Collision of the Halley asteroid with a comet

[ahbouk]

1. The problem statement


a comet gets in the way of the Halley asteroid, so the question is: what's the new trajectory of the asteroid (its excentricity, its orbital rotation and it perihelion, aphelion)

both objects have same mass and we suppose that the comet have an negilgeable initial velocity.

all variables and given/known data

what we know is :both objects have same mass M=2.2*10^14 kg

the coefficient of restitution during collision is: 0.5

orbital period of Halley's asteroid: T=75.3 years
initial perihelion: 0.586 AU

initial excentricity: 0.967

Homework Equations

the kepler third law

conservation of angular momentum
relation between energy and excentricity equation and trajectory of asteroid are attached

The Attempt at a Solution

my attempts are to use the conservation of energy and angular momentum but i didn't know how to get the parameters of the trajectory from.

 

[mfb]

The object is called Halley's comet, and it is a comet, not an asteroid. Well, does not matter for the problem.

Is there a sketch provided? Where does the collision occur? The answer will depend on that.

Kinetic energy is not conserved in the collision.

 

[ahbouk]

reply

yes my fault it is Halley's comet and the asteroid is in the way of Halley's comet is explained by the joint image.
thnx

 

[mfb]

The given angle looks like the collision is supposed to be elastic - very unrealistic.

 

[paranormal]

I would approach this problem by first analyzing the given data and understanding the physical laws that govern the motion of celestial bodies. In this case, we are dealing with the collision of two objects with the same mass, so conservation of momentum and energy will play a crucial role in determining the new trajectory of the Halley asteroid.

To begin with, we can use the conservation of momentum to determine the final velocity of the asteroid after the collision. Since the comet has a negligible initial velocity, we can assume that the total momentum before and after the collision will be the same. Therefore, we can write the following equation:

mavai + mbvbi = mavaf + mbvbf

Where ma and mb are the masses of the asteroid and comet respectively, and vai and vbi are their initial velocities. Similarly, vaf and vbf are their final velocities after the collision. Since we are given the mass of the objects, we can solve for the final velocity of the asteroid.

Next, we can use the conservation of energy to determine the new orbital parameters of the asteroid. The total energy of the system (asteroid and comet) will remain constant before and after the collision. Therefore, we can write the following equation:

Ei = Ef

Where Ei is the initial energy of the system and Ef is the final energy after the collision. The initial energy of the system is given by the sum of the kinetic and potential energies of the asteroid and comet. The final energy will also be the sum of the kinetic and potential energies of the asteroid, but with new orbital parameters. We can use the equations for kinetic and potential energy in terms of mass, velocity, and distance to solve for the new orbital parameters.

Finally, we can use the Kepler's third law to determine the new orbital period of the asteroid. This law states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. Since we know the initial orbital period and semi-major axis of the asteroid, we can use this law to solve for the new orbital period after the collision.

In summary, to determine the new trajectory of the Halley asteroid after colliding with a comet, we can use the conservation of momentum and energy, equations for kinetic and potential energy, and Kepler's third law. By solving these equations, we can determine the new excentricity, orbital rotation, and perihelion and aphelion distances of the asteroid.