CoCalc -- 1906.sagews

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# Error propagation for d

l = var('lamda')
t = var('theta')
d = l/sin(t)
diff(d,t)

\newcommand{\Bold}[1]{\mathbf{#1}}\frac{-\mbox{lamda} \cos\left(\theta\right)}{\sin\left(\theta\right)^{2}}

# Propagate error for n by quadrature

# Declare function variables
d = var('d')
m = var('m')
R = var('R')
sigd = var('sigd')
sigt = var('sigt')

# Declare function for n
top = 4*R*d*sin(t)
bottom = R*d*sin(t)-4*m
n = sqrt(top/bottom)

# Take partial derivatives of n
dt = diff(n,t)
dd = diff(n,d)

# Calculate sigma_n
sigma_n = sqrt((dd*sigd)**2+(dt*sigt)**2)

<html><span class="math">\newcommand{\Bold}[1]{\mathbf{#1}}2 \, \sqrt{\frac{R d \sin\left(\theta\right)}{{\left(R d \sin\left(\theta\right) - 4 \, m\right)

/span> }}}

sigma_n

\newcommand{\Bold}[1]{\mathbf{#1}}\sqrt{\frac{{\left(R d \sin\left(\theta\right) - 4 \, m\right)} {\left(\frac{R^{2} d \sin\left(\theta\right)^{2}}{{\left(R d \sin\left(\theta\right) - 4 \, m\right)}^{2}} + \frac{-R \sin\left(\theta\right)}{{\left(R d \sin\left(\theta\right) - 4 \, m\right)}}\right)}^{2} \mbox{sigd}^{2}}{R d \sin\left(\theta\right)} + \frac{{\left(R d \sin\left(\theta\right) - 4 \, m\right)} {\left(\frac{R^{2} d^{2} \sin\left(\theta\right) \cos\left(\theta\right)}{{\left(R d \sin\left(\theta\right) - 4 \, m\right)}^{2}} + \frac{-R d \cos\left(\theta\right)}{{\left(R d \sin\left(\theta\right) - 4 \, m\right)}}\right)}^{2} \mbox{sigt}^{2}}{R d \sin\left(\theta\right)}}

# Collected data
tvalues = [
    {'t': 24,'sigt': 0.03333333333333},
    {'t': 18.0083333333333,'sigt': 0.05},
    {'t': 20.75,'sigt': 0.05},
    {'t': 15,'sigt': 0.03333333333333},
    ]

# Define constant values
R = 10974000
d = 1.6584E-06
sigd = 1.27E-09
m = 1


# Evaluate n_i with constant values
sig_n_i = sigma_n(R=R,d=d,sigd=sigd,m=m)


# Convenience function used to convert measured angles from degrees to radians
def rad(deg):
    return pi*deg/180
    

# Calculate error for each data point
for tvalue in tvalues:
    t = tvalue['t']
    sigt = tvalue['sigt']
    print float(sig_n_i(theta=rad(t), sigt=rad(sigt)))

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