Science: asteroid vs. hero physics

[Janx]

I'm working on a short story due in a few weeks (for an anthology, not school). I need all my physicsful friends ideas to adjust the plan.

The big climax is the hero has just bonded with her new super sci-fi space suit that will let her fly up and help protect the earth from asteroids and stuff. She can fly, propel matter, and using pico-printer-gel*, disassemble and reassemble matter.

In the current draft, she has about 15 minutes to fly up and prevent an asteroid that's going to splatter the earth. This is the "last one", since the previous about a 100 years ago (which aligned with Asteroid Bennnu's description and timing). Mankind can't survive another hit.

There's limits to how much mass she can move, we don't have numbers, but the asteroid is too big. She's a sniper (back on earth) and tends to deal with problems distantly. I decided she'd have to get close for this one (and thus risk her life).

Since she can't just superman shove the asteroid off course, I thought she'd try aikido. Let's say she just got up to space and there's 5 minutes left. The asteroid is on her left (relatively) and coming in to kill us all. She flies right, around the planet, picking up speed (a lot of speed), gathering up matter to build a lattice that she can ram/cushion with. She rejoins the asteroid from behind and pushes with all her super-pushy-power. Thus adding speed along a vector the asteroid is mostly going, and thus, causing it to skirt past the earth instead of slaughtering the last of humanity.

I don't need exact math, but I think there's a hole in the idea. To get around a planet of 24K miles circumference in under 5 minutes is a whole lot of speed and acceleration. Assuming she can now handle higher g-forces, wouldn't her new speed be very much faster than the asteroid, causing her to splat, instead of line up to shove?

Is there a better solution for dealing with an asteroid in 15 minutes (5 assuming it takes 10 to get up there)?

I don't think Nukes has the right vibe and lots of articles disproved that as a solution.

Is the original plan workable if I adjust the effective starting point for the asteroid so it will be far enough away and have just the right speed for her to join it by orbiting the planet once?

I can play with the parameters a bit since it's just fiction, but I need a short timeline and personal risk. Her flinging an object at it might work, but how would she herself be at risk to add tension?

This is the big finish to my post-Ragnarok coming of age biker cultist story about a fallen angel.

Thanks!

 

[Umbran]

Hm. This is a good one.

The kinetic energy of a non-relativistic object is 1/2 M V^2. So, there are two basic ways for it to have a lot of KE. One is for it to be big, and the other is for it to be fast. Note that the energy goes linearly with the mass, but goes like the square of the velocity. Double the mass, you double the KE. Double the velocity, and you *quadruple* the energy.

And, part of making this work, or at least be cinematically plausible - make the asteroid less small, but faster. That, overall, makes it easier to push around.

Now, not, pushing "along a vector it is mostly going" doesn't help. Any portion of her effort that moves along the line of the asteroid's current motion makes it reach Earth faster, and hit harder. She needs to add velocity more or less perpendicular to its current motion.

We can set up things to minimize how much she needs to do. If the thing is aimed dead center, she needs to move it 4000 miles in order to be a clear miss. If we set it up as an off-center, almost glancing blow, then she only needs to move the thing a few hundred miles. Mind you, she needs to move the thing a few hundred miles in 5 minutes. If it is, say, 400 miles in 5 minutes is like 4800 miles per hour. She has to add 5000 mph *to the mass of an asteroid* and that's if she takes the asteroid from its current path to +4800 MPH instantly. If she takes time to accelerate it, the first moments are slow, and the end speed must be even higher to succeed.

Note - this is basically saying that she, alone, can create an impact roughly equivalent to the asteroid's impact herself. She is capable of ending civilization. Is that the power level of your hero?

 

[Nagol]

The problem with dealing with asteroids with a (very) short timeframe is the any asteroid that can harm the denizens of Earth has to have a lot of mass and since you have so little time to react, tremendous forces need to be brought to bear.

