Stopping or re-routing comet 67p

[clint martin]

Hello, I am new here and I would like to know if anyone on here can answer a question for me. How far could a saturn V rocket (http://en.wikipedia.org/wiki/Saturn_V) push comet 67p off course if it were 100 million miles away? Also, how long would it take this rocket to stop the comet if it could burn for as long as needed/ or how many rockets would it take to stop it within the listed burn time of the rocket? The comet weighs 10 billion tons and is traveling at 84,000mph. I did some calculations, but I would like to see what you (smarter than me) physics patrons come up with. Good luck agreeing on an answer and thank you in advance.

-Clint

 

[phinds]

You need to show some work of your own.

 

[marcus]

Hello, I am new here and I would like to know if anyone on here can answer a question for me. How far could a saturn V rocket (http://en.wikipedia.org/wiki/Saturn_V) push comet 67p off course if it were 100 million miles away? Also, how long would it take this rocket to stop the comet if it could burn for as long as needed/ or how many rockets would it take to stop it within the listed burn time of the rocket? The comet weighs 10 billion tons and is traveling at 84,000mph. I did some calculations, but I would like to see what you (smarter than me) physics patrons come up with. Good luck agreeing on an answer and thank you in advance.-Clint

Wikipedia gives the thrust of the Saturn V.
Thrust 7,648,000 lbf (34,020 kN)

BTW how did you decide the comet's mass was 10 billion tons? Can we assume you mean metric tons?

How about as a warm-up exercise you take it out of the solar system context and just imagine that the comet is going in a straight line at some speed out in empty space?

Maybe you know all the basic physics. Let's look at a simpler problem. Out between the stars, at rest, you have a mass of 20,000 metric tons and you push on it with the Saturn V thrust of 34,020,000 Newtons, for 1000 seconds. Now how fast is it going?

the unit of momentum is "NEWTON SECOND", so you impart to the thing 34,020,000,000 units of momentum.

Now if you divide that by 20,000,000 kg you will get the speed in m/s. So it is 34,020/20 = 1701 meters per second. So it is about 1.7 km/s.
===========================

Wikipedia about comet 67P says the comet is currently going about 18 km/s, that is roughly 10 times as fast as the speed in that example.

Suppose something with a mass of 20,000 metric tons is going slightly less than the comet's speed, say 17 km/s. How long would it take to stop it, with Staturn V thrust? Obviously 10,000 seconds. Between 2 and 3 hours.

This may be trivial for you. I don't know your background. But that is somewhere to start. are you comfortable with this calculation in these units?
==================
Wikipedia http://en.wikipedia.org/wiki/67P/Churyumov–Gerasimenko gives the comet mass as 10¹³ kilograms. So that would be 10 billion metric tons. Agreeing with what you said.
But I want to check that and get back to this later.

Kind of interesting exercise. Were you talking about the perihelion speed?

 

[marcus]

Again, that Wikipedia page says the perihelion and aphelion distances are:
1.24 AU and 5.68 AU
and the orbit period is 6.44 years
If you know how to draw an ellipse with the two ends of the string fixed at the two foci of the ellipse then you can figure out
the AREA of the orbit from 1.24 and 5.68 AU (ask if you want help figuring that out) and that together with the 6.44 years tells you
the rate that area is swept out. And that tells you the SPEEDS at peri and aphelion.
Copy these two expressions into google window and press return
pi (5.68/1.24)^.5 (5.68+1.24) AU/(6.44 year) and it will say 34 km/second
pi (1.24/5.68)^.5 (5.68+1.24) AU/(6.44 year) and it will say 7.5 km/second

So if you wanted to make ChuryumovGerasimenko stop in its tracks and fall into the sun,
then you would merely have to wait till it is out near Jupiter at aphelion, going 7 and a half km/s and stop it. Canceling 7.5 km/s should be easy compared with trying to stop it when it is going 34 km/s.

Actually what is it you are imagining doing when you talk about "rerouting" the comet?

 

[clint martin]

Actually what is it you are imagining doing when you talk about "rerouting" the comet?

When I say "reroute" I am wondering how far you could push it off course if it were going to collide with the Earth.

 

[marcus]

Actually what is it you are imagining doing when you talk about "rerouting" the comet?​

When I say "reroute" I am wondering how far you could push it off course if it were going to collide with the Earth.

Ah!
That kind of thing has been studied. Not with ChuryumovG AFAIK but with other hypothetical bodies, e.g. asteroid-type.
One concern is the risk of breaking the body up in one's attempt to push it off course.

Obviously if one knows the orbit very precisely, well in advance, then a reasonably small change in velocity should be enough, applied well in advance so the effect would build up.

This is intuitive. Even changing the speed by 1 meter per second could be enough. The Earth is less than 7 million meters in radius. Intuitively if you can change the velocity of an object by 1 meter per second and you do it 7 million seconds ahead of the expected collision, you can change the path by 7000 km and convert a direct hit to a near miss. 7 million seconds is about 2 years. Timing is the key thing. And precise knowledge of the body's orbit is key.

