# I How is asteroid 101955 Bennu possible?

#### alva3

Summary
Five questions about the structure of asteroids; specifically 101955 Bennu.
Summary: Five questions about the structure of asteroids; specifically 101955 Bennu.

Please forgive my ignorance, but I need help reconciling a few things...
I'm curious about the images I've seen of asteroid Bennu:

1. If gravity is proportional to combined masses divided by their distance, how is it even possible that small boulders and gravel are being held together by each other on a rotating body?

2. If it is possible, once the asteroid's speed and rotation were matched, couldn't a satellite land on its surface simply by getting closer (without intentionally attempting to land) i.e. "be pulled"?

3. Wouldn't the force of a tether overcome the micro-gravity in a huge way and send a large portion of the gravel flying off into space? https://www.sciencedirect.com/science/article/abs/pii/S009457651731682X

4. How do van der Waals forces account for what friction and gravity cannot by themselves? https://www.sciencedaily.com/releases/2014/08/140813132037.htm

5. Lastly, how is the agglomeration of a bunch of debris like this not a violation of the second law of thermodynamics?

Sincere thanks for replies.

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#### davenn

Gold Member
1. If gravity is proportional to combined masses divided by their distance, how is it even possible that small boulders and gravel are being held together by each other on a rotating body?
you seem not to realise that it is a solid mass with a small bit of loose material on its surface
so the main mass IS NOT being held together by gravity

2. If it is possible, once the asteroid's speed and rotation were matched, couldn't a satellite land on its surface simply by getting closer (without intentionally attempting to land) i.e. "be pulled"?
Someone else maybe able to answer that

3. Wouldn't the force of a tether overcome the micro-gravity in a huge way and send a large portion of the gravel flying off into space? https://www.sciencedirect.com/science/article/abs/pii/S009457651731682X
Summary: Five questions about the structure of asteroids; specifically 101955 Bennu.

4. How do van der Waals forces account for what friction and gravity cannot by themselves? https://www.sciencedaily.com/releases/2014/08/140813132037.htm
5. Lastly, how is the agglomeration of a bunch of debris like this not a violation of the second law of thermodynamics?

Again, for all these Q's, refer to my answer to your Q #1

as you have a basic misunderstanding of the makeup of that asteroid

Dave

#### jbriggs444

Homework Helper
If gravity is proportional to combined masses divided by their distance
The force of gravity on a particular chunk of gravel on the [hypothetically spherical] surface would be proportional to the combined mass of all the other chunks divided by the radius squared. It would also be proportional to the mass of the chunk in question.

The gravitational potential deficit of a particular chunk of gravel on the [hypothetically sperical] surface would be proportional to the combined mass of all the other chunks divided by the radius [not squared this time]. It would also be proportional to the mass of the chunk in question.

If the rotational velocity is low enough so that the kinetic energy of a chunk of gravel on the surface is less than half of the potential energy deficit then that chunk can rest on the surface. If more than half and less then all then the chunk will go into orbit instead. If the kinetic energy exceeds the potential energy deficit then the chunk will escape.

• alva3

#### mfb

Mentor
It doesn't rotate that fast. You don't need a large force to keep things on the surface.
The critical rotation rate depends on the density only if we approximate the asteroid as sphere: $\frac{GMm}{r^2} = m \omega^2 r$ where G is the gravitational constant, M is the mass of the asteroid minus a small mass m (e.g. a rock on the surface), r is the radius of the asteroid, $\omega$ is the angular velocity. For a sphere the mass is $M=\frac 4 3 pi r^3 \rho$ with the density $\rho$, so plug that in: $\frac{4 G \pi r^3 \rho m}{3r^2} = m \omega^2 r$. Simplify: $\frac{4}{3} G \pi \rho = \omega^2$. For Bennu, $\rho=1190 kg/m^{3}$, leading to a maximal angular velocity of 0.000313 per second, or a rotation period of 5.4 hours. It rotates slightly faster, 4.3 hours, but it is not a perfect sphere, and some of it is held together simply by being a solid object.
2. If it is possible, once the asteroid's speed and rotation were matched, couldn't a satellite land on its surface simply by getting closer (without intentionally attempting to land) i.e. "be pulled"?
The position of spacecraft is controlled closely. You don't land unintentionally, unless something breaks in the spacecraft.
The asteroid is so small that the gravitational attraction and the escape velocity are tiny. To land you need to approach it very, very slowly, otherwise you might bounce off.
5. Lastly, how is the agglomeration of a bunch of debris like this not a violation of the second law of thermodynamics?
Why would it? Things collide, sometimes they stick together and release the impact energy as heat.

• alva3

#### alva3

If the rotational velocity is low enough so that the kinetic energy of a chunk of gravel on the surface is less than half of the potential energy deficit then that chunk can rest on the surface. If more than half and less then all then the chunk will go into orbit instead. If the kinetic energy exceeds the potential energy deficit then the chunk will escape.
This I get. Apparently the rotation rate is speeding up for no apparent reason, and stuff is flying off:

rotation: https://news.agu.org/press-release/asteroid-bennu-target-of-nasas-sample-return-mission-is-rotating-faster-over-time/
particle plumes: https://earthsky.org/space/challenges-osiris-rex-asteroid-bennu

Despite the science, I still have to admit it seems almost fictional to imagine Stone Mountain in GA., hurling through space, with gravel attached to the surface. The math computes, the mental image does not.

#### alva3

The critical rotation rate depends on the density only if we approximate the asteroid as sphere...
Thank you for the reply. Like I said, mathematically I get it. Conceptually (as a physical reality) I just do not. But hey, I've never been in space before.

#### alva3

This article does say however, that it's basically a "pile of rubble... with a bulk density much smaller than would be expected for a solid object." Admittedly, that is difficult to imagine. And, being such a low density pile of rocks, wouldn't landing on it seriously compromise not only the rotation, but also the orbit?

#### Bandersnatch

This article does say however, that it's basically a "pile of rubble... with a bulk density much smaller than would be expected for a solid object." Admittedly, that is difficult to imagine. And, being such a low density pile of rocks, wouldn't landing on it seriously compromise not only the rotation, but also the orbit?
This pile of rubble has a mass of ~70 million tonnes. That's enough inertia to remain completely unfazed by what mass-wise is comparable to a medium-sized car, even if the probe crash-landed onto the asteroid. At best, it would dislodge some surface material from the main body.
Picture 10 million elephants standing on very slippery ice, if you can. Whatever change to the motion of the entire group you'd want to make, be it push them or make them rotate, you'd need to overcome the inertia of each elephant to make the desired difference. It's a lot of work.

But the mission to Bennu doesn't even intend to land as such, just hover above and blow some nitrogen onto the surface with a robotic arm.

• alva3 and anorlunda

#### mfb

Mentor
But the mission to Bennu doesn't even intend to land as such, just hover above and blow some nitrogen onto the surface with a robotic arm.
That's nearly the same as landing for at an object with such a low mass. You need one minute to fall down 10 cm near its surface.

• alva3 and sophiecentaur