What is Velocity.length_squared?

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Homework Help Overview

The discussion revolves around the physics of an asteroid's motion as it enters Earth's atmosphere, focusing on concepts such as terminal velocity, ablation, and the forces acting on the asteroid. Participants explore the implications of these concepts in the context of a homework project.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking, Mixed

Approaches and Questions Raised

  • Participants discuss the relationship between current velocity and terminal velocity, questioning the validity of a proposed method for calculating velocity changes. There are inquiries about the relevant Newton's equations and the factors affecting ablation, such as temperature and air density. Some express uncertainty about their physics background and seek clarification on the concepts involved.

Discussion Status

Participants are actively engaging with the problem, raising questions and exploring different aspects of the physics involved. Some have offered guidance on considering forces and the chaotic nature of ablation, while others are still seeking foundational understanding and specific equations.

Contextual Notes

The original poster is in 7th grade and has limited physics knowledge, which influences the level of detail and explanation sought in the discussion. There is an acknowledgment of the complexity of the project and the need for careful consideration of various factors affecting the asteroid's motion.

  • #31
Amsalja said:
And is that the average?
Average what? The physics model calculates the instantaneous speed at each point in time.
Amsalja said:
If it is then all I need is the ablation.
That's easy to say, but meteoroid ablation is a really complicated subject that is not fully understood. Even a basic study in this area would be at the level of a final year project for an undergraduate. Also, most of the relevant texts are not freely available on the internet: you would need access to a university library for this.

Having said that, this paper quotes an equation for the ablation rate (quoted from V. A. Bronshten, Physics of Meteoric Phenomena, Reidel Publishing Co., Dordrecht, Netherlands, 1983)
$$ \frac{dm}{dt} = -\sigma K \rho_{air} m^{2/3} v^3 $$
where σ and K are constants. The paper also provides some values for σ between = 0.035 and 0.081 s2km-2, and another expression that after a bit of work gives ## Km^{2/3} = \frac 1 2 C_D A ##, so the equation above becomes
$$ \frac{dm}{dt} = - \frac 1 2 \sigma C_D A \rho_{air} v^3 = \sigma F_D v $$
I'm not sure this makes sense, but taking it at face value and coding it we have:

[code lang=Python title=GDScript]
# sigma is an input parameter in the range 0.035 - 0.081 s^2 km^{-2}
# so we need to convert to s^2 m^{-2}
convertedSigma = sigma / 1000000
# From the calculations at
# https://www.physicsforums.com/threads/7th-grade-asteroid-simulator.1053384/post-6908342
# we can update mass
mass -= convertedSigma * dragForceMagnitude * speed * delta
[/code]

Amsalja said:
Another thing, is drag is able to go below terminal velocity and I know that you said not to talk about terminal velocity, but, if I start my velocity at my terminal velocity, then I fall in, the velocity goes below it's terminal velocity due to drag, so does that mean my drag is wrong?
Yes there was an error in the code I posted: the calculation of the amount of deceleration due to drag was correct, but when converting this to a vector to get it in the right direction I forgot to use a unit vector. The correction is below, I have amended this in the post above:
[code lang=Python title=GDScript]
# Aerodynamic drag depends on speed squared...
speedSquared = Velocity.length_squared()
dragForceMagnitude = 0.5 * airDensity * speedSquared * dragCoefficient * crossSectionArea
# ...and acts in the opposite direction to the velocity so we create a vector,
# remembering to scale Velocity to a unit vector.
speed = sqrt(speedSquared)
DragForce = -dragForceMagnitude * Velocity / speed
[/QUOTE][/CODE]
 
Last edited:
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  • #32
What is Velocity.length_squared? Is it the length axis, or is it something else.
 

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