If you want to keep the time pressure, perhaps you could move the asteroid further out and unless its vector is changed in the next 5 minutes, the impact will be unavoidable? Assuming the answer is no, let's do some back of the envelope math!

I'll assume the rock is about 100m in radius and has a density of about 3, that means it masses 12 million tonnes.

Because the timeframe is short, you have to adjust the vector by a substantial amount. That mass is moving at quite a clip (~11 km/s). If you have 300 seconds, you're intercepting the asteroid about 3500 km from Earth. Earth has a radius just over 6,000 km. Worst case is a centre strike which would mean you'd need to change its vector by 45 degrees. But let's assume the impact is projected to be a grazing hit about 1000 km from the edge which means you'd need to shift its angle by about 20 degrees.

Now that shift needs to be instantaneous. Every second of delay/acceleration means the distance is closing and the angle needs to become more extreme. Vectors at these speeds are mostly additive so you need to impart a velocity of about 3 km/s which would have the rock just skim the atmosphere -- assuming we ignore gravitational attraction. Let's bump that up to 3.5 km/s for a basic safety margin. That change is what you'd need if you could impart it instantly. Let's assume you spend a whole minute of acceleration and thus need to achieve a higher velocity of about 6 km/s to simplify the math. A = v / t so 6km/60 seconds = 100 m/s-squared or about 10 g of acceleration. F = ma, so 12 billion kg x 100 m / s-squared is 1.2 trillion Newtons of force which is the same as 1.2 terawatts needs to be applied for the whole 60 seconds.

Regardless of how our hero applies the force -- whether directly to the asteroid threat or through a passive intermediary, the amount of energy remains the same. Since you want the hero to use an intermediary, there needs to be something that acts as a force multiplier. You don't have sufficient time to use the Earth's gravity well so let's look elsewhere.

One simple force multiplier would be a secondary large rock -- say a half the radius of the threat that is moving in a different orbit that is closer to the preferential vector that can be adjusted to impact the threat. With a mass of about 10% of the target rock, the energy required to change its vector is equally reduced. If the asteroids are mostly metallic then you could even potentially set up an elastic collision. In an perfect scenario, the larger mass would have its velocity changed by ~5% of the closing velocity between the rocks.

 

[Janx]

thanks for getting back to me so quick.

To umbran's question about her power level: not sure. The space suit was part of a fleet of these for defending the earth from ballistic attack (mass drivers pushing big rocks from Mars). So using math for evil would probably mean yes, she could. I want her constrained that she can't just fly up and superman nudge the threat away.

I was trying to come up with a different approach to solving the problem (instead of brute force), and aikido inspired me to have her use the rock's momentum/direction to her advantage. Sounds like for that to work, she needs to push perpendicular, not "with" the general direction of the rock.

I can change how long it takes to get from ground to space, and then from space to the rock. Mostly, I wanted a short enough time to be urgent, she she had to leave right away, and be able to exposition what's going on to the folks back home over radio for the first part of it, because people have a totally wrong understanding of what happened.

the rock should be aimed off-center, it's a misfire anyway, and 100 years later, we've come back around to meet it. I can change the 100 years to whatever sounds plausible. The first strike was timed to align with Asteroid Bennu (a real supposed danger). Since this was pushed toward earth, it can be smaller, with a higher velocity.

Other than space debris (dead satelites, etc), I'm not sure if there's another rock floating around for her to grab. Ironically enough, a named asteroid like Bennu coming by at just this same time would make for opportunity to be used as ammo.

Or she could just grab enough matter to make a space bullet and fly with it so she can maintain acceleration on it, thus killing or deflecting the asteroid with a bullet/herself. It's heroic, and it's the kind of idea a sniper would come up with.

So, it sounds like she needs a bullet that is about half the mass of the threat. Umbran suggests a smaller, faster rock. Not sure how small would work, to justify how much mass she could feasibly gather (think all that wrecked stuff from Gravity). Maybe there's 1-2 tons worth of movie-metal to grab in a hurry? Space is big and that's kinda bullcrap, but let's pretend that's possible for her to scoop up while zooming along the right path. I'm guessing that should be the limit of her power to move/manipulate anyway.

