Frontiers and Controversies in Astrophysics: Lecture 3 Transcript
January 23, 2007
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Professor Charles Bailyn:
Okay now, we didn't have sections this week, in case you didn't notice, and
therefore you didn't have an opportunity to discuss the problem set during section. So, I thought I would say a
few words about it now - here is the problem set. You probably can't read it at this typeface but that's okay.
So, let's see, problem zero is just a stupid way of making you read the policies. Never mind that. Problem set
one, problem one: here are exercises in one-digit scientific notation. I don't have rules for this. As I
mentioned last time, the only rule is common sense. I think there might be some difficulty with the last one.
This business of taking things to the one third power is important because you keep ending up with a cubed
equals something, and you have to figure out what to do about that. So, let me not do this particular problem,
let me do a different one for you.
Supposing you had (6 x 10
4
)
1/3
. And you might be tempted to say, well okay, that's 6
1/3
times 10
4/3
. And that
leads you to a bad place, because 10
4/3
is not the notation we want. We want this to be an integer up there.
What does it mean to be a 1 with 4/3 of a zero after it? And so, you don't like that. So, the way to deal with
this is to regroup. This is (60 x 10
3
)
1/3
. That's 60
1/3
x 10
1
. What's 60
1/3
? Well, 4 times 4 times 4, as it
happens, is 64, and that's close enough for me. So, this is 4 x 10
1
. So, that's just an example of how these
kinds of things where you take things to fractional powers, either the square root, which is to the 1/2, or the
cube root to the 1/3.
All right, the next problem. Let's see, Neptune's moon Nereid has an orbital period of almost exactly one
Earth year. If the mass of Neptune is something or other, what's its semi-major axis? So, you have
P
and
M
and you're asked for
A
. That's a completely straightforward plug-and-chug problem because there's an
equation that relates these three things and the only tricky thing about this is that you have to make sure the
units come out right.
All right, the next one looks similar in form, but it isn't. Consider a Sun-like star orbited by a planet with a
period of eighty years. So, we have
P
--the separation of the planet and the star appears to be 20 arc seconds.
So we have an angle, that's
Î±
. How far away is the star? And you want to know
D
. Okay, there is no equation
that contains all three of those things and so this, although it looks similar in form, is actually a substantially
more difficult problem.
Going on, problem four. Okay the important--in fact, there is such a star, blah, blah, does this fact make any
difference in the forgoing calculation? Explain. The important thing to note about this is that I'm not asking
you to do a calculation. This is not a calculation problem; this is a comment. You're supposed to say
something about how the calculation would go if you were to do it, but you don't have to actually calculate
anything there.