Niu: Created page with "=== Relativistic photon trajectory === center

 require("/home/falkner/Public/lightbending.git/lbscripts");  define lb_plot_ptracesketch( R, b..."

2018-05-02T11:43:00Z

Created page with "=== Relativistic photon trajectory === 800px|center <pre> require("/home/falkner/Public/lightbending.git/lbscripts"); define lb_plot_ptracesketch( R, b..."

New page

=== Relativistic photon trajectory ===
[[File:ptrace3.png|800px|center]]

<pre>
require("/home/falkner/Public/lightbending.git/lbscripts");

define lb_plot_ptracesketch( R, b ){

variable size = qualifier("size",16);
variable rmax = qualifier("rmax",10.);
variable index = qualifier("index","");
if( index !="" )
index = string( "\\ensuremath{_"+index+"}" );

variable dx = qualifier("dx",1.);

variable a1 = lb_a_ub( 1./R, b );
variable a2 = PI-a1;
variable p1 = lb_psi_ua_belob( 1./R, a1 );
variable p2 = lb_psi_ua_belob( 1./R, a2 ; b=b );
variable p = lb_p_b( b );
variable psip = lb_psi_ua_belob( 1./p, PI/2. ; b=b );

variable pon = 0;
if( qualifier_exists("periastron") )
pon = 1;
variable pmax = p1;
if(pon)
pmax = p2;

variable trace = lb_ptrace_belob( b; pmax=pmax, rmax=rmax);

variable xmax = abs(max(trace.r)*cos(min(trace.p)));
variable ymax = abs(max(trace.r)*sin(min(trace.p)));
variable tmp,dr;

variable xf;
if( qualifier_exists("addto") )
xf=qualifier("addto");
else{
xf = xfig_plot_new(size,size);
xf.world(-1.2*xmax,1.2*xmax,-1.2*xmax,1.2*xmax;xpad,ypad);
xf.axis(;off);
}

%Circle at R
tmp = [0:2*PI:#100];
xf.plot( R*cos(tmp), R*sin(tmp) ; line=2 );
tmp = 2.5/R*7./4.*PI;
xf.plot( [0,R*cos(tmp)], [0,R*sin(tmp)] ; line=2 );
xf.xylabel(.5*R*cos(0.93*tmp), .5*R*sin(0.93*tmp) , "$R$"+index );

%trace
xf.plot( trace.r*cos(trace.p), trace.r*sin(trace.p) ; width=4, color="red", depth=20);
xf.xylabel(dx*xmax,b,"photon"+index,.5,-.5);

% impact parameter
xf.plot( dx*[0.8*xmax, 0.8*xmax],[0,b] );
xf.xylabel( dx*0.8*xmax, b/2., "$b$"+index, .5,0);

ifnot( qualifier_exists("addto") ){
% observer sky
xf.plot( [1.1*xmax,1.1*xmax],[-1.2*ymax,1.2*ymax] ; line=3 );
xf.xylabel( 1.12*xmax, 0, "{\\tiny observer sky at infinity}",-.5,0 ; rotate=90 );

% line of sight
xf.plot( [0,xmax],[0,0] );
xf.xylabel( .5*(xmax+R),-.05*R,"\\tiny line of sight",.0,.5);
}
ifnot( qualifier_exists("nopsi") ){
% Psi R
xf.plot( [0,1.5*R*cos(p1)],[0,1.5*R*sin(p1)] ; depth=19 );
tmp = [0:p1:#100];
dr = .45;
xf.plot( dr*R*cos(tmp),dr*R*sin(tmp) );
dr += .2;
xf.xylabel( dr*R*cos(p1/2.), dr*R*sin(p1/2.), "$\\Psi_{R"+index+"}$");
}

