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Orbital Mechanics

Posted by: campbelp2002 - Thu Dec 23, 2004 7:49 pm
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Orbital Mechanics 

Could an object spiral into the Sun?
Of course! 64%  64%  [ 16 ]
No way! 28%  28%  [ 7 ]
I used to think so, but now I don't. 0%  0%  [ 0 ]
I didn't think so before, but now I do. 8%  8%  [ 2 ]
Total votes : 25

Orbital Mechanics 
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Post    Posted on: Mon Jan 24, 2005 8:02 pm
Ekkehard,

I would be very interested to get your Excel file, but not all million+ lines. Just the first few lines. I can duplicate the last line as many times as needed to see what the ultimate result would be. You can E-mail it to me at the address on my web page:
http://home.austin.rr.com/campbelp/astro.html

And my Excel file is posted here:
http://home.austin.rr.com/campbelp/orbit.xls

I have altered it to be more realistic. Now it has actual distances and speeds and places the Earth in a more realistic 147.5 by 152.6 million kilometer elliptical orbit. I have also multiplied each velocity and acceleration by 86,400 (seconds per day) to make it compute one step per day. This results in a complete orbit in about 365 days on row 368 of the file.

If you enter DeltaVx = -27.0, the simulation gets closest to the Sun on row 65 (about 62 days from the start) and then blows up. Don’t look at the graph, look down the R column to find the lowest value on row 65. (The graph will look bad due to wrong positions after perihelion because the 1 day intervals are too large so close to the Sun. Or you could limit the graph to showing only rows 2 through 65 and stretch it vertically many times.)

If you want finer calculations, change the 86,400 to 200 in cells C3, D3, E3 and F3, copy row 3 and paste into rows 4 through 65,535. This will give you a calculation every 200 seconds. Also change the graph to show data up to row 32,000. (Excel graphs allow a maximum of 32,000 values.) Now the object gets closest to the Sun on row 27,550 which is 27,547 intervals (of 200 seconds each) from the start, or about 64 days. Also, the simulation does not blow up. (Note that you don’t get quite close enough to the Sun to hit it. This is because of the faster speed of the Earth at perihelion where the simulation starts. You would need a DeltaV of 27.4 km/s to hit the Sun starting from Earth’s perihelion and only 26.5 km/s starting from aphelion. I tried it both ways. Yes, this means it is easier to hit the Sun by starting from farther away.)

If that is still not a fine enough calculation, remove the 86,400 completely from cells C3, D3, E3 and F3 and copy row 3 to rows 4 through 65,535. And delete the graph because 32,000 points will not be enough. This will give you 1 second per calculation and require about 5.5 million calculations to reach the Sun. Since Excel allows only 65,535 rows you will have to break the calculation into 85 parts. Simply copy the VALUES from row 65,535 to row 3 to see the next 65,532 seconds (use paste special, values. And don’t press enter, click the mouse on the OK or in another cell to complete the paste). Do this 84 times and you will see the result of 5.5 million 1 second calculations. The result will be very similar to the rough results above. The object will get closest to the Sun on row 4890 of the 85th page of calculations. Yes, I did try it. It took about 10 minutes.

You can also plug in whatever accelerations (DeltaVs) you wish at each line and get any result you like. I suggest doing this initially with the 1 day time intervals as a rough estimate before refining to the shorter time intervals, but you don’t have to. In particular notice that your DeltaV of 7.4 directly toward the Sun (DeltaVy=-7.4) never gets closer to the Sun than 119 million kilometers. An additional DeltaV of 20 km/s directly toward the Sun from that low point (DeltaVx=-20) gets you within 90 million kilometers, but not closer.

And thanks Sigurd,
99% of the reads are no doubt Ekkehard and I. But at least one other person reads it sometimes. You did! :D


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Post    Posted on: Tue Jan 25, 2005 3:02 am
Actually, I've rather enjoyed this thread and would like to keep it going. I hope at some point to chime in. Meanwhile, if you want to do some real simulating, get Garcia's Numerical Methods text, write your code in FORTRAN and run it on an Athlon64 Linux box.


