## Lecture 10: Pluto, Minor Planets, and Asteroids

Free video lectures for anyone with curiosity and a web browser.
RJN
Baffled Boffin
Posts: 1670
Joined: Sat Jul 24, 2004 1:58 pm
Location: Michigan Tech

### Lecture 10: Pluto, Minor Planets, and Asteroids

The lecture video is embedded below but also available here in MP4 format.
Additionally, slides used in the lecture are embedded below but also are available here in Powerpoint format.
Click to play embedded YouTube video.
Wikipedia entries:

Smallfish
Asternaut
Posts: 2
Joined: Sun Feb 14, 2010 11:48 am

### Lecture 10

Dear all!

I enjoy listenning to these lectures. I determined to watch all of them, watching the video file and the pps file simultaneously. Switching between them all the time. (Alt+tab)

I've just stuck here with counting...

In the 10th lecture you can see Kepler's laws. The third one is quite simple. (see: 14th pic or 22:09 in the vid) It is a simplification of the REAL Kepler's 3rd law (http://en.wikipedia.org/wiki/Kepler%27s ... ary_motion see Deriving Kepler's third law ). Still, it becomes fuzzy when Mr. Nemiroff starts to count. (25:57) Somehow it is not OK. Firstly you may think that because he misses the "/M" part of the formula. But the formula is actually wrong. "/M" needn't be there. And what's then? Still wrong result you get. Because the official radius is estimated from the Perihelion (closest to the Sun) and the Aphelion (furthest from the Sun). It is the mean of these numbers.

(Q + q)/2=r
r=(2.544+2.987)/2=2.7655

Mr. Nemiroff supposes, that the ellipticity (~excentricity) is the problem. So it is. But It wasn't so convincing...

I still enjoy this course, and looking forward for more "fun stuff" as he calls it. I mean counting.

Smallfish
from Hungary

RJN
Baffled Boffin
Posts: 1670
Joined: Sat Jul 24, 2004 1:58 pm
Location: Michigan Tech

### Re: Lecture 10

Smallfish,

Thanks for your questions. In the wikipedia link you highlight below on Kepler's laws, it shows that really the full relation for Kepler's third law would include mass. In the "Non-Planetary Mass" section, one sees that a^3/P^2 is proportional to M+m. Since M for the Sun is so much higher than m for a planet, the planetary mass can be ignored. Next, since M is the same for all of the planets -- they all revolve around the same Sun -- the proportionality constant is the same for all of the planets and so one can just estimate that a^3 is proportional to P^2.

Next, yes, I assumed in applying Kepler's third law that the orbit is close enough to circular that "a", actually half the major axis, is close enough to all other distance measures between a planet and the Sun. Even if this is off by 20%, I felt that simplicity was more important that accuracy at that level. I apologize if you found this confusing.

- RJN

rhiansung14
Asternaut
Posts: 1
Joined: Thu Aug 05, 2010 3:35 am

### Re: Lecture 10

The lecture is about our solar system, right? I was interested when it comes to that discussion. Kepler's laws were derived for orbits around the sun, but they apply to satellite orbits as well.

JCGJ

### Re: Lecture 10: Pluto, Minor Planets, and Asteroids

I'm taking a highschool astronomy class, and I am doing a research paper on Pluto and the Dwarf Planets. This lecture was very helpful and informative. After watching this one, I would like to watch some of your other lectures as well. Thank you very much for this very helpful resource.

SpaceTas

### Re: Lecture 10: Pluto, Minor Planets, and Asteroids

Kepler's laws apply to any (non relativistic) orbit. If express semi-major axis in AU, and period in years, the simple version works. All laws can be dreived from Newtons laws of motion and his law for Gravity. So Yes, they works for moon, artificial satellites and stars.

Gary S

### Re: Lecture 10: Pluto, Minor Planets, and Asteroids

In lecture 10 slide 9 you state about Pluto, "Diameter 2/3 smaller than the moon."
I think that is a confusing way to put it - it's diameter is 2/3 AS LARGE as the moon's."
"2/3 smaller" would mean it is only 1/3 as large.
But thanks for your efforts anyway.
Gary