Assignment_01

# Assignment_01 - circle). (b) How fast does the spacecraft...

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SCIENCE 238 Assignment #1 1) For a place at a latitude of 55 degrees determine how high above the horizon the Sun is at noon on (a) the Vernal Equinox, (b) the Summer Solstice, and (c) the Winter Solstice. (Marks:1) 2) If the sidereal period of the Moon was 29.0 days (instead of the correct 27.32 days) what would be its synodic period? (Hint: consider how far around the Sun the Earth/Moon will have traveled in 29.0 days. The textbook discusses these concepts on more detail.) (Marks: 2) 3) (a) How long does it take for an unpowered spacecraft to move from Earth's orbit to Mars' orbit? The orbit will be a standard Keplerian elliptical orbit around the Sun! Use the spacecraft orbit that has perihelion at the Earth’s orbit (which is very close to a circle – assume it is a perfect circle) and aphelion at Mars’ orbit (also assume that this is a
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Unformatted text preview: circle). (b) How fast does the spacecraft need to be moving at the beginning of its trip (i.e. when it is at the Earth's orbit)? The velocity v (at any point in any orbit!) is given by the vis viva v 2 GM 2 r 1 a where M is the mass of the Sun, r is the distance from the Sun (which varies continuously except in the special case of a circular orbit), and a is the semi-major axis of the orbit. Show your calculations and a sketch of the three orbits (the Earth's, the Mars', and the spacecraft's orbits). This is referred to as the "least energy" transfer orbit and is the most efficient way to move a spacecraft from one planet to another. (Hint: you will need to look up somewhere the size of the Earth’s and Mars’ orbits.) (Marks: 3)...
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## This note was uploaded on 12/06/2010 for the course SCI 238 taught by Professor Kines during the Spring '06 term at Waterloo.

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