A comet at its closest approach to the Sun

[Alexanddros81]

Homework Statement

14.102 A comet at its closest approach is 125 x 10⁶ km from the center of the sun
(between the orbits of the Earth and Venus), where its speed is 45.5 km/s. (a) Show that the
comet has an elliptical orbit around the sun. (b) Determine the period of the orbit in years
(1 year = 365.26 days). (c) Compute the maximum distance between the comet and the sun,
and compare it with the radius of the solar system (the orbital radii of Neptune and Pluto,
the two outermost planets, are 4510 and 5890 x10⁶ km, respectively).

Homework Equations

The Attempt at a Solution

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Can you check my solution?

 

[mfb]

I checked (c) via conservation of energy and it fits, and (b) fits to c and the given initial conditions, so everything should be right.