Is it feasible to launch a 4 ton rock from the asteroid belt toward earth, miss (let's say somebody had second thoughts after the first launch and interfered) and have it eventually come around a century later and be a threat that our last Valkyrie can solve? Would that 4 ton rock be a threat?

 

[Nagol]

thanks for getting back to me so quick.

To umbran's question about her power level: not sure. The space suit was part of a fleet of these for defending the earth from ballistic attack (mass drivers pushing big rocks from Mars). So using math for evil would probably mean yes, she could. I want her constrained that she can't just fly up and superman nudge the threat away.

I was trying to come up with a different approach to solving the problem (instead of brute force), and aikido inspired me to have her use the rock's momentum/direction to her advantage. Sounds like for that to work, she needs to push perpendicular, not "with" the general direction of the rock.

I can change how long it takes to get from ground to space, and then from space to the rock. Mostly, I wanted a short enough time to be urgent, she she had to leave right away, and be able to exposition what's going on to the folks back home over radio for the first part of it, because people have a totally wrong understanding of what happened.

the rock should be aimed off-center, it's a misfire anyway, and 100 years later, we've come back around to meet it. I can change the 100 years to whatever sounds plausible. The first strike was timed to align with Asteroid Bennu (a real supposed danger). Since this was pushed toward earth, it can be smaller, with a higher velocity.

Other than space debris (dead satelites, etc), I'm not sure if there's another rock floating around for her to grab. Ironically enough, a named asteroid like Bennu coming by at just this same time would make for opportunity to be used as ammo.

Or she could just grab enough matter to make a space bullet and fly with it so she can maintain acceleration on it, thus killing or deflecting the asteroid with a bullet/herself. It's heroic, and it's the kind of idea a sniper would come up with.

So, it sounds like she needs a bullet that is about half the mass of the threat. Umbran suggests a smaller, faster rock. Not sure how small would work, to justify how much mass she could feasibly gather (think all that wrecked stuff from Gravity). Maybe there's 1-2 tons worth of movie-metal to grab in a hurry? Space is big and that's kinda bullcrap, but let's pretend that's possible for her to scoop up while zooming along the right path. I'm guessing that should be the limit of her power to move/manipulate anyway.

Is it feasible to launch a 4 ton rock from the asteroid belt toward earth, miss (let's say somebody had second thoughts after the first launch and interfered) and have it eventually come around a century later and be a threat that our last Valkyrie can solve? Would that 4 ton rock be a threat?

A 4 ton rock would need so much velocity to be a threat that if it missed on the first pass it would exit the solar system.

 

[Nagol]

The only way an intermediary helps is if it already has energy that can be used against the target. If you have to pick up the target and accelerate it, it is only helpful if you have extra time or if energy output of the suit is not the limiting factor for the acceleration. In other words, if the suit has the force to accelerate a 100 kg human at 50 g, but humans go unconscious at 3 g then the hero could afford to pick up and accelerate about another 1500 kg and stay conscious.

Let's change the asteroid's composition to have density of 8 (solid iron) and set the orbit to a ~100 year elliptical. The math for calculating the instantaneous velocity isn't hard, particularly, but I'm rusty enough not to do it on the back of an envelope. Let's guess the velocity at 1 AU would be about 3 times the base velocity of a circular orbit with the same period or 20 km/s and further assume its going counter to the planetary motion so we can increase the closing velocity to 50 km/s.

To achieve the same kinetic energy of my original assumption 12 million tonnes at 11 km /s, we have ~600,000 tonnes at 50 km/s and it has about a 25 m radius.

Let's push the rock further out to say the hero intercepts it 1 hour from Earth (about 180,000 km out). The necessary deflection is much smaller. We still need to shift about 1,000 km, but we have 3,600 seconds to complete the shift or merely about 350 m /s.

