Coarsely modeling impacts between bodies on a planetary scale

[SkyMarshal]

Wheeee! More confusing thread titles! Here, let me elaborate:

What I intend to do here is figure out a way to roughly model the results of planetary (or larger) bodies impacting, or a planetary (or larger) sized body being impacted by a smaller body that is moving with enough relative velocity as to have an effect other than leaving an amusing crater.

...Now let me give an example, as I am horrible at explaining things:

Say you have a Earth or Mars sized planet, and an asteroid impacts it. From the impact, you can get the velocity (and thus momentum) of each object in regards to the other, point of impact on each (Each object is a perfect sphere being extrapolated as a circle with the radius of the sphere for the purposes of the simulation, so you will just get a value describing the impact point as the number of degrees off of the "bearing" of the body, which is a bit arbitrary to be honest. Either way, point of impact and the velocity.) as well as the densities of each object (assumed continuous throughout for simplicity) and the positions the objects were in when they collided (cartesian co-ordinate system).
From this, I am looking to be able to produce a beleivable result of the "impact" that occurred between the bodies.

Any thoughts as to how I should go about this? These impacts will vary anywhere from a spaceship impacting a planet at relativistic speeds to an asteroid smashing into a gas giant. Thanks in advance!

 

[twofish-quant]

Designing a video game, are we?

O.K. The way that I'd go about it is to start with conservation of energy and momentum. You start with N particles come in an angles and velocities v1, v2, v3. You leave with M particles leaving with given angles and velocities.

You'll find that the equations won't be constrained. I.e.. you'll have some free variables. At that point you put together some matrix that fills in the free variables with something that looks plausible.

 

[SkyMarshal]

Sounds good, but my real issue is handling a situation wherein a body would be split, such as a moon entering the roche limit of a gas giant or a asteroid slamming into a planet at relativistic velocity. Any idea how I would I approximate the results of such an impact?

 

[mrspeedybob]

Simulate each body as a number of smaller bodies held together by gravitational and contact forces. In the case of a planet being hit by a relativistic star ship I would model the ship as a single body and the planet as perhaps 20 or 30 smaller bodies arranged a rough sphere. If the results don't look plausible increase the number of sub-bodies.

 

[pmacias]

I find this topic very interesting and challenging. Coarsely modeling impacts between bodies on a planetary scale is a complex task that requires a deep understanding of physics, mathematics, and computer simulations.

To begin with, it is important to define the variables and parameters that will be used in the model. These include the mass, velocity, and density of the impacting bodies, as well as the point of impact and the relative velocity between the bodies. These parameters will determine the magnitude and direction of the force exerted during the impact.

Next, it is crucial to consider the physical properties of the bodies involved. For example, the composition of the impacting body and the target body will affect the outcome of the impact. The size and structural integrity of the bodies will also play a role in determining the extent of the impact.

In order to accurately model the impact, it is necessary to use advanced mathematical equations and computer simulations. These can take into account the various forces at play, such as gravitational attraction, momentum, and energy transfer. It is important to note that the results of the model will be an approximation, as there are many factors that can affect the outcome of an impact on a planetary scale.

In terms of practical applications, coarsely modeling impacts between bodies on a planetary scale can provide valuable insights into the formation and evolution of planets and other celestial bodies. It can also help us better understand the potential consequences of impacts, such as asteroid collisions with Earth.

In conclusion, while this is a challenging task, with careful consideration of all the variables and advanced mathematical and computational tools, it is possible to coarsely model impacts between bodies on a planetary scale. This can lead to a better understanding of the physical processes involved in these events and their implications for our universe.