Sagittarius Project - Sagittarius.xls

The Sagittarius.xls EXCEL program is the first phase of the Sagittarius Project. The Sagittarius Project involves a simulation of 10 mini BH's which rotate around the BH which lies in centre of our Galaxy i.e. the constellation Sagittarius. For more detail select: Sagittarius Project For the source of the program select: Sagittarius.zip
This zip file consists of the program:

1. Not available

1 Introduction

Sagittarius A* is a compact astronomical source at the center of the Milky Way. This location also harbours a Black Hole. For more detail select this link: https://en.wikipedia.org/wiki/Sagittarius_A*. Around this BH in Sagittarius A* rotate a certain number of Stars. It is the purpose of the Sagittarius Project to simulate these stars.
For more detail select this link: https://en.wikipedia.org/wiki/Sagittarius_A*#Orbiting_stars. The next 10 stars are considered:

id1 a e i (°) omega w (°) Tp (yr) P (yr) Kmag q (AU) v (%c) dv m0 S1 0.5950 0.5560 119.14 342.04 122.30 2001,800 166.0 14.70 2160.7 0.55 0.03 12.40 S2 0.1251 0.8843 133.91 228.07 66.25 2018,379 16.1 13.95 118.4 2.56 0.00 13.6 S4 0.3570 0.3905 80.33 258.84 290.80 1957,400 77.0 14.40 1779.7 0.57 0.01 12.2 S6 0.6574 0.8400 87.24 85.07 116.23 2108,610 192.0 15.40 860.3 0.94 0.00 9.2 S8 0.4047 0.8031 74.37 315.43 346.70 1983,640 92.9 14.50 651.7 1.07 0.0 13.2 S9 0.2724 0.6440 82.41 156.60 150.60 1976,710 51.3 15.10 793.2 0.93 0.02 8.2 S12 0.2987 0.8883 33.56 230.10 317.90 1995,590 58.9 15.50 272.9 1.69 0.01 7.6 S13 0.2641 0.4250 24.70 74.50 245.20 2004,860 49.0 15.80 1242.0 0.69 0.01 10. S14 0.2863 0.9761 100.59 226.38 334.59 2000,120 55.3 15.70 56.0 3.83 0.06 10. S62 0.0905 0.9760 72.76 122.61 42.62 2003,330 9.9 16.10 16.4 7.03 0.04 10. Table 1

The three most important parameters to consider at present are Tp, P and V. Tp is the epoch of pericentre passage, P is the orbital period in years and v is the pericentre speed in percent of the speed of light
This information is important because the parameter Tp in all cases is different, means that the speed v cannot be used directly as an initial state for all the stars.
For example: at Tp 2001,8 for S1 the speed v=0.55*C. However at that same instance the speed of all the other stars is unknown.
That is exactly what the program Sagitarrius.xls tries to solve: To calculate the initial parameters for a specific initial date.
For example: Suppose you want to calculate the initial parameters at TP2000, than this is okay for the stars S4, S8, S9 and S12 because each of TP values are before TP2000. To solve that you have to subtract the value of P (orbital period) from TP.

• In case of S1 you have to subtract P once and you get: TP = 2001,800 - 166 = 1835,8
• In case of S2 you have to subtract P twice and you get: TP = 2018,379 - 2*16.1 = 1986,179
• In case of S62 you have to subtract P once and you get: TP = 2003,330 - 9.9 = 1993,43

2. General Excel Program Description

To calculate the initial conditions at one specific date each star is handled individual and is considered a binary system together with the Black Hole.
The simulation performed is a 2D simulation using Newton's Law.
Each simulation in 2D requires the following parameters for each star: a, e, TP, v and m0
To do the same in 3D requires the folloing additional parameters: omega, inclination and w

The EXCEL program consists of 4 pages: Blad1, Sphere, Ellipse and JD Test.

1. page Blad1 contains a database with all the parameters for the 10 stars but also for the planets. This is important to test certain program details for both environments.
2. page Ellipse contains the simulation software for the 10 stars.
   The page contains one button marked Simulate. When the button Simulate is selected the program runs automatically.

