### Author Topic: Kepler Motion  (Read 308632 times)

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Kepler Motion
« on: January 29, 2004, 06:22:37 pm »
Registed user can get files related to this applet for offline access.
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During the last quarter of the 16 century, the Danish nobleman Tycho Brahe provide careful observation of the planets over an extended period of time (20 years).
He hoped to use his data to verify his own model of the solar system, in which the sun orbited th earth and all other planets orbited the sun.
At Brahes death at 1601, his assistant Johannes Kepler inherited the data that Brahes had accumulated.
Kepler spend some 20 years analyzing these data, looking for mathematical regularities.
He came to the conclusion that the ideal of circular orbits should be discarded and replaced with elliptical orbits.
Kepler summerized his laborious study of planetary motion with the following three laws:
1. The planets move in elliptical orbits with the sun at one focus.
2. A line from the sun to any planets sweeps out equal areas in equal time.
3. The square of a planet's period is proportional to the cube of the planet's mean distance from the sun.
This java applet let you play with Kepler's laws and learn more physics insight.

Study ,

when initial conditions changed

The red circle at the center of the screen represent the sun.
The moving yellow circle is the planet.
The initial condition is represented by the blue arrow.
The planet start from the starting point of the blue arrow,
and its initial velocoty is proportional to the length of the arrow.

You can drag the blue arrow to change its initial condition in three different modes:
1. fixed kinetic energy
2. fixed angular momentum
3. arbitrary
Find out the relation between shape and size of the trajectory with the above parameters.

Right click the mouse button to suspend the animation. Click it again to resume.
What if you click it with the left mouse button? Find out by yourself.
Use reset button to clear the screen. (Try to compare different trajectorys before press it!)
You can select four different mode to play with it.
For the energy mode or while you drag the mouse button:
The lower green curve is the potential energy : U(r)=-GMm/r
another one is the effective potential energy Ueff(r)=-GMm/r + L2/(2mr2)

The following is a flash movie which shows you what you can do with the above simulation.

Two horizontal red lines show the total energy of the particle. (watch the small moving dots! )
The period of the particle motion is also shown in real time unit.

Registed user can get files related to this applet for offline access.
Problem viewing java?Add http://www.phy.ntnu.edu.tw/ to exception site list

• Guest
##### topic9
« Reply #1 on: January 30, 2004, 12:23:48 pm »
Subject: Re: thanks!
Date: Sat, 05 Dec 1998 18:52:08 -0500
From: dgoodwin <dgoodwin@1st.net>
To: Fu-Kwun Hwang <hwang@phy03.phy.ntnu.edu.tw>
Thanks so much for taking the time to send me the http for circular motion and
ang. mo. I really appreciate it. It's great stuff. Bye for now. Dave G.

Fu-Kwun Hwang wrote:

> I am really sorry for the late reply. This message was misplaced.
> There are two java applets related to the angular
> Kepler motion: http://www.phy.ntnu.edu.tw/java/Kepker/Kepler.html
> and circular motion
> http://www.phy.ntnu.edu.tw/java/circularMotion/circular3D_e.html
>
> dgoodwin wrote:
>
> > Do you have any applets on angular momentum??
> >
> > Fu-Kwun Hwang wrote:
> >
> > > dgoodwin wrote:
> > >
> > > > We were reviewing vector addition this evening at a study session.
> > > > Someone asked about help from the internet, so we searched and happened
> > > > to find your page. There were a few "ah-ha's" when the program showed
> > > > the parallelogram method for adding vectors so clearly. Thanks.
> > >
> > > I am very happy to know that you are enjoy the java applets. Any
> > > suggestions you might have about my java applets will be highly
> > > appreciated! Or , if you would like to have java applet one any topic
> > > related to physics,
> > > Just send me a note! Enjoy the virtual physics laboratory!

• Guest
##### topic9
« Reply #2 on: January 30, 2004, 01:44:33 pm »
Subject: Very Nice Applet
Date: Sun, 01 Aug 1999 18:34:25 -0500
From: Greg Hecht <ghecht@ix.netcom.com>
To: hwang@phy03.phy.ntnu.edu.tw
Very interesting and educational java applet, sir. My compliments.

I am not an astronomer but studied Kepler's laws years ago. Your applet
is the best tool I have ever seen to allow one to grasp the concepts.
Thank you for creating and sharing it.