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Post    Posted on: Tue Jan 25, 2005 4:12 am
FORTRAN. ... I remember that. I had that in school, on an IBM 360. Along with the (then) required engineering slide rule class. :lol:


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Post    Posted on: Tue Jan 25, 2005 7:58 am
Well, I for one have been reading this conversation fairly regularly (well, in spurts, but all of it nonetheless...I honestly didn't think this could actually go on this long). I would also like to congradulate both Peter and Ekkehard for their tenatious attempts to try and communicate clearly their vision of this 'problem'. Peter, I like the Java applet - it works so nice and fast (not like the clunky thing I threw together and subsequently burried).

For curiosity sake, I would like to see these calculations that Ekkehard is performing in his excel spreadsheet (not the millions of lines, though...). Is there somewhere that you (Ekkehard) would be able to post them in their logical entirety?


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Post    Posted on: Tue Jan 25, 2005 1:41 pm
:o You read all of it? I didn't think ANYBODY read it all!

And I am eagerly waiting for Ekkehard's Excel file too. Math is a better language for this discussion than either English or German.


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Post    Posted on: Tue Jan 25, 2005 5:25 pm
I was just considering my earlier post, the one that shows it takes less energy to hit the Sun if the acceleration is applied farther from the Sun. The reason is the slower orbital speed at the higher altitude requires less deceleration to cancel. Then I thought, what if I deliberately accelerated to send the rocket in an elliptical orbit with an aphelion much farther from the Sun and then decelerated to hit the Sun from there? Would the savings from the lower required deceleration overcome the cost of sending the vehicle so far away. And the answer was yes! It makes a BIG savings. Here are two examples.

Starting from Earth’s perihelion the required deceleration is 27.4 km/s to hit the Sun.

Starting from the same place, a 10 km/s acceleration sends the vehicle almost to Saturn. At that point it is only moving at 4.5 km/s and a deceleration of only 4.4 km/s will result in hitting the Sun. A total velocity change of only 14.4 km/s!

So my initial claim that it takes twice as much energy to hit the Sun as it does to escape the solar system, the claim that started this whole long series of posts, is just totally wrong! :oops: In theory, leaving Earth’s orbit with exactly the solar escape velocity would result in stopping at infinite distance. Then an infinitely small velocity change would be enough to start on a straight line path that would eventually hit the Sun! So the Sun can be hit with the same energy expenditure as escaping the solar system, if you don’t mind taking the long route.

I have been concentrating on how much the vehicle speeds up as it approaches the Sun, which makes it harder to hit the Sun. I totally neglected the fact that the opposite happens as the vehicle moves away from the Sun.
Funny thing…
http://www.theofficialjohncarpenter.com ... sscpla.wav


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Post    Posted on: Tue Jan 25, 2005 8:09 pm
hmm,
That (specific) thought didn't seem to occur to any of the rest of us either. (The opposite end of the ellipse must have been a bit outside of the box, I guess).

On an other note, would there be any way that I can get a copy of your javascript code for your orbital simulator? My interest has been somewhat piqued lately, and I'm beginning to have crazy thoughts of re-animating my own simulator, with options of applying thrust at any time in the orbit. If I can see your code (private message or not), I may be able to see where my code is horribly inefficient.


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Post    Posted on: Tue Jan 25, 2005 9:30 pm
Certainly. Excuse the lack of comments, etc..

import java.applet.*;
import java.awt.*;
import java.awt.event.*;

public class OrbitViewer extends Applet implements Runnable, ActionListener
{
Button slower;
TextField speed;
Button faster;
Button drop;
Button fire;
TextField thrust;
TextField duration;
Button right;
Button left;
public void init()
{
slower = new Button("Slower");
add(slower);
slower.addActionListener(this);

this.speed = new TextField("64",2);
this.speed.setEditable(false);
add(speed);

faster = new Button("Faster");
add(faster);
faster.addActionListener(this);

drop = new Button("Drop");
add(drop);
drop.addActionListener(this);

left = new Button("-10");
add(left);
left.addActionListener(this);

right = new Button("+10");
add(right);
right.addActionListener(this);

fire = new Button("Fire");
add(fire);
fire.addActionListener(this);

this.thrust = new TextField("0.0",1);
this.thrust.setEditable(true);
add(thrust);

this.duration = new TextField("0.0",4);
this.duration.setEditable(true);
add(duration);

