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The motion of Halley’s comet and its motion. Halley’s comet travels in an elliptical orbit of...

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Physics

The motion of Halley’s comet and its motion. Halley’s comettravels in an elliptical orbit of eccentricity ϵ = 0.97 around theSun. At perihelion (closest approach), Halley’s comet is observedto be approximately 0.59 AU from the Sun. At aphelion the distanceis about 35.08 AU, the semi-major axis of the elliptical orbit is17.83 AU, and the orbital period is about 75.3 Earth years.

1) Since Earth has an essentially circular orbit that is 1 AUfrom the Sun. Use any approach that you like to determine theEarth’s orbital speed is v_E = sqrt(GM_S/R_E) and then determine anumerical value in kilometers/second.

2) Use the perihelion, aphelion, semi-major axis, and periodabove for Halley’s comet to determine the value of thecharacteristic length, r_c, that describes the elliptical orbitalpath, r(φ), for Halley’s comet.

3) Use the definition of r_c to estimate the speed of Halley’scomet at perihelion. Write the result in symbolic first, whichshould look like the result in part 1, then write it as the resultfrom part (a) and appropriate ratios to estimate the numericalvalue of Halley’s comet’s speed at perihelion.

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