def transit_prob(Rp, aR, e=0, w=90):
"""
Function to calculate period of rotation of a planet
Parameters
-----------
Rp: float;
radius of the planet in unit f the stellar radius
aR: float;
Scaled semi-major axis i.e. a/R*.
e: float;
eccentricity of the orbit.
w: float;
longitude of periastron in degrees
"""
#eqn 5 - Kane & von Braun 2008, https://core.ac.uk/reader/216127860
prob = (1 + Rp)/aR * (1 + e*sin(radians(w))/(1-e**2) )
return prob
def inclination(b, a, e=0, w=90):
"""
Function to convert impact parameter b to inclination in degrees.
Parameters:
----------
b: Impact parameter of the transit.
a: Scaled semi-major axis i.e. a/R*.
e: float;
eccentricity of the orbit.
w: float;
longitude of periastron in degrees
Returns
--------
inc: The inclination of the planet orbit in degrees.
"""
ecc_factor = (1 - e**2) / (1 + e * sin(radians(w)))
inc = degrees(acos(b / (a * ecc_factor)))
return inc
def transit_duration(P, Rp, a, b=0, e=0, w=90, inc=None, total=True):
"""
Function to calculate the total (T14) or full (T23) transit duration
Parameters:
----------
P: Period of planet orbit in days
Rp: Radius of the planet in units of stellar radius
b: Impact parameter of the planet transit [0, 1+Rp]
a: scaled semi-major axis of the planet in units of solar radius
inc: inclination of the orbit. Optional. If given b is not used. if None, b is used to calculate inc
total: if True calculate the the total transit duration T14, else calculate duration of full transit T23
Returns
-------
Tdur: duration of transit in same unit as P
"""
#eqn 30 and 31 of Kipping 2010 https://doi.org/10.1111/j.1365-2966.2010.16894.x
factor = (1-e**2)/(1+e*sin(radians(w)))
if inc == None:
inc = inclination(b,a,e,w)
if total is False:
Rp = -Rp
sini = sin(radians(inc))
cosi = cos(radians(inc))
denom = a*factor*sini
tdur= (P/np.pi) * (factor**2/sqrt(1-e**2)) * (asin ( sqrt((1+Rp)**2 - (a*factor*cosi)**2)/ denom ) )
return tdur
def effective_ringed_planet_radius(rp, rin, rout, ir):
"""
Calculate effective radius of a ringed planet accounting for possible overlap between ring and planet. - eqn (2) from zuluaga+2015 http://dx.doi.org/10.1088/2041-8205/803/1/L14
Parameters:
-----------
rp : float, ufloat;
Radius of the planet hosting the ring
rin, rout : float, ufloat;
Inner and outer radii of the ring in units of rp.
ir : float, ufloat;
Inclination of the ring from the skyplane. 0 is face-on ring, 90 is edge on
Returns:
--------
eff_R : float, ufloat;
effective radius of the ringed planet in same unit as rp
"""
cosir = cos(radians(ir))
sinir = sin(radians(ir))
y = lambda r: sqrt(r**2 - 1) / (r * sinir)
def eff(r):
if r * cosir > 1:
eff_r = r**2 * cosir - 1
else:
eff_r = (r**2 * cosir * 2 / np.pi *
asin(y(r))) - (2 / np.pi * asin(y(r) * r * cosir))
return eff_r
rout_eff2 = eff(rout)
rin_eff2 = eff(rin)
Arp = rp**2 + rp**2 * (rout_eff2 - rin_eff2)
return sqrt(Arp)
def impact_parameter(inc, a, e=0, w=90, format='deg'):
"""
Function to convert inclination to impact parameter b.
input format of angles as 'deg' or 'rad'.
see eq. 1.19 in https://www.astro.ex.ac.uk/people/alapini/Publications/PhD_chap1.pdf
also https://arxiv.org/pdf/1812.08549.pdf
Parameters:
----------
inc: float;
inclination of the planetary orbit
a: float;
scaled semi-major axis in units of solar radii
e: float;
eccentricity of the orbit.
w: float;
longitude of periastron
format: str; - "deg" or "rad"
unit of the `inc` and `w`
Returns
-------
b: impact parameter
"""
if format == 'deg':
inc = radians(inc)
w = radians(w)
ecc_factor = (1 - e**2) / (1 + e * sin(w))
return a * cos(inc) * ecc_factor
def get_earth_observer_vector_fast(time):
"""Calculate the position vector of an observer on the earth in
barcentric cartesian coordinates, approximately and hopefully
abit faster.
"""
n = time-Time('2000-01-01T12:00:00', format='isot', scale='utc')
# mean longitude of the sun
L = (280.460 + 0.9856474*n.jd) % 360.0
# mean anomaly of the sun
g = (357.528 + 0.9856003*n.jd) % 360.0
# ecliptic longitude of the sun
l = L + 1.915*np.sin(np.radians(g)) + 0.020*np.sin(np.radians(2*g))
# axial tilt of the earth
# Obliquity of the ecliptic
epsilon = 23.439 - 0.0000004*n.jd
return np.array([
np.cos(np.radians(l)),
np.cos(np.radians(epsilon))*np.sin(np.radians(l)),
np.sin(np.radians(epsilon))*np.sin(np.radians(l))]) * -1.0