}

Thread Orbit;
boolean stop;
public void start ()
{
Orbit = new Thread(this);
stop=false;
Orbit.start();
}
public void stop ()
{
stop=true;
}
double x = -147500000.0;
double y = 0.0;
double Vx = 0.0;
double Vy = -30.25;
double Ax = 0.0;
double Ay = 0.0;
double R = 147500000.0;
double xp = -147500000.0;
double yp = 0.0;
double Vxp = 0.0;
double Vyp = -29.8;
double Axp = 0.0;
double Ayp = 0.0;
double Rp = 147500000.0;
double U = 132712440000.0;
double T = 0.0;
double D = 0.0;
double A = 0.0;
double Px = 0.0;
double Py = 0.0;
double Qx = 0.0;
double Qy = 0.0;
double Sp = 64.0;
double Met = 0.0;
int Day = 0;
int Hour = 0;
int Min = 0;
int Sec = 0;
String sp;
String st="Fire";
String V;
String r;
int dr = 0;
int tick = 0;
String ver;
public void paint (Graphics g)
{
ver = (" Java Version: " + System.getProperty("java.version")+ " from "+System.getProperty("java.vendor"));
slower.setLocation(5,5);
speed.setLocation(50,5);
faster.setLocation(80,5);
drop.setLocation(130,5);
left.setLocation(175,5);
right.setLocation(210,5);
fire.setLocation(249,5);
thrust.setLocation(285,5);
duration.setLocation(340,5);
g.drawString("g",317,18 );
g.drawString("Sec.",390,18 );
g.drawString(ver,5,598);
g.drawOval (298, 298, 4, 4);
R=Math.sqrt(x*x+y*y);
Met=Met+Sp;
Ax=-U*x/R/R/R;
Ay=-U*y/R/R/R;
Vx=Vx+Ax*Sp;
Vy=Vy+Ay*Sp;
if (D > 0.0)
{
if (D>Sp)
{
Vx=Vx-T*Math.cos(A)*Sp;
Vy=Vy-T*Math.sin(A)*Sp;
D=D-Sp;
}
else
{
Vx=Vx-T*Math.cos(A)*D;
Vy=Vy-T*Math.sin(A)*D;
D=0.0;
}
duration.setText(String.valueOf((double)(D)));
}
else if (st=="Stop")
{
st="Fire";
fire.setLabel(st);
}
tick++;
if (tick > 100 || R < 696000 )
{
tick=0;
Day = (int)(Met / 86400);
Hour = (int)((Met - (double)Day * 86400) / 3600);
Min = (int)((Met - (double)Day * 86400 - (double)Hour * 3600) / 60);
Sec = (int)(Met - (double)Day * 86400 - (double)Hour * 3600 - (double)Min * 60);
g.drawString(String.valueOf((int)Day)+":"+String.valueOf((int)Hour)+":"+String.valueOf((int)Min)+":"+String.valueOf((int)Sec),420,25);
V=String.valueOf((double)(Math.rint(Math.sqrt(Vx*Vx+Vy*Vy)*10))/10.0);
r=String.valueOf((double)((int)(R/100000.0)/10.0));
g.drawString(V+" km/s "+r+" Million km",420,12);
}
x=x+Vx*Sp;
y=y+Vy*Sp;
Px=8*Math.cos(A+0.2);
Py=8*Math.sin(A+0.2);
Qx=8*Math.cos(A-0.2);
Qy=8*Math.sin(A-0.2);
if (dr == 1)
{
xp=x;
yp=y;
Vxp=Vx;
Vyp=Vy;
Axp=Ax;
Ayp=Ay;
Rp=R;
dr=2;
}
else if (dr == 2)
{
Rp=Math.sqrt(xp*xp+yp*yp);
Axp=-U*xp/Rp/Rp/Rp;
Ayp=-U*yp/Rp/Rp/Rp;
Vxp=Vxp+Axp*Sp;
Vyp=Vyp+Ayp*Sp;
xp=xp+Vxp*Sp;
yp=yp+Vyp*Sp;
if (Rp < 696000 )
{ dr=0; }
if (xp < 178800000 && yp < 178800000 && xp > -178800000 && yp > -178800000)
{ g.drawLine (300+(int)(xp/600000.0), 300+(int)(yp/600000.0), 300+(int)(xp/600000.0), 300+(int)(yp/600000.0)); }
}
if (x < 174000000 && y < 174000000 && x > -174000000 && y > -174000000)
{
g.drawLine (300+(int)(x/600000.0), 300+(int)(y/600000.0), 300+(int)(x/600000.0)+(int)Px, 300+(int)(y/600000.0)+(int)Py);
g.drawLine (300+(int)(x/600000.0), 300+(int)(y/600000.0), 300+(int)(x/600000.0)+(int)Qx, 300+(int)(y/600000.0)+(int)Qy);
}
}

