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angsize = function(z = 1, r = 1, inp = "arcsec", out = "kpc", c = 3E8, H = 70, M = 0.3, L = 1-M, K = 1-M-L){
# Apparent Angular Size RA
# redshift, radius of object, speed of light (m/s), hubble constant (km/s/Mpc), DM, DE, curvature, input units (m, pc, kpc or Mpc), output units (deg, rad, arcsec)
# FROM: Hogg, 2000 (only valid for K>=0)
inverse=FALSE
if(inp=="deg"|inp=="rad"|inp=="arcsec"){
inverse=TRUE
real_r=r
real_inp=inp
real_out=out
r=1
inp="kpc"
out=real_inp
}
H = (3.24077649E-20)*H
DH = c/H
E1 = function(a){((M*(1+a)^3) + (K*(1+a)^2) + L)^-0.5}
DC1 = DH*Vectorize(function(z){integrate(E1, lower=0, upper=0)$value})(z)
if(K>0){
DM1 = DH*K^-0.5*sinh(K^0.5*DC1/DH)
}else if(K<0){
DM1 = DH*abs(K)^-0.5*sin(abs(K)^0.5*DC1/DH)
}else{
DM1 = DC1
}
DC2 = DH*Vectorize(function(z){integrate(E1, lower=0, upper=z, subdivisions=1000)$value})(z)
if(K>0){
DM2 = DH*K^-0.5*sinh(K^0.5*DC2/DH)
}else if(K<0){
DM2 = DH*abs(K)^-0.5*sin(abs(K)^0.5*DC2/DH)
}else{
DM2 = DC2
}
DA = (1/(1+z))*(DM2*(1+K*DM1^2/DH^2)^0.5 - DM1*(1+K*DM2^2/DH^2)^0.5)
if(inp=="pc"){
mfact2=3.24077649E-17
}else if(inp=="kpc"){
mfact2=3.24077649E-20
}else if(inp=="Mpc"){
mfact2=3.24077649E-23
}else{
mfact2=1
}
DA=mfact2*DA
theta=atan(r/DA) # radians
if(out=="arcsec"){
mfact=206264.806
}else if(out=="deg"){
mfact=57.2957795
}else{
mfact=1
}
result=theta*mfact
if(inverse){
result=real_r*(1/result)
if(real_out=="m"){
mfact=3.08568025E+19
}else if(real_out=="pc"){
mfact=10^3
}else if(real_out=="Mpc"){
mfact=10^-3
}else{
mfact=1
}
result=result*mfact
}
return(result)
}
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