The galaxy rotation curve is flat.
The same program "Gal_2D" is also written in Visual Basic 5.0
For the operation information of this program select: Visual Basic program "VB Gal 2D" - Description and operation
For the executable of the program select: VB Gal 2D.zip
19 17 11 18 12 10 3 4 2 21 13 5 0 1 9 17 6 8 7 14 16 22 15 24 23 Example 1 of 3 rings Each with 4 Starsone star in each ring (i.e. the stars numbered 1,9 and 17). This is the source star. Only one star has to be calculated because the acceleration of the stars in each ring is identical. The acceleration of star 2 until 8 is identical as star 1 etc
<----a----><----a----> m2/v2 m1/v1 0 m1/v1 m2/v2 star 4 2 0 1 3 <----------b---------><---------b---------> G/(2a)^2 * m1 G/(a+b)^2 - G/(b-a)^2 * m2 = v1^2/a G/(b-a)^2 + G/(a+b)^2 * m1 G/(2b)^2 * m2 = v2^2/b f(1,1) * m1 f(1,2) * m2 = v1^2/a f(2,1) * m1 f(2,2) * m2 = v2^2/b Example 2 with 2 rings Each with 2 stars.
<----a----><----a----> <----a----><----a----> m1/v1 0 m1/v1 m1/v1 m0 m1/v1 star 2 0 1 2 0 1 acel = G * m1/(2*a)^2 = v1^2/a acel = G * m1/(2*a)^2 + G * m0/a^2 = v1^2/a Example 3 with 1 ring with 2 stars. Example 4 with 2 stars and one star in center
<----a----><----a----> m3/v3 m2/v2 m1/v1 m0 m1/v1 m2/v2 m3/v3 star 6 4 2 0 1 3 5 <----------b---------><---------b---------> <--------------c---------------><---------------c------------> G/(2a)^2 * m1 G/(a+b)^2 - G/(b-a)^2 * m2 G/(a+c)^2 - G/(c-a)^2 * m3 = v1^2/a - m0*G/a^2 G/(b-a)^2 + G/(a+b)^2 * m1 G/(2b)^2 * m2 G/(b+c)^2 - G/(c-b)^2 * m3 = v2^2/b - m0*G/b^2 G/(c-a)^2 + G/(c+a)^2 * m1 G/(c+b)^2 + G/(c-b)^2 * m2 G/(2c)^2 * m3 = v3^2/c - m0*G/c^2 f(1,1) * m1 f(1,2) * m2 f(1,3) * m3 = v1^2/a - m0*G/a^2 f(2,1) * m1 f(2,2) * m2 f(2,3) * m3 = v2^2/b - m0*G/b^2 f(3,1) * m1 f(3,2) * m2 f(3,3) * m3 = v3^2/c - m0*G/c^2 Example 5 with 3 rings Each with 2 stars and star in centre = m0The above sketch shows the situation when 3 rings are involved. In that case 3 masses have to be calculated.
To stop the simulation: Enter Escape, E to End or N to continue with a New simulation.
m2/v2 C b b*sin(g) <----a----> m1/v1 0 m1/v1 F B 0 A E <----a----> b m2/v2 D Example 6 with 2 rings Each with 2 stars. star 1 = A star 2 = B star 3 = C and star 4 = D Distance between star A (and B) and centre 0 is a Distance between star C (and D) and centre 0 is b angle C0E = g angle F0D = g CE = FD = b*SIN(g) AE = b*COS(g) - a FA = b*COS(g) + a Force of A towards C: FAC = G/ (AE^2 + EC^2) = G/((b*COS(g) - a)^2 + b*SIN(g)^2) X component = FAC * AE / AC = FAC * (b*COS(g) - a) / SQR(((b*COS(g) - a)^2 + b*SIN(g)^2) Y component = FAC * CE / AC = FAC * b*SIN(g) / SQR(((b*COS(g) - a)^2 + b*SIN(g)^2) Force of A towards D: FAD = G/ (AF^2 + FD^2) = G/((b*COS(g) + a)^2 + b*SIN(g)^2) X component = FAD * FA / AD = FAD * (b*COS(g) + a) / SQR(((b*COS(g) + a)^2 + b*SIN(g)^2) Y component = FAD * FD / AD = FAD * b*SIN(g) / SQR(((b*COS(g) + a)^2 + b*SIN(g)^2)For the matrix component f(1,1) (i.e. the force A towards B) there is no difference.
To test this situation perform the program and select # of rings = 2 and # of stars is 4. When the message "Perform Simulation, Yes No (E = End)" Enter R for repeat. Do this again and again. Each time observe the mass values for each ring and the values for ax and ay. You will see that the mass values are different and that ay has almost the same value as ax (except for the first time)
Perform the same test but now for 2 rings and 40 stars. Observe that ay is small compared to ax.
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