Kepler's Law Worksheet - Name ~ Section Kepler’s Laws An...

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Unformatted text preview: Name - ~ . Section Kepler’s Laws: An Introduction Objective To review Kepler's three laws; to determine the properties of an ellipse; to relate these properties to the orbits of planets. Materials 15 cm Ruler, CalcUlator V Exercise 1. Refer to your lecture notes or book and clearly label the - Focus _o Semi—Major axis 0 Major axis 0 . Center parts on the following diagram of an ellipse: 2. Eccentricity is a measure of the degree of “flattening” of the ellipse. Mathematically, the eccentricity of an ellipse is defined as the distance from a focus to the center of the ellipse divided by the length of the semi-major axis. Calculate the eccentricity of this ellipse: ,4 6 WM 3. A circle is a special ellipse: one with the foci at the eccentricity of an orbit may run from 0 to 1, ' eccentncities for the following ellipses: 4.- in your own words, state how to determine the eccentricity of an ellipse. If you'd like, you may use a figure to express your thoughts. ' ymtam 4w Magma was ammo? .L" ‘ C): ‘6V \ . W M" m i . ’3, {2, O\ 5. Kepler‘s second law, which states that as a planet moves around its orbit it sweeps out equal areas in' equal times, is often a difficult, totally confusing'concept to picture, let alone understand. Since it is just a description, we are going to ignore it and state what the second law really means: that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. Examine the next figure of the "Planet D" orbiting the Sun “A” in a counter-clockwise direction and fill in the blanks with the correct letter: - Focus A Aphelion Perihelion B Increasing speesto g Decreasing speedzito; Planet has greatest speed Planet has lowest speed ' Not to scale. fig) .5— C. 6. Now, state Kepler's Second Law in your own words and give your reasoning as to why planets "behave" this way: WW W pLCw‘VLJrS OWL 5%qu meow) Prom 4M, 3mm ‘ a I ( a ' ~ , - limo) <30 @astm. l he (swim s grow l‘tcrtl GNU pu ll l3 _ fir 69 Q44” » ' . o (r LC’QV flat/«.8, 7. Kepler‘s Third Law relates the period (P) it takes a planet to go around the Sun in an orbit fa given . , ' semi—major axis (a). Assume that the mass of the Sun is much, much greater than any of the planets (which it is), and measure P in years and a in astronomical units. The simplified relationship (formula) is: 2 P :61: The following two orbits have about the same value for at How do their values of P compare? Kepler's Third Law means that all orbits with the same semi—major axis-have the same period. Explain how this can be when the orbits look so different, and why this makes sense, ' OrbH-sg (if a- (’onSA—awjr Wye/mas rm, plat/mt)? CAMS «Cast Quad “F‘vv SMWS glow“? ...
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