ENAE404 Spring 2007 Answers to Exam #1
March 13, 2007
75 minutes
L. Healy
1. [20 points] For each of the following earthorbiting satellites, identify
whether the orbit is circular, elliptical, parabolic, or hyperbolic. Give
a brief justification.
(a) Position vector is 7000
ˆ
I
+8000
ˆ
J
+750
ˆ
K
km at 03:21:19 UTC and
again at 08:23:19 UTC the same day.
Elliptical
; because the orbit returns on itself, it is closed (circu
lar or elliptical). The possibility of circular orbit can be eliminated
as follows. The time interval 5 hours 2 minutes must be a multi
ple of the period. If it is equal to the period, then the semimajor
axis is
a
= 1
.
491
×
10
4
km, if it is twice the period,
a
= 9393 km.
Any higher multiple and the semimajor axis would be less. But
the actual geocentric distance is
r
= 1
.
066
×
10
4
km. Since this is
not the semimajor axis
r
=
a
, the orbit cannot be circular and so
must be elliptical.
Note: several students determined that the semimajor axis of a
circular orbit with the period equal to the time interval did not
match that of a circular orbit. They then concluded that it was
an elliptical orbit. However, they did not consider that multiple
orbits (two, three, etc.) could have occured in the time interval
stated.
(b) Energy
ε
= 12
.
4
km
2
/
s
2
and angular momentum magnitude
h
=
62000
km
2
/
s
.
Hyperbolic
, because the energy is positive.
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 Spring '11
 circular orbit, semimajor axis, L. Healy, conic section equation, pergiee radius

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