Find the perihelion and aphelion of Earth, Jupiter, Saturn, Uranus, Neptune, and

Question

Find the perihelion and aphelion of Earth, Jupiter, Saturn, Uranus, Neptune, and Halley's Comet in a) Let 4 and P be the respective aphelio n and perihelion for an arbitrary planet. Verify the polar equation for the orbit with the Sun at one focus is an ellipse given by)A+P)-(A-P) cos(0) 2AP where le= b) Find the Polar Form equation for each planetary body listed above. Sketch the orbits of Jupiter, Saturn, Uranus, Neptune, and Halley's Comet on the same polar graph neatly and accurately. Provide a scale. (Ignore Earth.) c) The period for Halley's Comet is approximately 76 years. How long does Halley's Comet take to pass through the "perihelion arc" of the orbit? d) Provide mathematical and graphical evidence for any point(s) of intersection between the orbits of Earth and Halley's Comet. Does Halley's Comet pass through Earth's orbit? Why not? Take 5 minutes and read about the Orionids. e) Mr. Fear Propaganda has found a comet roughly the size of North America! He finds the points of intersection with Earth's orbit and claims we're doomed! The polar model for its orbit about the Sun-Fre) - 20 r-/(0) = 5-6cos(0) Are we actually doomed? Why or why not? Explain. Give mathematical and graphical evidence. Suppose the comet misses the Earth as it travels around the Sun. Do we need to worry about this comet again? Why or why not? f) Include the graph of the orbital path for the comet in part (e) to your graphs from parts (b) and (d). Label each orbital path. Be neat and accurate.

Explanation / Answer

Here, the period (p) = 76 years &

we find out the distance (a)= ? in AU

Now, we kwon from Kepler's law :-

[P2 = a3]

So, (76)2 = a3

a3 = 5776

a = 5776

a = 17.94 AU

Hence, the Hally's comet take to pass through the perihelion arc of the orbit is about 18 AU.

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