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Unformatted text preview: AST 3018
Key HOMEWORK #4 1. I wish to launch a spacecraft from the Earth to Venus and another to Mars. If the semi—
major axis of Venus’ orbit is 0.72 AU and that of Mars’ orbit is 1.52 AU how long will it
take the respective spacecraft to reach their destinations if they travel in "least energy”  ?
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w 53' Page £5 2. Ifthe Sun had eight times its present mass and the Earth’s orbit were twice its present size, what would then be its orbital period? 2, 3
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t 9 Pi 3. Find the separation d between two small bodies, each of unit mass, lined up with a large
body of mass M, at a distance R from the nearest of the small bodies, such that the
gravitational attraction between the small bodies is just equal to the differential gravitational force a between them caused by their attraction to the large body. The
answer should be in terms of G, M and R. M F M ii? Wt. {:1 :2 6»» MM apeswzémaé
r—ww—WW..{W g P Q , . v—"ﬁg (F3 3.6;th Li+ dﬁﬁdms‘ing ﬂﬂltﬁfjl 4. Compute the relative tide—raising effectiveness of the Sun and the Moon. For this
approximate calculation, assume that the Earth is 80 times as massive as the Moon, that
the Sun is 300,000 times as massive as the Earth and that the Sun is 400 times as distant
as the Moon. méﬂgOﬂ/LM , {33
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light years distance and its period is 60 years what is the sum of the masses of the two stars in units of solar mass? 7 u;
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Arm ‘ jéﬁﬁfiﬁ‘ﬁ‘ﬁﬁ ' 6. In an eclipsng binary in which the eclipses are exactly central, and in which a small star
revolves about a considerable larger one, the interval from first to second contacts is
one hour and from first to third contacts is four hours. The entire period is three days.
The centers of the stars are separated by 11,460,000 km. What are the diameters of the st ? a ,
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TE _. {ﬁg game‘s” km {‘32, 7. A satellite is in a circular orbit around the Earth. If! desire to boost the satellite into an escape orbit by what factor must I increase its velocity? Express the increase in terms of
vc, the circular satellite velocity. ﬂ 2% Ear: rm Escﬁfg @ﬁi’éa’t’ N“? wa m ‘
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 Fall '08
 Lada

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