Is this right? Stoping a Spinning Asteriod Problem

[RuBisCO]

Lets say you have asteroid, here are its parameters:

radius 15.12 m

diameter 30.24 m

volume 14479.1805220239 m^3

mass 19981.269120393 tons

Rotation 0.21 hours

Circumference 95.0017618446 m

Angular velocity 0.0083110917 rad/s

Moment of Inertia 1827202340.47887 kg*m^2

Rotational Energy 63106.3109279942 (kg*m^2)/s^2 (Joules)

So I calculate this asteroid has 63 kJ of rotational energy, ok sure only problem is that just 0.65 kg of fuel burned with a ISP of 450 s (4400 m/s) could stop the spin of this 20 kt rock if I compared kinetic energy to rotational energy. So what am I doing wrong?

[K^2]

Because you don't use 100% of energy to do work against asteroid. You use almost all of it to accelerate exhaust off into space.

What you should be looking at is angular momentum and torque. I'm getting something like 2.2 tons of fuel with the above parameters.

[RuBisCO]

Because you don't use 100% of energy to do work against asteroid. You use almost all of it to accelerate exhaust off into space.

What you should be looking at is angular momentum and torque. I'm getting something like 2.2 tons of fuel with the above parameters.

And the math for that is?

[K^2]

ÃŽâ€L = ÉI = mvr

[RuBisCO]

Angular momentum? how?

[Nikolai]

Change in angular momentum. If you want to stop a spinning thing, you need to reduce its angular momentum to zero.

[RuBisCO]

Ok how do I do the cancellations?

[N_las]

The exhaust you are expelling has the angular momentum of L = exhaust velocity * asteroid radius * exhaust mass.

If you do some approximations, you can say:

Asteroid moment of inertia * asteroid angular velocity = exhaust velocity * asteroid radius * exhaust mass.

I am getting around 230 kg of fuel to stop the asteroids rotation.

Edited February 9, 2015 by N_las

[K^2]

Ah, yes, I looked at the wrong number and used 450m/s for exhaust velocity. 230kg sounds right.

[RuBisCO]

Ok, good alright here cp from spreedsheet, does it look correct?

Spinning Asteroid

density 1.38 tons/m^3

radius 15.12 m 1512 cm

diameter 30.24 m

volume 14479 m^3

mass 19981 tons 19981269 kg

Rotation 0.21 hours 12.6 min

Circumference 95.00 m

angular velocity 452 m/h 0.13 m/s 0.0083110917 rad/s

Moment of Inertia 1827202340 kg*m^2

Rotational Energy 63106 (kg*m^2)/s^2 63106 J

Angular momentum 15186046 kg*m^2/s

Fuel mass 228 kg

Fuel velocity 4413 m/s 450 isp

Kinetic energy 2216213612 Joules

Angular momentum 15186046 kg*m^2/s

Ratio AM/AM 1.00

I get 410 kg for 250 s ISP attitude control thrusts, so for an asteroid of this mass it would be very realistic to be able to stop it's spin using on-board propellant.

Edited February 10, 2015 by RuBisCO
Forgot rad/s

[Drunken Hobo]

I'm tired, so I may not be thinking straight, but I'm not sure how such an asteroid could even exist. The low density indicates that it's probably a rubble pile (or extremely icy), yet it's rotating too quickly for gravity alone to be holding it together (escape velocity is ten times slower than the equatorial velocity). Perhaps it's a fragment of a comet? I demand an explanation!

[RuBisCO]

I'm tired, so I may not be thinking straight, but I'm not sure how such an asteroid could even exist. The low density indicates that it's probably a rubble pile (or extremely icy), yet it's rotating too quickly for gravity alone to be holding it together (escape velocity is ten times slower than the equatorial velocity). Perhaps it's a fragment of a comet? I demand an explanation!

...*cough*http://www.lpi.usra.edu/books/AsteroidsIII/pdf/3016.pdf

"They could be held together, however, by very meager bonds; even the fastest known rotator, 2000 DO8, with a period of 1.30 min and a long axis of ≈80 m, has a centrifugal acceleration at the ends of the long axis of only ≈0.26 m/s^2, and the minimum required tensile strength for it is on the order of 2 × 10^4 Pa, which is ≈10^–3 less than the typical tensile strength of well-consolidated rock (see Ostro et al., 1999). While they are sometimes called “monoliths,†their internal structure can, however, be almost anything except “true†rubble pile. In the framework of the definitions proposed by Richardson et al. (2002)"

For example compressed snow has a tensile strength of up to 20 kPa. 2000 DO8 (no longer the fastest rotating asteroid, latest fastest is 2008 HJ which rotates once every 42.7 seconds and is 12-24 m wide) is only 40 m wide and rotates every 78 seconds, yet it could be made out of something as flimsy as compressed snow (not that I'm suggesting it is snow, only that it is as weak as snow and certainly very low density like snow)

Edited February 9, 2015 by RuBisCO

[K^2]

Could easily be a "dirty snowball" of water and amonia ice with some rocks in it. It'd have sufficient structural strength and have that sort of density.

You are assuming a perfect sphere with uniform density, which it almost certainly isn't. But it's going to be good enough for a ball park estimate. Since asteroid is going to turn around its maximum moment of inertia, or close to it, expect the figure to be a bit higher.

[RuBisCO]

Well compared to a planet I would put a good bet <150 m wide asteroids would often have very uniform densities (relatively), it is just a round shape is probably the rare part.