% alpha
if( qualifier_exists("alpha") ){
tmp = [p1-a1:p1:#100];
dr=.4;
xf.plot( R*cos(p1)+dr*R*cos(tmp), R*sin(p1)+dr*R*sin(tmp) ;depth=19);
xf.xylabel( R*cos(p1)+.7*dr*R*cos(p1-a1/2.), R*sin(p1)+.7*dr*R*sin(p1-a1/2.),
"$\\alpha$"+index );
dr = 1.;
xf.plot( R*cos(p1)+[0,dr*R*cos(p1-a1)],R*sin(p1)+[0,dr*R*sin(p1-a1)] ; line=1,depth=19);
}

if(pon){
ifnot( qualifier_exists("nopsi") ){
% Psi R prime
xf.plot( [0,1.5*R*cos(p2)],[0,1.5*R*sin(p2)] ; depth=19);
tmp = [0:p2:#100];
dr = .15;
xf.plot( dr*R*cos(tmp),dr*R*sin(tmp) );
dr += .3;
xf.xylabel( dr*R*cos(.5*(psip+p2)), dr*R*sin(.5*(psip+p2)), "$\\Psi^*_{R"+index+"}$");

% periastron
xf.plot( [0,p*cos(psip)],[0,p*sin(psip)] );
tmp = [0:psip:#100];
dr = .3;
xf.plot( dr*R*cos(tmp), dr*R*sin(tmp) );
dr += .2;
xf.xylabel( dr*R*cos(.5*(psip+p1)), dr*R*sin(.5*(psip+p1)), "$\\Psi_{p"+index+"}$");
}
if( qualifier_exists("alpha") ){
% alpha prime
tmp = [p2-a2:p2:#100];
dr = .4;
xf.xylabel( R*cos(p2)+.6*dr*R*cos(p2-a2/2.), R*sin(p2)+.6*dr*R*sin(p2-a2/2.),
"$\\alpha^*$"+index );
xf.plot( R*cos(p2)+dr*R*cos(tmp), R*sin(p2)+dr*R*sin(tmp) ;depth=19);
dr = 1.5;
xf.plot( R*cos(p2)+[0,dr*R*cos(p2-a2)],R*sin(p2)+[0,dr*R*sin(p2-a2)] ; line=1,depth=19);

if(qualifier_exists("symm")){
% alpha prime at alpha
tmp = [p1:p1+a2:#100];
dr = .4;
xf.xylabel( R*cos(p1)+.6*dr*R*cos(p1+a2/2.), R*sin(p1)+.6*dr*R*sin(p1+a2/2.),
"$\\alpha^*$"+index );
xf.plot( R*cos(p1)+dr*R*cos(tmp), R*sin(p1)+dr*R*sin(tmp);depth=19 );
dr = 1.;
xf.plot( R*cos(p1)+[0,dr*R*cos(p1+a2)],R*sin(p1)+[0,dr*R*sin(p1+a2)] ; line=1,depth=19);
}
}
}
return xf;
}

variable R = 2.5;
variable b = 2.9;

variable xf;
xf = lb_plot_ptracesketch( R, b );
xf.render("ptrace1.pdf");

xf = lb_plot_ptracesketch( R, b ; periastron );
xf.render("ptrace2.pdf");

xf = lb_plot_ptracesketch( R, b ; alpha,periastron,symm );
xf.render("ptrace3.pdf");

variable R2 = 1.5*R;
variable b2 = 1.3*b;
variable p1 = lb_psi_ua_belob( 1./R, lb_a_ub( 1./R, b ) );
variable p2 = lb_psi_ua_belob( 1./R2, lb_a_ub( 1./R2, b2 ) );
variable p3 = lb_psi_ua_belob( 1./R2, PI-lb_a_ub( 1./R2, b2 ));
xf = lb_plot_ptracesketch( R2, b2 ; nopsi,index="2",periastron,dx=0.9);
xf = lb_plot_ptracesketch( R, b ; nopsi, addto=@xf, index="1" );
xf.plot( R,0; sym=1, size=1,fill );
xf.plot( R*cos(p1),R*sin(p1); sym=1, size=1,fill,fillcolor="red",depth=18 );
xf.plot( R2,0; sym=0, size=4,fill );
xf.plot( R2*cos(p2),R2*sin(p2); sym=0, size=4,fill,fillcolor="red",depth=18 );
xf.plot( R2*cos(p3),R2*sin(p3); sym=0, size=4,fill,fillcolor="white",depth=18 );
xf.render("ptrace4.pdf");

exit;

</pre>

[[Category:SLxfig]]

Lightbending ptrace (xfig example) - Revision history

Niu: Created page with "=== Relativistic photon trajectory === center
require("/home/falkner/Public/lightbending.git/lbscripts"); define lb_plot_ptracesketch( R, b..."