Extra orbital data (position vector and velocity direction)

[DianaTavares]

A teacher during the interview asked for data to calculate the angular momentum. In the design meeting, it was decided that those data could be added as an extra parameter, with an option in the preference and a query parameter.

Those data will be shown on the first law screen/scene, in the panel readout, like this:

The information about the position vector will be visible only when the user selects “string”, that is when the d1 is displayed in the play area.

The velocity vector information will be displayed when the velocity vector is display in the play area (then it is active by default).

The info window will include information about that new data::

@AgustinVallejo please review and edit the vector's text.

The preference text like this:

@AgustinVallejo, what name is good for the Query Parameter?

[DianaTavares]

It was decided in the last design meeting to implement this idea. @arouinfar, please support us with the review of the English:

• Text in the Preference dialog:

More Orbital Data Display information about the planet's position and velocity vectors in the First Law Screen.

• Text in the information window:

Planet's position vector (|r| and θr): The vector magnitude |r| is equal to the distance between the star and the planet, in a reference system where the star is at the origin. The vector direction θr is measured from the horizontal.

Planet's velocity vector (|v| and θv): The vector magnitude |v| is equal to the planet speed. The vector direction (θc) is measured from the horizontal.

[DianaTavares]

my idea for the icons:

[DianaTavares]

I have the text comments:

• [x] @arouinfar, did you already review the text of this?

• [ ] As a title for the info window, I propose: “Parameters and Vectors".

• [ ] In the mockup, I put the next:

Thinking that, we can use d1 as a reference visualization of the r vector. This means that the readouts' panel needs to open when strings are active. Also, the panel needs to include this relationship between d1 and the magnitude of r.

• [ ] I think the display should be vector magnitude followed by vector direction, as the mockup:

• [ ] The most important, We wanted this data to allow advanced students more deeply calculations, like the conservation of the angular momentum. I tried to calculate that and it is hard! Student's have to calculate the angle between the v and r vector, and for that, you have to find the positions of the planet where one of the vectors is horizontal or vertical. for example, this one:

But the truth is that the vectors there are not completely vertical, neither horizontal. These are the values of the angles in the picture above:

I understand that we can tell the users to have “approximated” values. With this ellipse, I get an angular momentum magnitude of 26.42, 26.39 and 26.65 (well I only multiply the magnitude of v and r, and sin of the angle), in three different positions that I think a user can say, it is constant. But it was stressful that I got 89.8º for example for a vector, and I wonder if with a “step forward” I can get me closer to the 90º, and then I jumped to 91.4º!! It was better 89.8º that 91.4º, but I can't go a step back!!! I need to go all the orbit around again!!

Then I have 2 questions here @AgustinVallejo.

1. Apart from angular momentum, what other interesting calculations are required for the angle of each vector? Because I'm thinking that maybe we could directly give them the angle between r and v, so that no matter where, you can calculate the angular momentum magnitude without messing with the position of the planet.
2. Or let's add a step back button.

[arouinfar]

@DianaTavares @AgustinVallejo I reviewed the text in https://github.com/phetsims/keplers-laws/issues/60#issuecomment-1663280121

Overall, looks good. I noticed a small inconsistency in these vector direction sentences:

The vector direction θr is measured from the horizontal. The vector direction (θc) is measured from the horizontal.

I recommend adding parentheses around θr like you do for θc.

[AgustinVallejo]

This is mostly ready, moving discussion to this issue: https://github.com/phetsims/keplers-laws/issues/60