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Q5: Compute the separations for M1 to HCG7 and M13 for HCG7 using the small-angle approximation: $s = \sqrt{(\Delta\alpha)^2 \cos^2 \delta_{ave} + (\Delta\delta)^2}$. Where $\Delta\alpha$ and $\Delta\delta$ are the difference in RA and Dec respectively, and $\delta_{ave}$ is the average Dec of both objects. (Hint: if you use only Quantity operations, you shouldn't have to think about units at all) In [103]: import math print(M1) print(M13) print(HCG7) $\Delta\alpha_{m1} = ((M1.ra)-(HCG7.ra))$ $\Delta\alpha_{m13} = ((M13.ra)-(HCG7.ra))$ $\Delta\delta_{m1} = ((M1.dec)-(HCG7.dec))$ $\Delta\delta_{m13} = ((M13.dec)-(HCG7.dec))$ $\delta_{ave1} = ((M1.dec+HCG7.dec)/2)$ $\delta_{ave2} = ((M13.dec+HCG7.dec)/2)$ s1 = ((($\Delta\alpha_{m1}$)**2)*(np.cos($\delta_{ave1}$)(2))+(($\Delta\delta_{m1}$)2))**(1/2)

          Q5: Compute the separations for M1 to HCG7 and M13 for HCG7 using the small-angle approximation: $s = \sqrt{(\Delta\alpha)^2 \cos^2 \delta_{ave} + (\Delta\delta)^2}$. Where $\Delta\alpha$ and $\Delta\delta$ are the difference in RA and Dec respectively, and $\delta_{ave}$ is the average Dec of both objects.

(Hint: if you use only Quantity operations, you shouldn't have to think about units at all)
In [103]: import math
print(M1)
print(M13)
print(HCG7)
$\Delta\alpha_{m1} = ((M1.ra)-(HCG7.ra))$
$\Delta\alpha_{m13} = ((M13.ra)-(HCG7.ra))$
$\Delta\delta_{m1} = ((M1.dec)-(HCG7.dec))$
$\Delta\delta_{m13} = ((M13.dec)-(HCG7.dec))$
$\delta_{ave1} = ((M1.dec+HCG7.dec)/2)$
$\delta_{ave2} = ((M13.dec+HCG7.dec)/2)$
s1 = ((($\Delta\alpha_{m1}$)**2)*(np.cos($\delta_{ave1}$)**(2))+(($\Delta\delta_{m1}$)**2))**(1/2)

Q5: Compute the separations for M1 to HCG7 and M13 for HCG7 using the small-angle approximation: s = √((Δα)^2 cos^2 δave + (Δδ)^2). Where Δα and Δδ are the difference in RA and Dec respectively, and δave is the average Dec of both objects.

(Hint: if you use only Quantity operations, you shouldn't have to think about units at all)
In [103]: import math
print(M1)
print(M13)
print(HCG7)
Δαm1 = ((M1.ra)-(HCG7.ra))
Δαm13 = ((M13.ra)-(HCG7.ra))
Δδm1 = ((M1.dec)-(HCG7.dec))
Δδm13 = ((M13.dec)-(HCG7.dec))
δave1 = ((M1.dec+HCG7.dec)/2)
δave2 = ((M13.dec+HCG7.dec)/2)
s1 = (((Δαm1)**2)*(np.cos(δave1)**(2))+((Δδm1)**2))**(1/2)

Added by Aaron T.

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