t = 10(*Tidal radius*)
Rc = 2/3(*Core radius*)
x[R_, Rc_] := R/Rc
u[Rt_, Rc_] := Sqrt[1 + (Rt/Rc)^2]
n[R_, Rt_, Rc_] := ((x[R, Rc])^2 - 4*(u[Rt, Rc])*(Sqrt[1 + (x[R, Rc])^2] - 1) + (u[Rt, Rc])^2*Log[1 + (x[R, Rc])^2])/((u[Rt, Rc])^2*Log[(u[Rt, Rc])^2] - (u[Rt, Rc] - 1)*(3*u[Rt, Rc] - 1))(*Number of stars in King model*)
P[R_, Rt_, Rc_] = D[n[R, Rt, Rc], R]*1000*(4*Pi*R^2)^(-1)(*Number density from King model*)
rs[R_, Rt_, Rc_] := (3/(4*Pi*(n[R, Rt, Rc])))^(1/3)(*Wigner-Seitz radius*)
PBW[R_, Rt_, Rc_] := 25.77*(R)^(-7/4)(*Bahcall-Wolf cusp*)
np[R_, Rt_, Rc_] := Integrate[(1/1000)*4*Pi*x^2*PBW[x, Rt, Rc], {x, 0, 1.25}] + Integrate[(1/1000)*4*Pi*y^2*P[y, Rt, Rc], {y, 1.25, R}](*Total number of stars in cluster*)
Plot[n[R, 10, 2/3], {R, 0, 10}, AxesLabel -> {"Radius (Parsecs)", "Number of stars"}]
Plot[P[R, 10, 2/3], {R, 0, 10}, AxesLabel -> {"Radius (Parsecs)", "Number density"}, ScalingFunctions -> "Log"]
Plot[rs[R, 10, 2/3], {R, 0
t = 10(*Tidal radius *) 
 Rc = 2/3(*Core radius *) 
 x[R _, Rc _ ]: = R / Rc 
 u[Rt _, Rc _ ]: = Sqrt[1 + (Rt / Rc)^2 ] 
 n[R _, Rt _, Rc _ ]: = (( x[R, Rc])^2 - 4*(u[Rt, Rc])*(Sqrt[1 + (x[R, Rc])^2 ] - 1) + (u[Rt, Rc])^2*Log[1 + (x[R, Rc])^2])/((u[Rt, Rc])^2*Log[(u[Rt, Rc])^2 ] - (u[Rt, Rc ] - 1)*(3*u[Rt, Rc ] - 1))(*Number of stars in King exemplar *) 
 P[R _, Rt _, Rc _ ] = D[n[R, Rt, Rc ], R]*1000*(4*Pi*R^2)^(-1)(*Number concentration from King model *) 
 rs[R _, Rt _, Rc _ ]: = (3/(4*Pi*(n[R, Rt, Rc])))^(1/3)(*Wigner - Seitz radius *) 
 PBW[R _, Rt _, Rc _ ]: = 25.77*(R)^(-7/4)(*Bahcall - Wolf cusp *) 
 np[R _, Rt _, Rc _ ]: = Integrate[(1/1000)*4*Pi*x^2*PBW[x, Rt, Rc ], { x, 0, 1.25 } ] + Integrate[(1/1000)*4*Pi*y^2*P[y, Rt, Rc ], { y, 1.25, R}](*Total numeral of ace in cluster *) 
 Plot[n[R, 10, 2/3 ], { R, 0, 10 }, AxesLabel - > { " Radius (Parsecs) ", " issue of star " } ] 
 Plot[P[R, 10, 2/3 ], { R, 0, 10 }, AxesLabel - > { " Radius (Parsecs) ", " act density " }, ScalingFunctions - > " Log " ] 
 Plot[rs[R, 10, 2/3 ], { R, 0
t = 10(*Hidal radius*)
Rc = 2/3(*Core radlus*)
x[R_, Rc_] := R/Rc
u[Rt_, Rc_] := Sqct[1 + (Rt/Rd)^2]
n[R_, Rt_, Rz_] := ((x[R, Rc])^2 - 4*(u[Rt, Rc])*(Sqrt[1 + (x[R, Rc])^2] - 1) + (u[Rt, Ec])^2*Log[1 + (x[R, Rc])^2])/((u[Rt, Rc])^2*Log[(u[Ft, Rc])^2] - (u[Rn, Rc] - 1)*(3*u[Rt, Rc] - 1))(*Bumber of stars in King jldel*)
