Physics 201 Homework 9
Mar 6, 2013
1. Suppose we are considering putting a rocket into low earth orbit. (The Apollo
program is the only example of human spaceflight beyond low earth orbit.) The
total ∆v required is 9.7 km/s. If the exhaust velocity of the rocket is 4.5 km/s,
calculate the percent of the initial total mass that must be propellant.
88%
2. Determine the length of time (in days) required for a space craft to travel along
the Hohmann transfer orbit from the Earth to the Moon. (The mean distance to
the Moon is 3.85 × 108 meters.)
4.86 days
3. An earth satellite is observed to have a height of perigee of 185 kilometers and
a height of apogee of 1,100 kilometers. Find the period of the orbit.
5,850 seconds = 1.63 hours
4. For a certain Earth satellite it is known that its semi-major axis is 9,140
kilometers. The orbit eccentricity is 0.2. (a) Find its perigee and (b) apogee
distances from the center of the earth. (c) Find the specific energy of its trajectory.
(a) r0 = 7,310 kilometers
(b) r1 = 11,000 kilometers
(c) 2.18 × 107 J/kg
5. A satellite is injected into an elliptical orbit with a semi-major axis equal
to 25,500 kilometers. When it is precisely at the end of the semi-minor axis it
receives an impulsive velocity change just sufficient to place it into an escape
trajectory. What was the magnitude of the velocity change?
∆v = 1.64 km/s
6. A communication satellite is in a circular orbit of radius 12,800 kilometers.
Find the minimum ∆v required to double the altitude of the satellite.
1.02 km/s
7. (a) Calculate the burnout velocity required to transfer a probe between the
vicinity of the Earth and the Moon’s orbit using a Hohmann transfer. (b) What
additional $Delta v$ would be required to place the probe in the same orbit as
that of the Moon? Neglect the Moon’s gravity in both parts.
(a) 11 km/s
(b) 0.88 km/s
8. A Venus probe departs from a 12,800 kilometers radius circular parking orbit
around the Earth with a burnout speed of 8.7 km/s. Find the excess escape speed.
3.7 km/s
9. To accomplish a certain measurement of phenomena associated with sunspot
activity, it is necessary to establish a heliocentric orbit with perihelion of 0.5 AU.
The departure from the Earth’s orbit will be at aphelion. What must the burnout
velocity be at an altitude of 1270 kilometers to accomplish this mission?
11.6 km/s
10. In 1910, on its sixth trip around the Sun after that of 1456, Halley’s comet
was observed to pass near the Sun at a distance of 9.0 × 1010 meters. Calculate
(a) how far the comet travels from the Sun at the outer extreme of its orbit, and
(b) the eccentricity of its orbit.
(a) 5.3 × 1012 meters
(b) 0.967
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