodic variations
were, in fact, periodic
Lagrange Laplace
Laplace eventually forms a theory for why the solar system is as it is
Laplace’s Traite de
mecanique celeste
becomes the
standard of celestial
mechanics
The “missing planets” problem
The Titus-Bode Law predicted a planet between Mars and Jupiter. At the time, Uranus
and Neptune had not been discovered
0.4 0.3 2 ,0,1,2,3,4,...ma where m
On March 13, 1781 William Herschel discovered Uranus
Its’ orbit matched the
Titus-Bode Law
Baron Franz Xaver von Zach
quickly forms the “Celestial
Police” to hunt down the
missing planet between Mars
and Jupiter
Purely by chance, Giuseppi Piazzi discovers
the “missing planet” on
January 1, 1801. He names it
Ceres
Ceres is “lost” for a while but Carl Friedrich Gauss, at the
Berlin Observatory, calculates an orbit and re-
finds it
Within a year Heinrich Olbers discovers another body he names
Pallas
By 1807, two more objects, Juno and Vesta are discovered
Olbers thought all the asteroids originated from
a single “exploded” planet but
orbital calculations
proved otherwise By 1850 over a dozen objects
had been discovered