In 1843, a comet passed extremely close to the sun, mass Ms: its distance from the perihelion was d = 6.1*10^3 * a0, where a0 is the radius of the Earth's orbit. Accurate measurements showed that the eccentricity of the comet was e=1-x with x = 9.4*10^-5. Given u = 30 km/s is the speed of revolution of the Earth around the Sun. (a) Express the product GMs as a function of u and a0. (b) Considering that the trajectory of the comet is quasi-parabolic, calculate its speed of passage vp at the perihelion. (c) Deduce the speed Va of transition to aphelion as a function of Vp and x. Do the digital application. (d) In what year will this comet return to the solar system?

In 1843, a comet passed extremely close to the sun, mass Ms: its distance from the perihelion was d = 6.110^3 a0, where a0 is the radius of the Earth's orbit. Accurate measurements showed that the eccentricity of the comet was e=1-x with x = 9.4*10^-5. Given u = 30 km/s is the speed of revolution of the Earth around the Sun. (a) Express the product GMs as a function of u and a0. (b) Considering that the trajectory of the comet is quasi-parabolic, calculate its speed of passage vp at the perihelion. (c) Deduce the speed Va of transition to aphelion as a function of Vp and x. Do the digital application. (d) In what year will this comet return to the solar system?

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