python – 无法重现使用astropy获取的源之间的距离值

我使用两种方法,据我所知,应该给出相同的结果,但不是.

第一种方法是应用astropy的separation_3d功能.第二种方法是使用表达式给出两个具有球面坐标的源之间的距离：

如here所示.

在下面的MCVE中,返回的值是：

91.3427173002 pc
93.8470493776 pc

这两个值不应该相等吗？

MCVE：

from astropy.coordinates import SkyCoord
from astropy import units as u
import numpy as np

# Define some coordinates and distances for the sources.
c1 = SkyCoord(ra=9.7*u.degree,dec=-50.6*u.degree,distance=1500.3*u.pc)
c2 = SkyCoord(ra=7.5*u.degree,dec=-47.6*u.degree,distance=1470.2*u.pc)

# Obtain astropy's distance between c1 & c2 coords.
print c1.separation_3d(c2)

# Obtain distance between c1 & c2 coords using explicit expression.
ra_0,dec_0,r_0 = c1.ra.radian,c1.dec.radian,c1.distance
ra,dec,r = c2.ra.radian,c2.dec.radian,c2.distance
alpha_delta_par = np.sin(dec) * np.sin(dec_0) * np.cos(ra - ra_0) +
    np.cos(dec) * np.cos(dec_0)
d_pc = np.sqrt(r**2 + r_0**2 - 2*r*r_0*alpha_delta_par)
print d_pc