Lecture5

# Lecture5 - Problem The Mars rover"Opportunity needs enough...

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Problem: The Mars rover “Opportunity” needs enough energy to keep its equipment warm throughout the Martian winter without draining Opportunity's batteries. Solution: Park Opportunity tilted towards the south, allowing the solar cells to absorb more energy from the Sun. Opportunity was instructed to climb onto the 15 degree incline of Greeley's Haven.

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Answers to homework #1 must be submitted no later than Thurs. January 26, 5:00 pm.

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Johannes Kepler (1571-1630) Greatest theorist of his day a mystic there were no heavenly spheres forces made the planets move Developed his three laws of planetary motion
Kepler’s First Law Each planet’s orbit around the Sun is an ellipse, with the Sun at one focus.

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Ellipse: a figure defined by points located such that the sum of the distances from the two foci is constant

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Semimajor axis = a Semiminor axis = b y X x 2 /a 2 + y 2 /b 2 = 1 focus Eccentricity e 2 = 1 - b 2 /a 2
The circle is a special form of an ellipse

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Kepler’s Second Law A planet moves along its orbit with a speed that changes in such a way that a line from the planet to the Sun sweeps out equal areas in equal intervals of time.
Consequence - planets move faster when they are closer to the sun and planets spend more time in the more distant parts of their orbits

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Kepler’s Third Law The ratio of the cube of a planet’s average distance from the Sun “a” to the square of its orbital period “P” is the same for each planet. a 3 / P 2 = constant
Consequence: Planets with larger orbits have longer orbital periods. a 3 / P 2 = constant Earth: a = 1 AU, P = 1 year So, if we use distance in AU and time in years, the constant in the 3rd Law is 1 AU 3 yr -2 Jupiter: a = 5.203 AU, P = 11.86 years

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Kepler's Laws 1. The Law of Orbits : All planets move in elliptical orbits, with the sun at one focus. 2. The
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## This note was uploaded on 02/21/2012 for the course AST-A 105 taught by Professor Dr.dash during the Spring '12 term at Indiana.

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Lecture5 - Problem The Mars rover"Opportunity needs enough...

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