In fact, more precise calculations suggest that ISON was on a hyperbolic, unbound orbit. How much more precise?
Find the minimal speed with which the comet would have had to be moving when observed at perihelion in order to eventually escape the Solar system, in km/s.
To calculate the minimal speed with which the comet ISON would have had to be moving when observed at perihelion in order to eventually escape the Solar System, we will consider the concept of escape velocity.
Escape velocity is the speed required for an object to break free from the gravitational pull of another object. In this case, we need to calculate the escape velocity from the Sun's gravitational pull.
The formula for escape velocity is:
V = sqrt(2GM/r)
Where:
V is the escape velocity,
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2),
M is the mass of the Sun (approximately 1.989 x 10^30 kg),
r is the distance from the center of the Sun to the comet (we will consider the distance at perihelion, the closest point to the Sun).
To convert the distance from kilometers to meters, we need to multiply it by 1000 (1 km = 1000 m).
Given that the perihelion distance of the comet ISON was approximately 1.170 x 10^6 km, the distance from the center of the Sun would be r = 1.170 x 10^9 m.
Let's plug these values into the formula to find the escape velocity:
V = sqrt(2 * 6.67430 x 10^-11 * 1.989 x 10^30 / 1.170 x 10^9)
Calculating this expression, we find:
V ≈ 617.9 km/s
Therefore, the minimal speed with which the comet ISON would have had to be moving when observed at perihelion in order to eventually escape the Solar System is approximately 617.9 km/s.