Lecture Notes

Day 13 February 25, 1997
WE WILL BE IN THE PLANETARIUM EVERY THURSDAY, EXECPT FOR MARCH 20 WHEN WE WILL HAVE QUIZ #2
• In class we reviewed the answers to quiz #1. The average was 15.2.

• We also showed slides of the multiple fragments of comet Shoemaker-Levy just before it impacted Jupiter. Is break-up into so many fragments means it must have been very fragile, consistent with it being a loosely held-together dirty snowball. Series of craters on Callisto and the moon were probably produced by similar multiple fragments of a comet.

• The equation of the week is Keplers Third Law: a cubed equals P squared: a3 = P2 Where a is the semi-major axis of an ellipse (also the radius of a nearly circular orbit) and p is the period. In our solar system, the equation works when a is measured in astronomical units and p is in years.

• For example, in the case of the earth a=1 and P = 1;

• In the case of Halleys comet, P = 76 years, and a is calculated to be 18 astronomical units, meaning that the average orbit of the comet is between Saturn and Uranus.

• Another example of the use of this equation is to calculate resonances in the asteroid belt. A 1:2 resonance with Jupiter, in which an asteroid orbits twice for every orbit of Jupiter and has therefore a period of 9.93 years, produces a gap in the asteroid belt at a distance of 3.28 au. This gap is one of many known as Kirkwoods gaps. Each of these gaps are smoking guns of this interaction with Jupiter which sends them across the orbits of Mars and Earth; many of them will impact on the surfaces of those planets. Other major resonances occur at 1:3, 1:4, 2:7,2:5, and 3:7, each of which has a Kirkwood gap associated with it. Read more about resonances in Chapter 15 and on page 352.

• Both comets and asteroids have rained down upon the earth in the past. The extinction events on the earth which appear to have a periodicity of 30 million years may have resulted from rains of comets coming into the inner solar system every 30 million years. They may have been triggered by a "death star", a faint, cool dwarf companion of the sun, too faint for us to have detected. That star may have an orbit that crosses the Oort comet cloud periodically, and releases some of its members. The total mass of the Oort comet cloud is large, some 100 earth masses; that of the asteroid belt is small by comparison, only .04% the mass of the earth.

• Chapter 4 deals with the Copernican revolution, which dagged humankind kicking and screaming from the geocentric cosmos to the heliocentric cosmos.

Read about its major figures: Copernicus, Tycho Brahe, Johannes Kepler, Galileo, and Newton in Chapter 4.