public void run()
{
repaint();
while (!stop)
{
if ( dr > 0 && xp < 178800000 && yp < 178800000 && xp > -178800000 && yp > -178800000)
{ repaint(298+(int)(xp/600000), 298+(int)(yp/600000), 4, 4); }
if (x < 178800000 && y < 178800000 && x > -178800000 && y > -178800000)
{ repaint(290+(int)(x/600000), 290+(int)(y/600000), 20, 20); }
else
repaint(0,0,20,20);
if (tick>99)
{
repaint(420,0,180,40);
}
if (R < 696000 )
{ stop = true; }
try
{}
catch(Exception e)
{}
}

}

public void actionPerformed(ActionEvent event)
{
Component c = (Component)event.getSource();
if (c == fire)
{
if (st=="Fire")
{
T=Double.valueOf(thrust.getText()).doubleValue();
T=T/100;
D=Double.valueOf(duration.getText()).doubleValue();
st="Stop";
fire.setLabel(st);
}
else
{
D=0.0;
duration.setText(String.valueOf((double)(D)));
st="Fire";
fire.setLabel(st);
}
}
else if (c == drop)
{
if (dr == 0)
{ dr = 1; }
}
else if (c == slower)
{
Sp=Sp/2.0;
if (Sp >0.6)
{ sp=String.valueOf((int)Sp); }
else
{ sp=String.valueOf(Sp); }
speed.setText(sp);
}
else if (c == faster)
{
Sp=Sp*2.0;
if (Sp >0.6)
{ sp=String.valueOf((int)Sp); }
else
{ sp=String.valueOf(Sp); }
speed.setText(sp);
}
else if (c == right)
{
A=A+0.174533;
if (A > 6.283)
{ A=0.0; }
}
else if (c == left)
{
A=A-0.174533;
if (A < 0.0)
{ A=6.283; }
}

}
}


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Post    Posted on: Wed Jan 26, 2005 10:57 am
Peter,

I will post a description of the spreadsheet here and send a copy of the spreadsheet to you by mail. I am forced to send a spreadsheet with no more than a few rows per table because the filled spreadsheet has a size of of 27 MB - too much for an attachment.

I didn't find time to be online yesterday so didn't know your desire until now.

I too contacted Sigurd and agree with him that you and me should end our discussion or at least the way it has gone until now. It doesn't make any sense and is misunderstood by some other people really because its complexity.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Post    Posted on: Thu Jan 27, 2005 2:18 am
Let's end this topic... campbelp2002, do you agree ? :)

From what I've seen and read... campbelp2002, you're stil talking about Spiraling the sun... while Ekkerhard actually isn't talking about that.. but about wether radioactive materials can be thrown into the sun without Fly-bys and without throwing the engine or drive into the sun too.

So this whole discussion is useless if both people talk about diffrent things with math.. representing DIFFRENT things lol

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Post    Posted on: Thu Jan 27, 2005 1:14 pm
Sigurd,

Thank You for your assist. I myself do post this only to fulfill my promise to post a description of my Excel spreadsheet.

To extract all the Excel-formulars and to write some explanations took a while since yesterday but it's ready now and may help to clarify something for the readers.

