Asteroid Response Help: Get Answers to Your Questions Here

[screamindivr145]

TL;DR Summary

Writing a paper on a response to an asteroid threat. I need help with it.

(If anyone could provide links to information it would be greatly appreciated.)

I'm currently taking a class on threats from outer space and have to write a paper on something that could be done in response to an asteroid/meteor coming towards Earth. One of the quickest responses would be to put a nuclear bomb near the said asteroid and set it off using the force produced to push the asteroid off course and away from Earth. As you all could imagine, for someone who doesn't really have a background in physics, let alone astrophysics, it's a bit hard to find all the information I need.

That being said, I'm trying to figure out a few things in regards to this. First, though, I'm going to assume a few things about the asteroid:

1. It is roughly spherical
2. Density of r = 3 gm/cm³
3. Traveling at a velocity of v = 20 km/sec
4. Diameter of d = 0.5 miles
5. Rated a 10 on the Torino Scale
6. Distance from Earth ≈ 5 years out

With that, I need to figure out the following:

1. An equation for how much force would be needed to push the asteroid off course (I'm aware that any amount of force could move an object in space so long as it's greater than the current amount of force being exerted from the object in the opposite direction)
2. How far the asteroid would need to be from Earth to not be a threat of any kind
3. *BONUS* Any other information you could see as relevant

Any help anyone could give would be greatly appreciated. If you need any more information regarding the specifics of the scenario, please let me know.

 

[screamindivr145]

EDIT: Diameter of d = 2 km

 

[willem2]

Summary:: Writing a paper on a response to an asteroid threat. I need help with it.

An equation for how much force would be needed to push the asteroid off course
(I'm aware that any amount of force could move an object in space so long as it's greater than the current amount of force being exerted from the object in the opposite direction)

You don't really need the force. The only force on the asteroid during it's flight will be the force of gravity, there is no need to oppose any force. Any force will produce a velocity change using you can compute with F = ma (force is mass times acceleration)

The thirst thing to do is to calculate the change in velocity required to make it miss the earth. The velocity change could be produced by a small force over a long time, or a large force over a short time. ..
A very crude approximation to get the order of magnitude of the needed velocity change, is to use
deflection = (velocity change) * time. This ignores the effects of gravity on the asteroid during the five years of its flight.
The required velocity change will still be quite small. five years is a long time.
A better calculation would use Kepler's laws to compute the orbits of the asteroid and the earth, and see how a small velocity change would affect the orbit of the asteroid. Make sure to try velocity changes in different directions. (forward, backward, left right, up, down)
You'll need some coordinate system to calculate in. v = 20 km/s is meaningless. The Earth moves with 30 km/s around the sun.
Try to look up some actual orbital parameters of future close encounters here https://cneos.jpl.nasa.gov/ca/

How far the asteroid would need to be from Earth to not be a threat of any kind

If you can deflect the orbit by the radius of the Earth + the radius of the satellite, you can make it miss the earth. It's important to also account for the precision of the measurements.
An object that passes close to the Earth will have its orbit deflected into a new orbit that still crosses Earth's orbit later. A detailed and very precise calculation will be needed to predict the orbit of the asteroid after a close encounter with a planet. (supercomputer, if it needs to be done quickly)

To get the nuclear bomb to work, it must be used close enough to the asteroid to evaporate some of the asteroid to produce hot gas that will push the asteroid, the same way a rocket works. Another difficult calculation here. If you're not a graduate student with months to spare for this, I'd look it up somewhere.
If you want to do calculations yourself deflection by an impact or a gravity tractor will be easier.

 

[screamindivr145]

This ignores the effects of gravity on the asteroid during the five years of its flight.
The required velocity change will still be quite small. five years is a long time.

I apologize, I probably should have stated that this is how long before the asteroid reaches Earth that we discover it and how long we have to respond (from the planning stage to putting together a launch and getting the bomb to the asteroid). According to this link on pg. 147, five years is the minimum we'd need to execute a plan to divert the asteroid, thus the quick response use of a controlled nuclear explosion.

Unfortunately, I'm only an undergrad with nowhere nears months to compute all of that, so I guess I will have to look up that data somewhere else. The information you have given though is greatly appreciated.

 

[sophiecentaur]

'Nuke it' is not a very good solution unless the detonation is very accurately timed and unless you can use a large mass (relative to the asteroid) to eject in the opposite direction of the required thrust. A rocket 'pusher' could be much better(Best value for Momentum change; much better value than relying on relatively small masses of gas being ejected). We have now proved the feasibility of landing and attaching to an asteroid so that could be a hopeful approach.
Nuclear Rocket engines are, surprisingly it appears, only twice as good (specific impulse) as chemical rockets but, as they don't exist yet in a practical way (?) chemical rockets would be the way to go. Background link. The health concerns for nuclear propulsion wouldn't apply for such an unmanned mission so it could be an application for that technology.
Any minute now we could identify a serious risk of collision and that would certainly apply the incentive to get a solution PDQ.

 

[skeptic2]

Possibly a more efficient method would be to drill into the asteroid and bury the nuclear device some distance below the surface. This would have the advantage of blowing out a large amount of material from the asteroid and creating a larger thrust. An additional factor in this solution would be the rotation of the asteroid. Either the explosion would have to be timed very precisely or the hole would have to be drilled at one of the poles of rotation. Presumably one of the poles would be better suited for redirecting the asteroid than the other.

 

[sophiecentaur]

The advantage of having a lot of ejected material would be countered by the controllability of a regular rocket.
If lack of time is not an issue then a high specific impulse is not required.
A difficult decision to make. Many factors.

 

[skeptic2]

https://en.wikipedia.org/wiki/Asteroid_impact_avoidance