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