# Force required to "move" asteroid

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1. Dec 4, 2015

### abhaybakshi

Hello All,

Consider below scenario.
Suppose there is a small asteroid in space rotating around itself. I reach to that asteroid in my spacecraft and match spacecraft's orbital speed with the rotation speed of the asteroid.
I eject my fancy carbon fiber net from my spacecraft which is sufficiently large to wrap asteroid.

Now, since I have captured the asteroid in my net, I want to bring it back to earth.

So my question -

1. If I want to "tow" that asteroid using my spacecraft, with how much force my spacecraft engine needs to "pull" the asteroid. In space there is nothing like weight. I guess the force required to "move" the asteroid should be slightly more than the gravitational pull that asteroid exerts on spacecraft.

Am I right ?

...Thanks.

2. Dec 4, 2015

### phinds

Well, first of all, you are overlooking the fact that the angular momentum of the asteroid has to be overcome before you can do anything other than just orbit around it.

Weight is irrelevant. What you have to do is move the mass. Do you understand the concept of inertia?

3. Dec 4, 2015

### abhaybakshi

Phinds,
Yes I know about inertia. It means unless you apply force, the object will continue to move or rest in the same place. I want to know how much force will be required if my spacecraft becomes stationery relative to the asteroid by matching it's speed, rotation etc.

4. Dec 4, 2015

### Bandersnatch

Close, but no cigar ;)

There is no lower limit on the force you need to apply to move the asteroid. You don't have to overcome any sort of friction, so you can, in principle, give it the slightest of nudges, and it'll start moving. All that the magnitude of force affects is how fast you'll be able to accelerate the thing. The acceleration of the asteroid is governed by $F=ma$, so it's easy to calculate what sort of force would produce what sort of acceleration.

What you are limited by, is the velocity at which you expel your propellant - it has to exceed the escape velocity of the asteroid. But since asteroids, especially those you'd be interested in feasibly collecting, are small, that escape velocity is small enough for virtually all propulsion systems to work, including a human standing on the surface and throwing rocks into space.

How powerful the engine doesn't affect whether you will be able to move the asteroid, but how soon can you expect it to arrive at the destination.

By the way, this feasibility study for asteroid collection might interest you:
http://www.kiss.caltech.edu/study/asteroid/asteroid_final_report.pdf
You can find the proposed propulsion system at page 22.

5. Dec 4, 2015

### abhaybakshi

Excellent ...thank you Bandersnatch. So does it mean if by some mechanism ISS "tugs" Earth through a cable long enough, will earth move out of orbit ??
This is silly question I know... but so I am :-)

6. Dec 4, 2015

### Bandersnatch

While possible in principle, pretty much impossible in practice.

7. Dec 4, 2015

### phinds

And you are ignoring what I said.

8. Dec 4, 2015

### Janus

Staff Emeritus
Yes, but you must realize that unless that tug is very very strong or acts for a very very long time the resultant change in the Earth's orbit will be negligible. And after its over, the Earth would still be in orbit, just a different one. To change the Earth's orbit, you have to change its orbital velocity. So let's say we want to change its velocity by just 1 cm/sec ( this would result in an orbital change that would be hard to even measure.

To do this, we will "tow" the Earth with a Saturn V first stage booster with a thrust of 34,020,000 Newtons. The Earth masses ~6e24 kg, so we would get an acceleration of 5.67e-18 m/sec^2 and at this rate, it would take us some 563 million years of constant thrust to get that 1 cm/sec velocity change (never mind where we would get the fuel to burn for that long), which would result in an infinitesimal change in the Earth's orbit.

9. Dec 6, 2015

### abhaybakshi

Got it. Thanks all !

10. Dec 6, 2015

### rootone

Remember the point Phinds made as well though.
If your asteroid is rotating you'll have to stop that first before you can drag it to Earth.
Sure you can match up your spacecraft's velocity so that it matches the asteroid's rotation, but then the spacecraft's direction of travel will be constantly changing.
That makes it very difficult, and in practice I think impossible, to pull it in a particular desired direction (towards Earth).

11. Dec 6, 2015

### Bandersnatch

If you have a propulsion system capable of transporting the asteroid, you then also must have a propulsion system capable of stopping the rotation.

12. Dec 6, 2015

### rootone

Sure, if you can stop the rotation all is good.

13. Dec 8, 2015

### Whyndham_UCL

It depends. A useful mission might not require losing all the acquired velocity. For example, he might merely wish to inject it into another orbit, around Mars perhaps, where something else can go and do something with it, like ... throw materials (water?) towards the surface.

And then there are aerobraking concepts to be had which mean that we can grab momentum change from the environment (though do be careful with that asteroid above my house please!).