Question

Problem 2: Haley's Comet (A Real Life Example): Important: for this problem, complete all numerical work to a precision of at least six significant digits. Specifically: use the following precise values for astronomical constants: • Mass of the Sun = 1.98855 x 1030 kg • 1 AU = 149,597,870,700 meters . G=6.67384 x 10-11 N·m²/kg? Neptune Uranus Saturn Jupiter 05 2000 2005 2000----1995 2010 19921989 1988 1987 2024 1986 2061 2040 2060 2045 2050 2055 2056 2057 2058 2059 In 1986, the distance of closest approach of Halley's comet to the Sun is 0.585978AU. (1 AU is the mean Earth-Sun distance) The comet's speed at closest approach was precisely 54.5721103 km/s. (a) - By 1989, Halley's comet had traveled to a distance corresponding to the orbit of Saturn at 9.56AU. What was the speed of Halley's Comet at that time? Give your answer in units of km/s. (b) - In 2024, Halley's comet will be at the furthest distance from the sun corresponding to precisely 35.08231AU. Use Conservation of Energy to determine the speed of Halley's Comet be at that time? Problem 2 Continues next page....

Answer 1

a Acconding to the conservation of Energy at the point of closet apparch and that at the position of the onbit of Saturn we get - En + Eplet closest aproven (En E) anbit of Saturn Where me mass of the comet's = Velocity and closest approch - 54.5721103 mm - 54572.1103 mm r = Distance of closest appweh = 0.585978 AU. V = Velocity at saturn's abit & Distance of satuan's anbit fun son = 9:56 AU. so Ws Zvanile - 11655.4105 mit = 11.6554105 km/h b Similarly if no furthest distance and V = Spud at that point V /24V - ante 911.5/86217 0.9115186 km =

c) According to the laws of - mortem tum - conservation of Angular- 1. we = If .wf movere - misfits 17 - Velc 5 157241103 X0.585978 35.08231 = 9115151211 m = 0.9115151211 han/h The value is quite similar to that we found is pont 6. Again 05.- (Vs.) vertical & avere (vs) vertical _545-12.1103 X 0.585477 = 9.50 = 3344.984942 mm = 3.344984942 km/h (vs.) ventical = V.com (90-8) 3.344984942 = - Sinß. 11.6554105 P = 16.67783