Here the description of my Excel spreadsheets and some explanations.

table 1 "starting conditions"

--------A---------|-------B---------|------------C-------------|---------D---------|----E----|---------------F---------------|--------------days per year | sec. per year | solar angle per sec. | ..Earth angle.. | velocity|..........vert.veloc.......... .....365,256.....|=A2*24*3600|..........=360/B2..........|= (180 - C2) / 2| .29,8. |= COS(D2 * PI() /180) *E2 | ---------------G---------------------|-------------H------------|--------------I-------------|---------J---------|---------K--------|-----------------
----- tang. veloc.-----|--diameter elevator-- |-------elev. veloc.-------|--mass Earth---|---mass sun---|.......................
29,7999999999998|=2 * 100000 + 12756|=H2*PI() / (24 * 3600)|=5,977*10^24|=1,99*10^30|--------------------------L-----|-----M-----|-----N-----.............................................................................................................................. force Earth sun|acc. Earth by sun.....................................................................=J2*K2*6,67*10^-20/150000000^2| =L2/J2| =1,99*10^30*6,67*10^-20


all constants in this table are got from books



table 2 "flight"

A B C D E F G H
vert. veloc. distance art. acc. to sun grav. acc result veloc tang. veloc. dir. angle remark
0 150000000
=A2+C3+D3 =B2-A3 -1,51878509768721E-13 =1,99*10^30*6,67*10^-20/B2^2 =A3/COS(G3 * PI() /180) 29,7999999999998 =ARCTAN(F3/A3) * 180 / PI() space elevator
vertical correction
all constants in this table except those in column C are constants are got from books
the constants in column C are got from the table 3 "vertical correction" except in the first row where a starting condition is used.
When the engine of the vehicle is switched on column C will contain for the first second since switching on 0.00981 (= 1 g - the acceleration provided by the pulsed fusion engine of Orion or/and Daedalus)
and =Ci+0.00981 in all following rows until the engine is stopped again. i is the index of the row.



table 3 "vertical correction"

A B C D E F
0 = COS(A1 * E2 * PI() /180) * C1 7,73602646536053 = B1 - 7,73602646536053 0,0000114075242204554
1 = COS(A2 * E3 * PI() /180) * C2 7,73602646536053 = B2 - 7,73602646536053 0,0000114075242204554 = B2 - 7,73602646536053 - D1

the vertical correction is required because the direction towards the artficial acceleration by the space elevator has gone will not change.
The impulse got by the elevator will start to point NOT to the center of the sun after the first second of flight. That means that this portion
of the velocity directly towards the sun has to be corrected. Only that portion of the vertical velocity that is caused by sun's gravity will
allways and permanently point towards the center of sun. This is the correction not calculated completely by me up to now.

Each formular in tables 2 and 3 is copied down to row 65535.

The column C in table 2 should be renamed as "operational acc. to sun" because this acceleration is completely under human control and can be
switched on and switched off as desired.

In future steps there will be columns added to these tables to provide data that decisions are based on.
The Break-Even-Point - the special situation - I have been speaking about already is defined by already existing columns of one of these tables.



legend:



table 1 "Starting Conditions"

This table is providing data for the first row of table 2 at the first second.

Only not-self-expalining columns-titels are explained here:

C solar angle per sec. = the angle at the sun between the direction from sun towards Earth at the beginning of a second and the direction from sun towards
Earth at the end of that second

D Earth angle = angle between the direction from Earth towards sun and the direction to the point where Earth has been on its orbit one second
before or where it will be one second later. Because of using a circle as approximation columns C and D are angles within a trianlge which has two equal sides.
Consequentially the two Earth angles are equal and given by this column.

E velocity = velocity according to my books and sources; total velocity

F vert. veloc = vertical component of total velocity at the beginning of a second. The use of the constants Pi and 180 is forced by Excel because
its functions are NOT based on 360 degrees

G tang. veloc. = velocity along a tangent touching Earth's orbit at that point where Earth is at the beginning of a second. Calculated by the
calculator of my PC using the sinus-function

H diameter elevator = diameter of the orbit the outer edge of the space elevator is moving along

I elev. veloc. = velocity the outer edge of the space elevator is moving along its orbit. Because of the elevators basics and physics and techniques
this outer edge always is exactly above the same point of Earth's surface despite being at much higher altitude than geosynchronous altitude. For this reason
the velocity is got by dividing the length of the very high orbit by the seconds per day.

L force Earth sun = gravitational force by which sun and Earth attracting each other. Formular and gravitational constant according to Wikipedia and my
books but corrections done for using km instead of m and kg instead of gramms

M acc. Earth by sun = acceleration by solar gravitation at the distance of Earth from sun calculated out of the gravitational force between the both bodies



table 2 "flight"

This table is calculating the velocities, accelerations and directions after each second.