3 Page Ellipse

3.1 Page Ellipse, Single Simulation, No Database update

The pupose of the 'single simultion' is to get a general idea what the Sagitarrius.xls program does. Only one mini BH is simulated.
Page Ellipse contains a certain # of Yellow cells which have to contain the folowing values:

1. The Cell dt row 5 should be 1000.
2. The Cell star# row 9 can have any value between 1 and 10, in order to select a star.
   In order to test enter # 10, which is star S62.
3. The Cell auto mode row 11 should be 0.
   In that case the results are not stored in a dB file.

   Picture 1

   When Picture 1 is not selected the display shows the operating console when only one BH is simulated. In this particular case S62. When Picture 1 is selected the display shows the operating console when all 10 mini BH's are simulated.

3.2 Page Ellipse, Complex Simulation, DataBase update

The purpose of this simulation is to simulate all then stars and and to store the results in a file.
In this case the Yellow Cells on Page Ellipse have to contain the folowing values:

1. The Cell dt row 5 should be 1000.
2. The Cell star# row 9 should be 0.
   The value of 0 means that all 10 stars are executed from from star #1 to star #10.
3. The Cell auto mode row 11 should be 3.
   In that case the results are stored in a file.
4. The following parameters are retrieved from the database in Blad1: m1, dist(a), e, star #, star name, P and TP
5. These same parameters are stored in column 3 of Page Ellipse : m1 in row 2, dist(a) in row 3, e in row 4, star # in row 9, star name in row 10 , P in row 12 and TP in row 13.

3.3 Page Ellipse right half.

The right half of page ellipse contain the intermediate results of each simulation.

• In case when only one simulation is performed (auto = 0) this section immediate slow the final result.
• In case when 10 simulations are perfomed (auto = 3) this section is overwritten 10 times.

Picture 2

When picture 2 is not selected Picture 2 shows the results of S62 row 2 shows the initial conditions when S62 is at aphelion. Column T shows the distance r1 from center of gravity, which is now at its maximum value. Column V shows the speed v1, which is now at its minimum value. row 8 shows the stuation when S62 is at perihelion. This was in 1993. Column T shows the distance r1, which is now at its minimum value. Column V shows the speed v1, which is now at its maximum value i.e. 7% of the speed of light. row 21 shows the stuation when S62 is at perihelion. This was in 2003. When picture 2 is selected Picture 2 shows the results for Sagitarrius A* Column S shows the distance r0 from center of gravity, which is now at its maximum value. Column U shows the speed v0, which is now at its minimum value.

Picture 2 shows the result for star #10 or S62.
The most important information is in column T and V.
Column T shows the distance from the BH and Column V shows the speed of the star #10.
Column V is the easiest because it shows two waves. The higest speeds are in 1993 and 2003 when the star is at perihelion. Column T shows this shorest distance. This data is in agreement with Table 1

3.4 Page Elipse - Detailed discussion of S62

4 Excel Program description

• Subroutine READDB
  This subroutines reads the 11 records in the file "sagittarius.db.txt"
  Record #1 contains the 6 integers: jyear,jmth,jday,jhr,jmin and jsec. Record #2 to 11 contains the following values:

  value 1 the star # as an integer. Value 2 the star name as a string.
  The values 3 to 10: x0, y0, x1, y1, vx0, vy0, vx1 and vy1 as double precision.

• Subroutine CALCDATE This subroutine calculates the 6 date parameters from a Julian Date number
• Subroutine CALCJD This subroutine calculates the Julian Date number from 3 date parameters (Year, month and day)
• Subroutine Convert_DATE_To_Fraction This subroutine converts a Date in 6 date parameters into a fraction. Table 1 contains dates represented as a fraction.
• Subroutine Convert_Fraction_To_DATE This subroutine converts a date as a fraction to a Date in 6 date parameters.
• The field imax (row 6) is calculated as a function of dt.
  The standard values for dt and imax are 1000 and 6000000.
  In auto mode when dt is changed to 500 than imax is calculated as 12000000. The simlation will take longer and the accuracy will increase.
• The field Auto (row 11) recognizes 3 values.
  The value = 0 means manual mode. The field imax is not calculated.
  The value = 1 means auto mode. No data base update.
  The value = 3 means auto mode. Data base update. During the simulation the value changes to 1.

Reflection part 1

Reflection part 2

Feedback

Back to my home page Contents of This Document