BDS Software - Stellar System Thoughts 04

Stellar System Thoughts - Page 4

To deal with these problems, let's do the following:

● Eliminate the grid and the red orbit lines, but leave a 1-pixel border around the outer edges of the canvas.

● Eliminate all the asteroids except Vesta, Juno, and Ceres; and renumber the list of planets..

● Adjust the solar and planet images to provide slightly improved visibility.

● Space out the image orbits a little more to provide for better definition..

Let's assemble this data in tabular form, as follows:

● PNum = Orbit Number beginning with closest to Star and ending with furthest from Star.

● PID = Planet Name or ID.

● PDia = Planetary Image Diameter, pixels*.

● PRad = Actual orbital image radius to use, pixels.

● PRate = Rotation in orbit, micro-radians per Earth Day

● PIPos = Position in orbit at an arbitrary t = 0, micro-radians.

● PIX = Position x-coordinate in orbit at an arbitrary t = 0, pixels**.

● PIY = Position y-coordinate in orbit at an arbitrary t = 0, pixels**.

PNum PID PDia PRad PRate PIPos PIX PIY

1 Mercury 9 20 71424 636871

2 Venus 13 36 27963 4059461

3 Earth 13 52 17202 4220032

4 Mars 9 68 9146 3476870

5 Vesta 9 84 4140 720472

6 Juno 9 84 4140 2128429

7 Ceres 9 84 4140 4275708

8 Jupiter 17 116 1450 942303

9 Saturn 17 148 584 3618940

10 Uranus 13 204 204 89884

11 Neptune 13 260 104 5780007

12 Pluto 9 310 69 4852015

PNum	PID	PDia	PRad	PRate	PIPos
1	Mercury	9	20	71424	636871
2	Venus	13	36	27963	4059461
3	Earth	13	52	17202	4220032
4	Mars	9	68	9146	3476870
5	Vesta	9	84	4140	720472
6	Juno	9	84	4140	2128429
7	Ceres	9	84	4140	4275708
8	Jupiter	17	116	1450	942303
9	Saturn	17	148	584	3618940
10	Uranus	13	204	204	89884
11	Neptune	13	260	104	5780007
12	Pluto	9	310	69	4852015

* The Sun's image diameter is 20 pixels.

** PIX and PIY are calculated as follows:

r_i = PRad, pixels

θ_i = ((PIPos + (PRate * t)) / 1000000), radians

where "pixels" refers to the side-to-side (not the diagonal) dimension of the screen's pixels, and t is expressed in Earth Days. Also, we note a previous error in the calculations on Page 3 -- the divisor in the equation for θ_i should be 1000000, not 2000000.

And, we can then convert these polar coordinates to cartesian coordinates (x_i, y_i) as follows:

x_i = (r_i * cos(θ_i)), pixels

y_i = -(r_i * sin(θ_i)), pixels

where the pixel dimensions are relative to the center of the Solar System Image at (320, 320) in actual image coordinates. The unary minus sign in the equation for y_i is provided to accomplish the counterclockwise rotation of the planets.

Also:

PIX = (mdjRound(x_i) + 316), pixels

PIY = (mdjRound(y_i) + 316), pixels

We use 316 for Mercury, Mars, Vesta, Juno, Ceres, and Pluto; we use 314 for Venus, Earth, Uranus, and Neptune; and we use 312 for Jupiter and Saturn.

And the result is:

This is better, but perhaps it can be improved even further...

M.D.J. 2018/07/13