This document describes the program FIGURE
This program is part of SUNRAD, PLANETS and PROVE
This figure is part of virtual mass calculation described in chapter 4 of program SUNRAD.
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This figure is part of the center of the Sun calculation (oblateness) described in chapter 2 and 3 of program SUNRAD.
Now perform the program: FIGURE.EXE
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This figure is part of the center of the Sun calculation (oblateness) described in chapter 2 and 3 of program SUNRAD.
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Figure 3 of program planets shows the movement of the planet Mercury for different positions of the Sun when the Sun moves through our Galaxy for c = 300000 km/sec
The Sun is shown at four positions: Top, Left , Bottom and Right.
In order to select the Sun use the TAB key
With each position of the Sun, Mercury is also shown at four positions
In order to select Mercury use the four arrows keys.
Centre of Galaxy has a speed of 230 to the right
The Sun moves counter clockwise with a speed of 250 km/sec At top position to left : 250 - 230 = 20 km to the left At bottom position to the right : 250 + 230 = 480 km to the right
Now perform the program: FIGURE.EXE
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This figure shows the movement of our Galaxy, the Sun and Mercury relative to the plain of the Sun. The dimensions are wrong.
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This figure shows what an observer sees when an invisible object (dark matter) moves between the observer and a visible star at different distances.
The area in grey at each position has the same surface. This is the amount of light influenced by (the gravity of) dark matter.
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The above figure is calculated using the following method.
Radius invisible star is R0.
Radius of area that is effected is R1
For x between R0 and R1 we calculate the variable a
Light in this area (between R0 and R1) is bended, the further away the more from its straight path. The new distance from R1 is b.
h is the distance behind the invisible star
The density at h = 0 is every where the same i.e. dens1
What we want to calculate is the density at h<>0 i.e. dens2
There are two strategies.
First we can divide a in small increments.
The density dens2 between b2 and b1 is then equal to:
This becomes difficult to draw as a figure when the two parts starts to overlap. This becomes difficult for h > 1
A second strategy is not to divide a in small segments, but b.
From equation (1) we can solve:
h * c1 * a² + a - b = 0 -1 + SQR(1 + 4*b*c1*h) a = ---------------------- (2) 2*c1*hif a > R0 then a = R0
At distance b1 we can calculate a1 using (2)
At distance b2 we can calculate a2 using (2)
dens1 * (PI * a2²-PI * a1²) = dens2 * (PI * b2²-PI * b1²) dens2 = dens1 * (a2 + a1) * (a2 - a1) / (b2 + b1) * (b2 - b1)
b1 and b2 are the distance to R1 (b1 = R1 - b)
b3 and b4 are the distance to -R1 (b3 = R1 + b)
At distance b3 we can calculate a3 using (2)
At distance b4 we can calculate a4 using (2)
The density dens3 between b4 and b3 is then equal to:
Total density is then equal to:
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In order to see our Galaxy in 3D perform the following:
Our galaxy consists of two parts:
In order to make the calculation "smooth" the mass of the disk is considered to continue into the bulge.
The density of the bulge is a function of 1/R
The density of the disk is constant.
For the disk three parameters are important:
For x < R0 the height of the disk is constant i.e. z = z0
For R0 < x < R1 the height of the disk changes linear towards z = alpha * z0
For x > R1 the height of the disk z = 0
Between R0 < x < R1
Subtracting (2) from (3) yields:
Entering (5) and (4) into (1) yields:
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This demonstration shows how a light ray is bended around the Sun using only Newton's Law
For factor select 1 (normal) 2 and 4.
The results of the demonstration shows that the angle is twice to small as accordingly to general accepted concepts.
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The program uses the following standard feature:
In order to simulate the different conditions the parameter selection display is used
From the Parameter Selection Display the following parameters can be changed:
0 = Select test display1 = Set standard parameters.
2 = Screen mode. Valid values are 7,8,9 and 12. Standard value = 9 3 = Wait time in second. Physical wait time between each simulation cycle. Standard value = 0