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PROBLEM 12.84
The periodic time (see Prob. 12.83) of an earth satellite in a circular polar
orbit is 120 minutes. Determine (a) the altitude h of the satellite, (b) the time
during which the satellite is above the horizon for an observer located at the
north pole.
PROBLEM 12.85
A 500 kg spacecraft first is placed into a circular orbit about the earth at an altitude of 4500 km and then is
transferred to a circular orbit about the moon. Knowing that the mass of the moon is 0.01230 times the mass
of the earth and that the radius of the moon is 1737 km, determine (a) the gravitational force exerted on the
spacecraft as it was orbiting the earth, (b) the required radius of the orbit of the spacecraft about the moon if
the periodic times (see Problem 12.83) of the two orbits are to be equal, (c) the acceleration of gravity at the
surface of the moon.
PROBLEM 12.85 (Continued)
PROBLEM 12.86
A space vehicle is in a circular orbit of 2200-km radius around the moon.
To transfer it to a smaller circular orbit of 2080-km radius, the vehicle is
first placed on an elliptic path AB by reducing its speed by 26.3 m/s as it
passes through A. Knowing that the mass of the moon is 73.49 21
10 kg,
determine (a) the speed of the vehicle as it approaches B on the elliptic
path, (b) the amount by which its speed should be reduced as it
approaches B to insert it into the smaller circular orbit.
PROBLEM 12.87
As a first approximation to the analysis of a space flight from the
earth to Mars, assume the orbits of the earth and Mars are
circular and coplanar. The mean distances from the sun to the
earth and to Mars are 6
149.6 10km and 6
227.8 10km,
respectively. To place the spacecraft into an elliptical transfer
orbit at point A, its speed is increased over a short interval of
time to
A
v which is 2.94 km/s faster than the earth’s orbital
speed. When the spacecraft reaches point B on the elliptical
transfer orbit, its speed B
v is increased to the orbital speed of
Mars. Knowing that the mass of the sun is 3
332.8 10 times the
mass of the earth, determine the increase in speed required at B.
PROBLEM 12.88
To place a communications satellite into a geosynchronous orbit (see
Problem 12.80) at an altitude of 22,240 mi above the surface of the
earth, the satellite first is released from a space shuttle, which is in a
circular orbit at an altitude of 185 mi, and then is propelled by an upper-
stage booster to its final altitude. As the satellite passes through A, the
booster’s motor is fired to insert the satellite into an elliptic transfer
orbit. The booster is again fired at B to insert the satellite into a
geosynchronous orbit. Knowing that the second firing increases the
speed of the satellite by 4810 ft/s, determine (a) the speed of the satellite
as it approaches B on the elliptic transfer orbit, (b) the increase in speed
resulting from the first firing at A.
PROBLEM 12.88 (Continued)
PROBLEM 12.89
A space vehicle is in a circular orbit of 1400-mi radius around the moon.
To transfer to a smaller orbit of 1300-mi radius, the vehicle is first placed
in an elliptic path AB by reducing its speed by 86 ft/s as it passes through
A. Knowing that the mass of the moon is 21 2
5.03 10 lb s /ft, determine
(a) the speed of the vehicle as it approaches B on the elliptic path, (b) the
amount by which its speed should be reduced as it approaches B to insert
it into the smaller circular orbit.
PROBLEM 12.90
A 1 kg collar can slide on a horizontal rod, which is free to
rotate about a vertical shaft. The collar is initially held at A by a
cord attached to the shaft. A spring of constant 30 N/m is
attached to the collar and to the shaft and is undeformed when
the collar is at A. As the rod rotates at the rate
16 rad/s,
the
cord is cut and the collar moves out along the rod. Neglecting
friction and the mass of the rod, determine (a) the radial and
transverse components of the acceleration of the collar at A,
(b) the acceleration of the collar relative to the rod at A, (c) the
transverse component of the velocity of the collar at B.
PROBLEM 12.91
A 1-lb ball A and a 2-lb ball B are mounted on a horizontal rod
which rotates freely about a vertical shaft. The balls are held in
the positions shown by pins. The pin holding B is suddenly
removed and the ball moves to position C as the rod rotates.
Neglecting friction and the mass of the rod and knowing that
the initial speed of A is 8
A
v
ft/s, determine (a) the radial and
transverse components of the acceleration of ball B
immediately after the pin is removed, (b) the acceleration of
ball B relative to the rod at that instant, (c) the speed of ball A
after ball B has reached the stop at C.
