An alien spacecraft in an elliptical orbit about Earth might possess which of the following properties?
a) A bound orbit with Earth at one focus of the ellipse
b) Orbital eccentricity e = 0.15
c) An orbital period of 24 hours
d) Positive total energy measured against Earth
e) It is possible for a comet on an elliptical orbit to have all of these properties
f) (a) and (b)
g) (a) and (c)
h) (a) and (d)
i) (b) and (c)
j) (b) and (d)
k) (c) and (d)
l) (a), (b), and (c)
m) (a), (b), and (d)
n) (a), (c), and (d)
o) (b), (c), and (d)
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A. The elliptically-orbiting object definitely has the earth at one of the foci - this is a fundamental aspect of elliptical orbits. The more elliptical the orbit, the farther the primary focus deviates from the center, and vice versa.
B. An eccentricity of 0.15 is entirely possible. This would describe a fairly elliptical orbit, because an eccentricity of 0 would correspond to a circular orbit. The Earth's eccentricity is about 0.017, which corresponds to a difference of about 2 million miles in our closest and farthest approaches to the sun (out of about 93 million miles on average)
C. An orbital period of 24 hours is possible, because an elliptical orbit sets no limits on the total orbital period.
D. The elliptical orbit would definitely NOT have positive total energy. Positive total energy would correspond to a hyperbolic orbit; the object would use that positive ("extra") energy to escape the orbital pull of the sun.
E. It is not possible for an elliptically orbiting body to have all of these properties, because D is mutually exclusive to B.
Therefore the correct option is L: A, B and C.
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