sundial seen "from space"

gengiskunk shared this question 6 years ago
Answered

Hello to all,

I'm trying to show the functioning of a sundial on earth seen "from space."

I am attaching the file that has not yielded the expected results.

The trace left of the shadows on the "floor" terrestrial poli1 (in solidarity with the movement of the earth's rotation) does not generate the hyperbole that I expected.

Looking good, the trace left by the point P does not lie on poli1 but is represented in the 3D view.

It will be what maybe the problem?


As usual, thanks in advance for your attention.

P.

https://ggbm.at/563845

Comments (5)

photo
1

Hi gengiskunk,

Hello to all,

I'm trying to show the functioning of a sundial on earth seen "from space."

I am attaching the file that has not yielded the expected results.

The trace left of the shadows on the "floor" terrestrial poli1 (in solidarity with the movement of the earth's rotation) does not generate the hyperbole that I expected.

Looking good, the trace left by the point P does not lie on poli1 but is represented in the 3D view.

It will be what maybe the problem?

Indeed, the point P sometimes becomes undefined.

If you define

P=Intersection[p, j]

Do you get the result you are looking for?


Cheers, :wink:

Phil

photo
1

Hello Lph,

the file is a "model", an attempt to simulate the behavior of a meridian as seen from space.

P is the intersection between p and poli1.

This is because P represents the extreme of the stylus shadow (OH, if I remember) projected on the Earth's surface (poli1).

The problem is that I expected to see moving P on a hyperbola (solstitial line), but this does not happen....


I don't know if I made something wrong rappresenting the behavior of a meridian.....or something else.


Thankyou for your attenction

photo
1

Hi gengiskunk,

Hello Lph,

the file is a "model", an attempt to simulate the behavior of a meridian as seen from space.

P is the intersection between p and poli1.

This is because P represents the extreme of the stylus shadow (OH, if I remember) projected on the Earth's surface (poli1).

The problem is that I expected to see moving P on a hyperbola (solstitial line), but this does not happen....

I understand the model.

Have you tried the proposed modification?


My tests seem to show similar results to those you describe: there is a superposition of two hyperbolas (see below).

Indeed, poli1 is contained in the plane j. Therefore, P=Intersection[p, j] is always defined and point P describes all the solutions. With uniquely the rotation of earth, it is sufficient to limit the branches of the hyperbolas. In addition, combining the rotation of the earth around the sun, you get a complete trajectory as a flattened ellipse (see below).


If this is not what you want, can you post a picture of the desired result?


Cheers,

Phil5e51c8dd58b8214f6adbb85ecb023d4e

3a370d98193918ebc49fe717eca3ecda

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Beautiful images, LPH!


But my intention was to obtain a locus on poli1.

Below I have attached a picture taken from the file I attached.


be2df5ff6a664bf5d8bac6eb2ab4dc4c


https://ggbm.at/563925


This file shows the sundial and the solstitial lines seen by the observer on the earth.

I was expecting to see the same situation on poli1.


If the model is not wrong ..... the cause may be the aspect ratio? in your opinion?


In this case there is a way to hold the second view of 2D fixed on poli1?

So I can follow it as it moves.


Cheers,

Paolo

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1

Hi Paolo,

This file shows the sundial and the solstitial lines seen by the observer on the earth.

I was expecting to see the same situation on poli1.

From your file, you can create a 2D view of plane j and you have the following snap view of the point P trajectory (see below).


Maybe the solution you're looking for is a portion of the point P trajectory in the time period corresponding to a day (to be verified).


This is a very interesting problem, but it takes a little work and inspiration to propose something more successful.


Cheers, :wink:

Phil

PS: There are some difficulties in adjustment of the rate of rotation of the earth, which seems incorrect. It is a fundamental parameter in your problem.80e39ef6130f8a6916f07b4256a9236a

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