What I would suggest is you first look at at the resources needed to change the speed of an object (with a mass large enough to be dangerous) by a modest amount like 1 meter/second.

Say the thruster puts out F (Newtons), and the mass of the body is M (kilograms) then you have to run the thruster for T (seconds) where

T = (1 m/s)M/F

So if M = billion kg
and F = 1000 Newtons
you have to run the thruster for a million seconds (roughly four months)

1000 Newtons is roughly the weight of 100 kg. I'm thinking of an ion thruster---they make fairly efficient use of propellant and have low thrust so they have to be run for long periods of time for the change in velocity to build up. The thruster itself could be used to GET itself to the orb in question. An ion thruster that could deliver 1000 Newtons is futuristic. Real ones are currently much less powerful, like a tenth of a Newton ( this is a "what if" sample calculation).

BTW did you know that the DAWN ion-drive spacecraft will arrive at the dwarf planet CERES next year?
Dawn's set of three ion thrusters only develops a TENTH of a Newton : ^) so it would be a humongous ten thousand-fold scale-up to imagine a 1000 Newton ion space tug. but who knows?
http://en.wikipedia.org/wiki/Dawn_( spacecraft )

 

[D H]

How far could a saturn V rocket (http://en.wikipedia.org/wiki/Saturn_V) push comet 67p off course if it were 100 million miles away?

Not very. Fortunately, we don't have to worry about that comet, and least not for a long time. 67P/Churyumov–Gerasimenko doesn't cross Earth's orbit.

Suppose it did. Suppose it's perihelion was 0.9 AU instead of 1.2432 AU, making the comet cross not only Earth's orbit, but also Mars' and Jupiter's. Suppose the next crossing of Earth's orbit it will intersect rather than cross, and suppose we didn't do anything to stop it until it was 100 million miles away. Two words fully describe this scenario:

Too late.

As you most likely have discovered, you would need well over a thousand Saturn Vs to have a chance of deflecting the comet at that close range to the Earth. There are only two months until impact. That means a rather hefty delta V needs to be imparted, on the order of a meter per second. The delta V needs to be applied close to orthogonal to the comet's velocity vector. That is highly suboptimal in general, but its the only choice when the comet is close by.

When the impactor is close we would have no choice but to push it aside. A much better option exists given adequate warning. Instead of pushing it aside, the delta V is applied along or against the velocity vector. This changes the comet's orbital energy and hence it's period. The change is much more significant with this kind of change than an orthogonal delta V thanks to the Oberth effect. This approach is particularly useful if the delta V can be applied at perihelion, one or more orbits prior to impact. This makes the required delta V drop from a meter per second to less than a centimeter per second.

Using rockets is also a bit suboptimal. One problem is getting there. With a rocket-type approach, you have to match speeds with the comet, and then you need to land on it. As we've just seen with Philae, that's not easy. The weapon of choice amongst most of those who study this problem seriously is nuclear weapons. The explosion bathes the target part of the object with lots of high energy particles. This will vaporize a thin veneer of material, which then will blast off the target. It's the third law response to that vaporized material blasting off from the comet that provides the delta V to the comet. You don't need to land the weapon on the comet. Close counts in horseshoes, hand grenades, and nuclear weapons.

 

[meemoeuk]

hello, I've just been looking at some pics of comet 67-P by the philae lander.
Am I right in thinking this is a rocky surface? That's what's bugging me. I know comets were thought to be made of ice, but these pictures are of rock. But how does this fit with comet densities being of hollow ice ? about 500kg/m^3 Are they ice underneath the rocks?

 

[Vanadium 50]

I know comets were thought to be made of ice, but these pictures are of rock.

How do you tell rock from ice from a photograph? Indeed, how are you distinguishing the concepts of "rock" and "ice"?

 

[meemoeuk]

Dunno. It just looks like its rocky. I would say because it looks dark, and also jagged and stoney, lots of little stones. It looks similar to rocky outcrops on Earth, and sort of like what I'd expect rocks in space to look like.

I had not seen ice that looks similar to these picture. But actually to be fair now I've google searched I'm surprised at how ice can mimic rocks a bit.
http://i.telegraph.co.uk/multimedia/archive/02167/dirty-iceberg_2167407k.jpg

I distinguish ice from rock because ice can turn into water. Also ice is reflective of light, but that surface looks dark.

 

[meemoeuk]

>How do you tell rock from ice from a photograph?

I think I've got it. Rock outcrops erode by turning into scree slopes. And that's what is seen in that Philae lander pic. Ice doesn't do that. Its not like its random stones that pile up on the surface evenly. There is a scree slope under the rock outcrop.
Also, the flat parts, are they ice or sand? I recall at the time of the photos 1st release, there was debate in the media about that. I remember thinking they looked like deserts, because they had waves ( dunes ) in them, ice doesn't do that. Also they look sandy, rather than icy.
This break up of rock into sand is expected due to erosion by solar wind.

Am I right? Feel like I'm exploring with just my own thoughts here.

dunes!

I love these pictures.