An Earth-observing satellite has horizon sensors that can measure the angle θ shown in the accompanying figure on the next page. Let R be the radius of the Earth (assumed spherical) and h the distance between the satellite and the Earth’s surface. (a) Show that sin θ = R R + h . (b) Find the angle θ , to the nearest degree, for a satellite that is 10 , 000 km from the Earth’s surface (use R = 6378 km ).
An Earth-observing satellite has horizon sensors that can measure the angle θ shown in the accompanying figure on the next page. Let R be the radius of the Earth (assumed spherical) and h the distance between the satellite and the Earth’s surface. (a) Show that sin θ = R R + h . (b) Find the angle θ , to the nearest degree, for a satellite that is 10 , 000 km from the Earth’s surface (use R = 6378 km ).
An Earth-observing satellite has horizon sensors that can measure the angle
θ
shown in the accompanying figure on the next page. Let
R
be the radius of the Earth (assumed spherical) and
h
the distance between the satellite and the Earth’s surface.
(a) Show that
sin
θ
=
R
R
+
h
.
(b) Find the angle
θ
,
to the nearest degree, for a satellite that is
10
,
000
km
from the Earth’s surface (use
R
=
6378
km
).
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