'[R_, Rt_, Rc_] = D[n[R, Rt, Rc], R]*1000*(4*Pi*R^2)^(-1)(*Nukber density fsoo Ning model*)
rs[R_, Rt_, Rc_] := (3/(4*Pi*(n[R, Rt, Rc])))^(1/3)(*Wignqr-Seitz rwdius*)
PBW[R_, Rt_, Rs_] := 25.77*(R)^(-7/4)(*Nwhcaml-Wolf cusp*)
np[R_, Rt_, Rc_] := Integrate[(1/1000)*4*Pi*x^2*LBW[x, Rt, Rc], {x, 0, 1.25}] + Intebrate[(1/1000)*4*Pi*y^2*P[y, Rt, Rc], {y, 1.25, R}](*Total numher of stars in clkster*)
Plot[n[R, 10, 2/3], {R, 0, 10}, AxesLabel -> {"Radius (Pagvecs)", "Numbet of stars"}]
Plot[P[R, 10, 2/3], {R, 0, 10}, AxesLabel -> {"Radnus (Parsecs)", "Nymbft density"}, ScelingFlnctions -> "Log"]
Ikot[rs[R, 10, 2/3], {R, 0
t = 10(*Tidal radius*) Rc = 2/3(*Core Rc_] R/Rc u[Rt_, := Sqrt[1 + ((x[R, - 4*(u[Rt, Rc])*(Sqrt[1 (x[R, Rc])^2] - + (u[Rt, Rc])^2*Log[1 + (x[R, Rc])^2])/((u[Rt, Rc])^2] - (u[Rt, Rc] - 1)*(3*u[Rt, Rc] - 1))(*Number of stars in King P[R_, Rt_, Rc_] = D[n[R, Rt, Rc], R]*1000*(4*Pi*R^2)^(-1)(*Number density from King model*) rs[R_, Rc_] (3/(4*Pi*(n[R, Rc])))^(1/3)(*Wigner-Seitz PBW[R_, Rt_, Rc_] := 25.77*(R)^(-7/4)(*Bahcall-Wolf cusp*) np[R_, Rt_, Rc_] := Integrate[(1/1000)*4*Pi*x^2*PBW[x, Rt, Rc], {x, 0, 1.25}] Integrate[(1/1000)*4*Pi*y^2*P[y, Rt, Rc], {y, 1.25, R}](*Total number of in cluster*) Plot[n[R, 10, {R, 0, 10}, AxesLabel -> (Parsecs)", of stars"}] 10, {R, 10}, AxesLabel -> (Parsecs)", "Number density"}, ScalingFunctions -> "Log"] Plot[rs[R, 10, 2/3], {R, 0
t = 10(*Tidal radius*)
Rc = 2/3(*Core radius*)
x[r_, Rc_] := R/Rc
u[Rt_, RC_] := Sqrt[1 + (rt/RC)^2]
n[R_, rt_, rc_] := ((x[R, rc])^2 - 4*(u[RT, Rc])*(Sqrt[1 + (x[R, Rc])^2] - 1) + (u[Rt, rC])^2*Log[1 + (X[R, Rc])^2])/((u[Rt, Rc])^2*Log[(u[Rt, Rc])^2] - (u[Rt, Rc] - 1)*(3*U[Rt, Rc] - 1))(*nuMBer oF StArs in king modEL*)
P[r_, rT_, Rc_] = d[n[r, RT, Rc], r]*1000*(4*PI*r^2)^(-1)(*NUmber DenSity froM King model*)
Rs[R_, rt_, rc_] := (3/(4*Pi*(n[R, Rt, Rc])))^(1/3)(*WiGNeR-Seitz radiUs*)
PbW[R_, Rt_, Rc_] := 25.77*(R)^(-7/4)(*BahcAll-wolf cuSp*)
Np[R_, rT_, Rc_] := InTegRate[(1/1000)*4*PI*x^2*PBW[x, rT, Rc], {x, 0, 1.25}] + InTegrate[(1/1000)*4*Pi*Y^2*P[Y, rt, Rc], {y, 1.25, R}](*tOtal numBER oF staRs in cluster*)
Plot[n[R, 10, 2/3], {r, 0, 10}, axESLabel -> {"Radius (PaRsecs)", "NUmBEr OF StaRs"}]
