Omni-directional KE

[sageof8paths]

Hello there,

What would the KE formula for growing a sphere omnidirectionally?

Thanks

 

[DontTalkDT]

Let's assume a sphere of constant density p and radius r, which grows m times larger over the time t.

A point that initially has a distance of d from the center after the growth has a distance of m*d from the center, meaning it moved m*d-d = (m-1)d far.
In that case, point of that nature have a KE per volume of 0.5*p*(m-1)d/t.
Points of that nature build a sphere with initial radius d. The sphere has a surface area of 4*pi*d^2.
So the KE per thickness of sphere is 0.5*p*(m-1)d/t * 4*pi*d^2 = 2*pi*p*(m-1)*d^3 / t.
Next we need to "sum up" all these spheres. So we integrate that over d from 0 to r.
Integral 0 to r of (2*pi*p*(m-1)*d^3 / t) dt = (pi * (m - 1) * p * r^4) / (2 * t)
And that's your KE.... I think.

@Ugarik does that make sense or should I have gone the safe derivative approach after all

 

[sageof8paths]

Let's assume a sphere of constant density p and radius r, which grows m times larger over the time t.

A point that initially has a distance of d from the center after the growth has a distance of m*d from the center, meaning it moved m*d-d = (m-1)d far.
In that case, point of that nature have a KE per volume of 0.5*p*(m-1)d/t.
Points of that nature build a sphere with initial radius d. The sphere has a surface area of 4*pi*d^2.
So the KE per thickness of sphere is 0.5*p*(m-1)d/t * 4*pi*d^2 = 2*pi*p*(m-1)*d^3 / t.
Next we need to "sum up" all these spheres. So we integrate that over d from 0 to r.
Integral 0 to r of (2*pi*p*(m-1)*d^3 / t) dt = (pi * (m - 1) * p * r^4) / (2 * t)
And that's your KE.... I think.

@Ugarik does that make sense or should I have gone the safe derivative approach after all

This is hella confusing but thanks so much I’ll try and plug in the values and get back to u to check if I did anything wrong

 

[sageof8paths]

Let's assume a sphere of constant density p and radius r, which grows m times larger over the time t.

A point that initially has a distance of d from the center after the growth has a distance of m*d from the center, meaning it moved m*d-d = (m-1)d far.
In that case, point of that nature have a KE per volume of 0.5*p*(m-1)d/t.
Points of that nature build a sphere with initial radius d. The sphere has a surface area of 4*pi*d^2.
So the KE per thickness of sphere is 0.5*p*(m-1)d/t * 4*pi*d^2 = 2*pi*p*(m-1)*d^3 / t.
Next we need to "sum up" all these spheres. So we integrate that over d from 0 to r.
Integral 0 to r of (2*pi*p*(m-1)*d^3 / t) dt = (pi * (m - 1) * p * r^4) / (2 * t)
And that's your KE.... I think.

@Ugarik does that make sense or should I have gone the safe derivative approach after all

I just plugged in the values for this feat and got multi galaxy level for smth that shiuod be around solar system level. Could I just give u the values and you help me plug them in?

 

[DontTalkDT]

Solar System level

Ehhhh, what's the chance that you accidentally did FTL KE?

Anyway, you can give me the values, but if you do I would prefer to see the feat as a whole.

 

[sageof8paths]

Ehhhh, what's the chance that you accidentally did FTL KE?

Nope, close though it’s around 0.81c. I’m just now realizing that it needs to account for relativity.

Anyway, you can give me the

I’ll assemble the values rn and send them to u it’ll take a long time though.

but if you do I would prefer to see the feat as a whole.

its kaguya’s etso. It expands omnidirectionally (from a planet) to collapse a dimension big enough to house a star inside. Assuming the distance is similar from the earth to the sun would be the radius (146.9 million km)

It’s stated that it was going to envelop the dimension really fast and needed to be stoped “right now” so I used 10 minutes as a timeframes.

Used the density of rock (3500) (its far denser (can tank and repel an Odama rasengan from 2 halves of the 9 tails (odama rasengan are stated to be able to carve out mountains)) but from lowballing sake)

 

[DontTalkDT]

ETSB are made from energy. You can't use KE for that.
(And you also can't really use it for a spacetime erasing sphere, as KE has space and time components, but that's just the second problem)

 

[sageof8paths]

ETSB are made from energy. You can't use KE for that.
(And you also can't really use it for a spacetime erasing sphere, as KE has space and time components, but that's just the second problem)

I plan to address the validity of the calc in a thread. I need it done first though