Homework #4, AST 3018, Fall, 2011

# Homework #4, AST 3018, Fall, 2011 - the Sun is 300,000...

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AST 3018 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” orbits? 2. If the Sun had eight times its present mass and the Earth’s orbit were twice its present size, what would then be its orbital period? 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. 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
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Unformatted text preview: the Sun is 300,000 times as massive as the Earth and that the Sun is 400 times as distant as the Moon. 5. The true relative orbit of ξ Ursae Majoris has a semi-major axis of 2.5 arcsec. If it is 0.41 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? 6. In an eclipsing 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 stars? 7. A satellite is in a circular orbit around the Earth. If I desire to boost the satellite into an escape orbit by what factor must I increase its velocity? Express the increase in terms of v c , the circular satellite velocity....
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