Cheers,

Greg Hecht, MCSE
The Riverpoint Group, Ltd.
Kansas City

• Guest
##### topic9
« Reply #3 on: January 30, 2004, 01:49:23 pm »
Subject: kepler motion applet
Date: Thu, 23 Sep 1999 06:00:13 -0700 (PDT)
From: lee taishen <leetaishen@yahoo.com>
To: hwang@phy03.phy.ntnu.edu.tw
Dear Mr. Hwang,

Referring to the kepler motion applet in the below
http://www.phy.ntnu.edu.tw/java/Kepler/Kepler.html
I find it very interesting. However, I have some
difficulties when using the applet.

1. For second kepler law, the area of the shaded area
and non-shaded area should be the same. However, there
is no data showing what the area is.

2. for third kepler law, i observed that there is no
indication of the period of the planet. There is this
T value indicated in the applet but it is not the
period. i would appreciate if you can explain what the
T value is.

thank you.

best regards
leetaishen

#### shiva

• Newbie
• Posts: 1
##### topic9
« Reply #4 on: September 20, 2005, 12:07:53 am »
Dear Friend,
I am looking for applets related to rotational motion, angular momentum, torque and kepler's laws to teach my students.

Can anybody help me?

with thanks,
Shiva: s_iva20290@yahoo.co.in

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### topic9
« Reply #5 on: September 21, 2005, 08:16:02 am »
Please write down in more detail what kind of simulation you really want? (What kind of presentation/GUI view/...)

#### wuenscher

• Newbie
• Posts: 1
##### Source Code
« Reply #6 on: June 22, 2006, 04:19:32 pm »
Hallo,

you have written a nice applet.

I want to start writing physical applets. Could you send me some source code? It would help me to understand applet programming. :!:

At first I want to write an applet about the Kepler problem perhabs with an r^-a potential, so your applet would be a good start for me.

Thanks.

michael

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### topic9
« Reply #7 on: June 22, 2006, 04:34:51 pm »

#### Prihatmoko

• Newbie
• Posts: 1
##### Re: topic9
« Reply #8 on: March 03, 2007, 01:53:30 pm »
Hello Mr Hwang

I do believe that it is more beatiful if this applet give some addition by giving user a chance to change the eccentricity of ellips, so people like me can also watch how much different between the rotation of earth and pluto...even it is a planet no more

Thanks....

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Kepler Motion
« Reply #9 on: March 04, 2007, 10:50:26 am »
You can do what you want with that applet.
If you did not change the default setting in the applet: Fix kinetic energy when change initial conditions.
You will get planet motion with the same eccentricity of ellips.

However, if you change it to "fix angular momentum", then you will get  planet motion with different eccentricity of ellips.

That is why I add the following sentences in the page:
Quote
You can drag the blue arrow to change its initial condition in three different modes:
1. fixed kinetic energy
2. fixed angular momentum
3. arbitrary
Find out the relation between shape and size of the trajectory with the above parameters.

I hope students can really play with it and discover the difference , and figure out some relations!

#### tropical72

• Newbie
• Posts: 1
##### Re: Kepler Motion
« Reply #10 on: April 23, 2007, 01:57:10 pm »
Dear Mr.Hwang

I'm a student majoring in CS. I'm preparing a code of Kepler's law.

Luckly I found your homepage and saw the simulation. That's really cool and great.

I tried your simulation for a long time and became curious how it was implemented.

If it's possible, could you send me the source code of the simulation?

That's would be greatly helpful to know the Kepler's Law and the Java programming both.

Hyuck

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Kepler Motion
« Reply #11 on: April 23, 2007, 04:39:08 pm »
I just sent you the source code. You should have received it now.

#### shiksha12

• Newbie
• Posts: 3
##### Re: Kepler Motion
« Reply #12 on: October 01, 2007, 07:19:17 am »

« Last Edit: October 07, 2007, 06:11:59 am by shiksha12 »

#### Fu-Kwun Hwang

• Hero Member
• Posts: 3062
##### Re: Kepler Motion
« Reply #13 on: October 06, 2007, 06:51:11 pm »
I do not know how to help because you did not say what kind of help you need!

#### shiksha12

• Newbie
• Posts: 3
##### Re: Kepler Motion
« Reply #14 on: October 07, 2007, 06:11:18 am »

« Last Edit: October 09, 2007, 01:24:30 am by shiksha12 »