It is also very easy to do Newtonian orbits in etoys, if full precision is 
used for acc, vel, and position properties. The script looks just as one 
would like: do this in a playfield with origin at center, place the sun 
there, and the vector distance of the earth is also its distance to the 
sun. It's not science to claim inverse square, but it's one of the 
plausible hypotheses with an analogy to the intensity of light. Newton 
actually proved his stuff as math long before he got to the last books 
where he looked to see how the phenomena in the world behaved. Given this 
as an hypothesis, the script is straightforward: the strength of the force 
being inversely proportional to the square of the distance, and the 
direction of the accelleration is the opposite direction of the vector that 
is the Earth.

Cheers,

Alan

At 01:18 PM 12/23/2004, Alan Kay wrote:
>First, I strongly suggest that you get the Powerful Ideas in the Classroom 
>book and use the sequence of projects to help your child build some 
>competence in thinking along the lines of etoys. It has some approaches to 
>helping children think about speed and accelleration.
>
>Also, there is a very good way for younger children to find out and derive 
>a nice script that does what gravity does near the surface of the earth 
>(as Galileo found out 400 years ago). The difference between this and 
>Newton's more complex theory is less than 1 part in a million near the 
>surface of a planet like Earth. This is good science for 4th and 5th graders.
>
>There are any number of ways to do Lunar Lander. After doing the above, 
>you should see if you can induce the vertical landing one. This is a fair 
>amount of stuff for a 9 year old to handle (if you want him to really be 
>doing it and not just doing "air guitar").
>
>I don't think that I quite understand what you want to do with heading. 
>However, you can do something like the following:
>
>ship gravity ticking
>     ship's accelleration <-   -1.0
>     ship's speed increase by ship's accelleration
>     ship's y increase by ship's speed
>
>This will always try to pull the ship vertically downwards, by "eating 
>speed". But you can also move the ship around according to where it is 
>pointing.
>
>ship moveAround ticking
>     ship forward joy's updown
>     ship turn joy's leftright
>
>This doesn't do F=ma, but is still quite fun for children since they still 
>have to take care not to crash because of gravity.
>
>An independent project that is also very interesting is F=ma for 
>spaceships, which can easily be done by using the "vector vocabularly" 
>that is normally turned off for young children. The idea here is that each 
>object in etoys is de facto a 2D vector (it has an x and y coordinate). 
>The playfields of etoys have their own coordinate systems, and there is a 
>"playfield option" in the red menu that will put "origin at center". This 
>allows you to make a smallish playfield and plop a small dot of paint into 
>it that will act as a vector quantity (there is a nice lead up to this). 
>"increase by" works both for numbers and on players themselves, so you can 
>have a little blob of paint that acts as an accelleration vector, one that 
>is the speed vector, and the spaceship itself is its own vector. It is 
>very easy to use the y axis of the joystick to provide accelleration in 
>the direction the ship is heading, and the x axis to turn the ship with 
>its gyros. This gives a very good model of F=ma. If the spaceship, its 
>vectors and its controls are put in a playfield, a copy of the playfield 
>will yield another playfield with a spaceship and controls with all local 
>references done properly. The second spaceship can then be repainted, etc.
>
>However, I suggest not doing this for a while with your child. A large 
>part of adults helping children learn powerful ideas is to moderate the 
>tempo of most children. Like most humans they want results more than 
>learning ideas. It is the adults' main job to keep the tempo both slow 
>enough and thinking deep enough so that the kid will not just be making up 
>a cookbook of pragmatic patterns in their head, but actually understanding 
>what is going on. It is the lack of understanding (and not understanding 
>that they don't understand) that makes people quite scary.
>
>Cheers,
>
>Alan
>
>
>
>At 06:33 PM 12/22/2004, Blake wrote:
>>On Wed, 22 Dec 2004 14:21:44 +0100, Bert Freudenberg <bert at impara.de>
>>wrote:
>>
>>>Am 22.12.2004 um 09:02 schrieb Blake:
>>>>The Lunar Lander project I have in mind requires the ship to be able to
>>>>actually change its heading, but I can't just use the forward script,
>>>>obviously, because the effects of gravity have to be considered.
>>>
>>>That sounds overly complicated. Adding in gravity is just accelerating
>>>along y, right? No heading needed for that ...
>>
>>Adding in the gravity isn't the problem. Adding in the thrust is. Changes
>>to momentum along the X and Y axis caused by the thruster are,
>>
>>I could get the same ultimate result, I think, by moving forward and then
>>pulling the ship down--but that would look terrible, since the two motions
>>would be discrete, creating a step-like appearance when the ship is
>>travelling up and to the right.
>>              /
>>           /\/
>>        /\/
>>     /\/
>>  /\/
>>/
>>Unless I miss something.
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