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 different types of trajectories as follows:
for ellipses
for parabolas
for hyperbolas
v(x) =
1
√ « (² – ²-)
a
with
a> 0
a = ∞
a < 0
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-¹s²).
(b) Determine the velocity (in km/s) of C/2023 IAAC for a distance of 0.8 AU to the Sun.
