Lecture notes - Week 1.
First lecture:
Course policies (separate handout)
Measuring the solar system with similar triangles:
Figure 1.4 of Consolmagno and Schaefer shows how to measure the ratio
(Distance Sun to Planet)/(Distance Sun to Earth)
(which is also the size of the planet's orbit in Astronomical Units) for inferior planets.
Here is the corresponding diagram for a superior planet:
Opposition
Quadrature
B
A
Quadrature
C
Conjunction
The triangles to be used to find the relative orbit sizes are labelled A-B-C. What do
you need to measure to get either angle ABC or angle BCA? Hint: What is at A?
What is at B? What is at C?
A fine point: Of course, Earth is moving too. So we imagine that we are sitting on a
turntable that rotates with Earth, i.e. one revolution per year. In that system, the
superior planet's motion is not simple, because Earth moves more quickly than the
superior planet does. However, as long as Earth's orbit is approximately circular, so
its motion is constant, we can go ahead and interpret the measurements as though
the Earth were at rest and the superior planet moving around it at constant speed.
In this coordinate system, the apparent motion of the planet is the difference
between its motion and Earth's motion. Opposition dates will be separated by the
Synodic Period, S, related to the true or Sidereal Period, P, by
1/S = 1 - 1/P
As P gets long - 250 years for Pluto, for example - S approaches 1.
This formula works only for planets with periods >1 year.
Note on orbits:
The orbits of the planets are nearly circular, so for the present set of exercises we
will pretend that they are circular. For circular orbits the distance Sun-Planet = the
radius of the orbit. In the more general case we will need to use the semi-major
axis, a:
2a
Measuring distances in the solar system:
The geometric methods give you just the relative distances to the planets, or,
equivalently, the distances in units of Astronomical Units = average Earth-Sun
distance. Measuring the AU in km requires measurement that relates the distances
in space to distances measured on the ground. What are some ways that that could
be done? The book discusses one or two; there are a number of others, and these
will be discussed in class/on HW1.
The question of how to measure the fundamental properties of astronomical objects
is not trivial. Consider some of the following:
The mass of Earth
The mass of the Moon
The mass of the Sun
The masses of planets other than Earth
Distances to the nearest stars
The temperature of the Sun's surface
The temperature of the center of the Sun
...
These are numbers that are easy to look up, now; but each of them presented a
major challenge to measure. We'll discuss many of these during the course of 342.
Lectue 2: This will emphasize discussion of Chapter 1, HW1, and some of the ideas
listed above.
Lecture 3: We will meet in the MacLab (Room B49) to give you a chance to work on
HW1 and explore the capabilities of the Voyager™ program.