1. 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.

2. 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

3. Measuring longitude requires determining your angle from a reference line on Earth

4. 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

5. 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.

6. Accurate ephemeredes of Jupiter’s moons became available in 1668 Gian Domenico Cassini

7. The problem was it isn’t possible to accurately measure the moons of Jupiter from the deck of a rolling ship

8. 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

9. Next came attempts to use the Moon to measure time An eclipse is seen by everyone on Earth at the same time

10. The location of the Moon with respect to the background stars could be used if…

11. Nevil Maskelyne, Astronomer Royal, published his first Nautical Almanac in 1766

12. Again, the problem is making astronomical observations from the deck of a rolling ship at sea

13. John Harrison came up with the solution: make an accurate and stable clock

14. Harrisons 1 st attempt in 1735 used a double pendulum design

15. He continues with several other models H3 front and backH4 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

16. His final model, H5 built in 1770, has better than the required accuracy

17. James Cook took one of the copies on a voyage to the Pacific

18. It took many years and a Royal Decree before Harrison was finally awarded £ 8,750 by act of Parliament in 1773

19. 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

20. The orbits of all the planets are known to have long-term variations

21. 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

22. Lagrange and Laplace showed the seemingly non-periodic variations were, in fact, periodic LagrangeLaplace

23. Laplace eventually forms a theory for why the solar system is as it is

24. Laplace’s Traite de mecanique celeste becomes the standard of celestial mechanics

25. 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

26. On March 13, 1781 William Herschel discovered Uranus Its’ orbit matched the Titus-Bode Law

27. Baron Franz Xaver von Zach quickly forms the “Celestial Police” to hunt down the missing planet between Mars and Jupiter

28. Purely by chance, Giuseppi Piazzi discovers the “missing planet” on January 1, 1801. He names it Ceres

29. Ceres is “lost” for a while but Carl Friedrich Gauss, at the Berlin Observatory, calculates an orbit and re- finds it

30. Within a year Heinrich Olbers discovers another body he names Pallas

31. By 1807, two more objects, Juno and Vesta are discovered

32. 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