PROBLEM 12.107 (Continued)
PROBLEM 12.107 (Continued)
PROBLEM 12.108
Halley’s comet travels in an elongated elliptic orbit for which the minimum distance from the sun is
approximately 1
2,
E
r where 6
150 10 km
E
r is the mean distance from the sun to the earth. Knowing that the
periodic time of Halley’s comet is about 76 years, determine the maximum distance from the sun reached by
the comet.
PROBLEM 12.109
Based on observations made during the 1996 sighting of comet Hyakutake, it was concluded that the
trajectory of the comet is a highly elongated ellipse for which the eccentricity is approximately 0.999887.
Knowing that for the 1996 sighting the minimum distance between the comet and the sun was 0.230 ,
E
R
where RE is the mean distance from the sun to the earth, determine the periodic time of the comet.
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PROBLEM 12.110
A space probe is to be placed in a circular orbit of radius 4000
km about the planet Mars. As the probe reaches A, the point of
its original trajectory closest to Mars, it is inserted into a first
elliptic transfer orbit by reducing its speed. This orbit brings it
to Point B with a much reduced velocity. There the probe is
inserted into a second transfer orbit by further reducing its
speed. Knowing that the mass of Mars is 0.1074 times the
mass of the earth, that rA 9000 km and rB 180,000 km, and
that the probe approaches A on a parabolic trajectory,
determine the time needed for the space probe to travel from A
to B on its first transfer orbit.
PROBLEM 12.110 (Continued)
PROBLEM 12.111
A spacecraft and a satellite are at diametrically opposite positions
in the same circular orbit of altitude 500 km above the earth. As it
passes through point A, the spacecraft fires its engine for a short
interval of time to increase its speed and enter an elliptic orbit.
Knowing that the spacecraft returns to A at the same time the
satellite reaches A after completing one and a half orbits,
determine (a) the increase in speed required, (b) the periodic time
for the elliptic orbit.
PROBLEM 12.111 (Continued)
PROBLEM 12.112
The Clementine spacecraft described an elliptic orbit of
minimum altitude 400
A
hkm and a maximum altitude of
2940
B
hkm above the surface of the moon. Knowing that
the radius of the moon is 1737 km and that the mass of the
moon is 0.01230 times the mass of the earth, determine the
periodic time of the spacecraft.
PROBLEM 12.113
Determine the time needed for the space probe of Problem 12.100 to travel from B to C.