Question

HELP ME PLEASE WITH THIS Comet EXERCISE: Comet JT2023, known as the Olympic Comet, was discovered by astronomers Bruce

Brolin and Frankus Mascinni through the Ancient Lights search project on September 15, 2001. This
comet had its closest approach to Earth on February 29, 2020. Its orbit has an eccentricity of
e=0.99920 and an aphelion distance of ra=2,799 UA. Given that the mass of the Sun is MS-1.99x1030
kg.
a) Sketch the orbit and positions of the comet and the Sun, as well as the elements of the elliptical
orbit.
b) Work geometrically and algebraically to find a formula that relates the eccentricity of the orbit, the
aphelion, and the semi-major axis.
c) Determine the speed of the comet at its aphelion.

Answer 1

For the Comet JT2023, sketching the orbit and positions of the comet and the Sun will help in understanding better its characteristics. The eccentricity of its orbit is e = 0.99920 and its aphelion distance ra = 2,799 UA.

Using the formula for the semi-major axis of an ellipse with given eccentricity and aphelion, a=ra(1+e)/(1-e), we can find that the semi-major axis of the comet's orbit is a = 2,820.8 UA.

Using the formula for the speed of an object in an elliptical orbit, v = (GM/a)^1/2, where G is the gravitational constant, M is the mass of the sun and a is the semi-major axis of the ellipse, we can find that the speed of the comet at its aphelion is v = 3.04 km/s.