Only not-self-expalining columns-titels are explained here:

A vert. veloc. = the total velocity after the second represented by the current row. This velocity is the sum of the velocity after the previous second,
the gravitational acceleration during the the represented second and the operational (or artificial) acceleration during that second.

B distance = distance towards sun after the second represented by the curent row. Got by subtraction of vertical velocity from the distance after
the previous second. Please note - this is NOT the distance gone along the path of the vehicle.

C art. acc. to sun = operational (or artificial" acceleration got by the space elevator, the pulsed fusion engine or something else. The negative value to
be seen here simply is a correction that is required by the fact that the direction the vehicle is going to after being released by the space elevator is no
longer the direction towards sun's center after the first second. So a recalculation is required which I inserted for simplicity in this column.

D grav. acc = acceleration by sun's gravity after the second represented by the current row.

E result veloc = total velocity of the vehicle calculated by the cosinus-function based on the directional angle and the vertical velocity. Use of the
constants Pi and 180 forced by Excel

G dir. angle = directional angle the vehicle is going to after the current second calculated by the vertical and the tangential velocity. Use of the
constants Pi and 180 forced by Excel

H remark = short information about the nature and the causes of the values in column C, steps and other things



table 3 "vertical correction"

This table is calculating the corrections of vertical velocity required for seconds without artificial (operational) acceleration towards the sun. During such
seconds the direction of the last artificial impulse is moving away from the direction to the center of sun.

A = current second

B = the artificial portion of the vertical velocity after the last artificial (operational) acceleration towards sun - CORRECTED by the solar angle
times the number of seconds given by colums A. The correct value of that velocity is the velocity measured along the ankathesis. The hypthenusis is pointing
to the point where the vehilce was at termination of artificial (operational) acceleration - the ankathesis is pointing to the current position of the vehicle.

C = artificial velocity at the end of artificial(operational) acceleration

D = difference between B and C. Negative sign provided by calculation to be able to keep the functions in tabel 2 as they are.

E = solar angle gone per second

F = the calculation here is required to avoid accumulation of corrcetions. Such accumulations were wrong.



May be that additional explanations are required - please ask for them.
May be too that slight differences between the explanations and the Excel abovhave occurred - I will look for them and correct them by EDIT.

Peter , I will sned you the spreadsheet tomorrow or during the next few days.



Dipl.-Volkswirt (bdvb9 Augustin (Political Economist)

EDIT: The description is looking extremely chaotic whereas the text file I prepared it by is structured very well. I will try to remove the chaos during the next days.


Last edited by Ekkehard Augustin on Fri Feb 18, 2005 12:43 pm, edited 73 times in total.



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Post    Posted on: Thu Jan 27, 2005 2:35 pm
That does seem unnecessarily complicated, so I will wait for the Excel files in my E-mail and not try to recreate them from that post. Please put the word "ORBIT" in the subject so I can easily find it in the flood of spam I get.


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Post    Posted on: Thu Feb 03, 2005 3:55 pm
Here is Ekkehard's Excel file. I deleted all but the first few lines to make it small enough to fit in my limited web space.
http://home.austin.rr.com/campbelp/orbitek.xls


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Post    Posted on: Fri Feb 04, 2005 10:12 am
Peter sent me a modification of the Excel file I emailed him by attachment. He asked me wether I agree that it doesn't change my mathematics but I still didn't fin time to check it.

I too didn't find time to provide an illustration of a correction I am using to correct my second step - I#m missing experiences with MS Paint.

I will answer your posts when I have the time again, Peter. The illustrating graphics will be a little bit complicated.



Dipl.-Volkswirt (bdvb) Augustin (Political Economist)


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Joined: Thu Jan 27, 2005 12:34 am
Posts: 450
Post    Posted on: Thu Mar 10, 2005 10:59 pm
No, I didn't read it all. So I am responding to the question.
Yes an object can spiral into the sun UNDER THRUST.
Yes, an almost passive load of trash could use a solar sail to spiral into the sun.
(or outward, but its progress would slow down rapidly with distance).
Yes, spiraling into a star seems to be predicted when relativistic effects are included.


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