Problem A.1: Parabolic Trajectory (4 Points)

As presented in the qualification round, the comet P/2023 IAAC circles the Sun in an elliptical or-

bit. There are other comets with a parabolic trajectory, for example the comet C/2023 IAAC.

(a) Explain the meaning of the letters P and C in the names of the two comets.

The vis-viva-equation can be extended for dierent types of trajectories as follows:

v(x) = s

µ



2

x

−

1

a



with

a > 0 for ellipses

a = ∞ for parabolas

a < 0 for hyperbolas

and µ = G(m1 + m2). Here, m1 is the comet’s mass, m2 the Sun’s mass (1.9 x 1030 kg), x the dis-

tance between the comet and the Sun, and G is the gravitational constant (6.67 x 10-11 m3kg-1s

-2).

(b) Determine the velocity (in km/s) of C/2023 IAAC for a distance of 0.8 AU to the Sun.​