我将如何计算“卫星地球”下方的面积，以便绘制卫星越过时所覆盖的大片土地？
在Skyfield中有什么可以帮助实现这一点的吗？
编辑：只是想我要澄清一下卫星下方区域的含义。考虑到地球是一个椭球体，我需要绘制卫星下方可能观察到的最大区域。我知道如何绘制卫星路径，但是现在我需要绘制一些线来表示该卫星飞过地球时可见的区域。
答案 0 :(得分：2)
您所做的编辑清楚了您想要什么。可以很容易地计算出卫星的可见区域（当地球被视为球体时）。 here是找到可见部分背景的好资源。当地球被视为扁球体时，要计算可见区域将要困难得多（甚至不可能）。我认为最好将问题的这一部分进行改革并将其发布在数学上。
如果要计算将地球视为球形时的可见区域，我们需要在Skyfield中进行一些调整。通过使用TLE api加载的卫星，您可以轻松获得地球上某个位置的子点。库将其称为Geocentric位置，但实际上是Geodetic位置（在这里地球被视为扁球体）。要纠正此问题，我们需要调整subpoint类的Geocentric以将计算用于Geocentric位置而不是Geodetic位置。由于reverse_terra函数中的错误和信息丢失，我们还需要替换该函数。而且我们需要能够检索地球半径。结果如下：
from skyfield import api
from skyfield.positionlib import ICRF, Geocentric
from skyfield.constants import (AU_M, ERAD, DEG2RAD,
IERS_2010_INVERSE_EARTH_FLATTENING, tau)
from skyfield.units import Angle
from numpy import einsum, sqrt, arctan2, pi, cos, sin
def reverse_terra(xyz_au, gast, iterations=3):
"""Convert a geocentric (x,y,z) at time `t` to latitude and longitude.
Returns a tuple of latitude, longitude, and elevation whose units
are radians and meters. Based on Dr. T.S. Kelso's quite helpful
article "Orbital Coordinate Systems, Part III":
https://www.celestrak.com/columns/v02n03/
"""
x, y, z = xyz_au
R = sqrt(x*x + y*y)
lon = (arctan2(y, x) - 15 * DEG2RAD * gast - pi) % tau - pi
lat = arctan2(z, R)
a = ERAD / AU_M
f = 1.0 / IERS_2010_INVERSE_EARTH_FLATTENING
e2 = 2.0*f - f*f
i = 0
C = 1.0
while i < iterations:
i += 1
C = 1.0 / sqrt(1.0 - e2 * (sin(lat) ** 2.0))
lat = arctan2(z + a * C * e2 * sin(lat), R)
elevation_m = ((R / cos(lat)) - a * C) * AU_M
earth_R = (a*C)*AU_M
return lat, lon, elevation_m, earth_R
def subpoint(self, iterations):
"""Return the latitude an longitude directly beneath this position.
Returns a :class:`~skyfield.toposlib.Topos` whose ``longitude``
and ``latitude`` are those of the point on the Earth's surface
directly beneath this position (according to the center of the
earth), and whose ``elevation`` is the height of this position
above the Earth's center.
"""
if self.center != 399: # TODO: should an __init__() check this?
raise ValueError("you can only ask for the geographic subpoint"
" of a position measured from Earth's center")
t = self.t
xyz_au = einsum('ij...,j...->i...', t.M, self.position.au)
lat, lon, elevation_m, self.earth_R = reverse_terra(xyz_au, t.gast, iterations)
from skyfield.toposlib import Topos
return Topos(latitude=Angle(radians=lat),
longitude=Angle(radians=lon),
elevation_m=elevation_m)
def earth_radius(self):
return self.earth_R
def satellite_visiable_area(earth_radius, satellite_elevation):
"""Returns the visible area from a satellite in square meters.
Formula is in the form is 2piR^2h/R+h where:
R = earth radius
h = satellite elevation from center of earth
"""
return ((2 * pi * ( earth_radius ** 2 ) *
( earth_radius + satellite_elevation)) /
(earth_radius + earth_radius + satellite_elevation))
stations_url = 'http://celestrak.com/NORAD/elements/stations.txt'
satellites = api.load.tle(stations_url)
satellite = satellites['ISS (ZARYA)']
print(satellite)
ts = api.load.timescale()
t = ts.now()
geocentric = satellite.at(t)
geocentric.subpoint = subpoint.__get__(geocentric, Geocentric)
geocentric.earth_radius = earth_radius.__get__(geocentric, Geocentric)
geodetic_sub = geocentric.subpoint(3)
print('Geodetic latitude:', geodetic_sub.latitude)
print('Geodetic longitude:', geodetic_sub.longitude)
print('Geodetic elevation (m)', int(geodetic_sub.elevation.m))
print('Geodetic earth radius (m)', int(geocentric.earth_radius()))
geocentric_sub = geocentric.subpoint(0)
print('Geocentric latitude:', geocentric_sub.latitude)
print('Geocentric longitude:', geocentric_sub.longitude)
print('Geocentric elevation (m)', int(geocentric_sub.elevation.m))
print('Geocentric earth radius (m)', int(geocentric.earth_radius()))
print('Visible area (m^2)', satellite_visiable_area(geocentric.earth_radius(),
geocentric_sub.elevation.m))