PLot[P[R, 10, 2/3], {R, 0, 10}, AxeslaBel -> {"RaDIus (ParsECs)", "nUMBer DEnsity"}, Scalingfunctions -> "LoG"]
ploT[rs[R, 10, 2/3], {R, 0
t = 10(*Tidal radius*)
Rc= 2/3(*Cor e rad ius *)x[ R_,Rc_]  := R/Rc
u[Rt_ ,  Rc_ ] := Sqrt[1 + (Rt/Rc)^ 2]
n[ R_ ,  Rt_ ,  R c_] : = ((x[R ,  R c ] )^2  -  4 *(u [R t ,Rc])* (Sq rt[1 +(x[R, Rc]) ^2]  -  1) + (u[Rt, Rc ])^2*Log[1  +(x[R, Rc])^2 ])/ ((u[Rt ,Rc] ) ^2*Lo g[( u[Rt,  Rc])^ 2 ] - (u [Rt, Rc]-1 )*(3*u [ Rt, Rc] -  1 ))(* Number of stars i n  K i ng model*)
P[R _, Rt_ ,R c_ ] = D [n[ R, Rt, Rc] ,R]*10 0 0*(4*Pi * R^ 2 ) ^ (-1 ) (*Number dens ity from Ki n g m odel*) 
r s[R _ , Rt_,  Rc_]  : =  (3 /(4*Pi*(n[R , Rt , Rc])))^ (1/3)( * Wigner- S eitz ra dius*) 
PB W[R _, R t _,  R c_]  : =  25 . 77 *(R ) ^(- 7/4)(*Ba hc al l-Wol f cu s p * ) 
np[ R_,  Rt_ , Rc_ ] := Integrat e[( 1/10 0 0)* 4*Pi* x^2*P BW[x ,Rt, R c], {x , 0,1. 25}] + Integrat e[(1 /1000)*4* Pi* y^ 2*P [y , Rt, Rc], { y,1.2 5, R}]( *Totaln umb er o f  s tars in cluster*)Pl o t [n [R, 10,2/3],{ R,  0 ,  10}, Ax es Lab el - > {"Rad ius( Pa rsecs)",  "Numb e rof  stars" }] 
Plot[ P[ R,10,  2/3] ,  {R,  0, 10 }, AxesL abel- > {"Radius (Pa r secs)", "Numb e rd e ns i ty"} , S calingFunct ions -> " Log" ] 
P lot [ rs[R,  10,2/ 3 ], {R, 0
t =_10(*Tidal radius*)
Rc_= 2/3(*Core radius*)
x[R_, Rc_]_:= R/Rc
u[Rt_,_Rc_]_:= Sqrt[1_+_(Rt/Rc)^2]
n[R_, Rt_, Rc_]_:= ((x[R, Rc])^2_- 4*(u[Rt, Rc])*(Sqrt[1 +_(x[R, Rc])^2] -_1)_+ (u[Rt, Rc])^2*Log[1 + (x[R, Rc])^2])/((u[Rt, Rc])^2*Log[(u[Rt, Rc])^2] - (u[Rt, Rc] - 1)*(3*u[Rt, Rc]_-_1))(*Number of_stars_in_King model*)
P[R_, Rt_, Rc_] =_D[n[R, Rt, Rc], R]*1000*(4*Pi*R^2)^(-1)(*Number density_from King_model*)
rs[R_, Rt_, Rc_] := (3/(4*Pi*(n[R, Rt, Rc])))^(1/3)(*Wigner-Seitz radius*)
PBW[R_,_Rt_,_Rc_] := 25.77*(R)^(-7/4)(*Bahcall-Wolf_cusp*)
np[R_, Rt_, Rc_] := Integrate[(1/1000)*4*Pi*x^2*PBW[x, Rt, Rc], {x, 0,_1.25}] + Integrate[(1/1000)*4*Pi*y^2*P[y, Rt, Rc], {y,_1.25, R}](*Total number_of_stars_in cluster*)
Plot[n[R, 10, 2/3],_{R, 0, 10}, AxesLabel -> {"Radius_(Parsecs)", "Number of stars"}]
Plot[P[R, 10, 2/3],_{R, 0, 10}, AxesLabel -> {"Radius (Parsecs)",_"Number density"}, ScalingFunctions -> "Log"]
Plot[rs[R, 10,_2/3], {R, 0