If she picks up 1,500 kg and accelerates at 2 g for the whole trip, it takes a bit over an hour to arrive (4200 seconds) and will be travelling a bit over 40 km/s compared to the Earth. That gives a relative closing velocity on the target of about 80 km/s. The 1,500 kg mass in an elastic collision would cause the target to gain about 400 m/s vector (and thus miss Earth) and the 1,500 kg slug would bounce back at nearly 80 km/s. Since it unlikely the slug could survive those g-forces, the hero would have to evade the expanding shrapnel cloud.

Actually, this assumes a side strike appropriately perpendicular to the target's forward motion. So toss in another hour or so of travel time to line the shot up.

 

[tomBitonti]

To be accurate, be careful to include both energy and momentum in the physics of the collision. If I have the right sense of it, a very fast small object hitting a larger relatively still object either, with an elastic collision, bounces off at high speed (transferring momentum and a little energy) or with an inelastic collision does a lot of local damage and transfers almost the same momentum. (This is a classic physics test problem, with the key observation being whether the collision is elastic or not, which tells you what analysis to do.)

As what Umbran said: The push should be perpendicular to the line of motion of the asteroid. A perpendicular push will create the greatest deviation. There is a case of a skimming trajectory, where the straight line motion of the asteroid would miss, but gravity curves the asteroid path into the earth, where it seems that speeding up the asteroid should work.

Some other considerations: How far away the asteroid starts from the earth, and at what speed, compared with escape velocity (11.2 km/s) and orbital velocity for a circular orbit (about 7.6 km/s): If the asteroid is left with less than escape velocity, the asteroid may go into orbit, or may impact the earth at a later time because of the particulars of the changed orbit the asteroid.

Thx!
TomB

 

[Janx]

the suit is made of pico-printer-gel (tinier than nanites) and it can modify/repair her such that she can probably handle twice the G. I made that up of course, but thus far, it's in specification for what I'd already figured out. Calling it a suit is really a simplification for our discussion.

So that might mean that she can go twice as fast, turning that hour long flight into aprox. 30 minutes (or as you added an hour, an hour instead of two).

I can still make it tense and "guys I need to go now" because she really does need to get there while it's still farther away. Add in radio fade out after the Q&A with the folks back home , a bit of time passes and as she lines up for the shot, bring the radio back in for final words.

I can even have the science guy explain it to the rest of the party, "of course, she needs to achieve a speed of 80km/s and impact at a perpendicular angle to blah-blah" or some such.

I don't want to cite too many numbers, but I wanted to have the strategy be interesting, heroic, and plausible if one of y'all crunched numbers.

I think I can make this work and be closer to plausible, since it is a sci-fi story.

Glad I asked y'all. Let me know if there's any holes with my recap of what I think you said, or a different way to approach the problem (besides let everybody die, which I already dealt with

 

[Janx]

To be accurate, be careful to include both energy and momentum in the physics of the collision. If I have the right sense of it, a very fast small object hitting a larger relatively still object either, with an elastic collision, bounces off at high speed (transferring momentum and a little energy) or with an inelastic collision does a lot of local damage and transfers almost the same momentum. (This is a classic physics test problem, with the key observation being whether the collision is elastic or not, which tells you what analysis to do.)

As what Umbran said: The push should be perpendicular to the line of motion of the asteroid. A perpendicular push will create the greatest deviation. There is a case of a skimming trajectory, where the straight line motion of the asteroid would miss, but gravity curves the asteroid path into the earth, where it seems that speeding up the asteroid should work.

Some other considerations: How far away the asteroid starts from the earth, and at what speed, compared with escape velocity (11.2 km/s) and orbital velocity for a circular orbit (about 7.6 km/s): If the asteroid is left with less than escape velocity, the asteroid may go into orbit, or may impact the earth at a later time because of the particulars of the changed orbit the asteroid.

Thx!
TomB

so are you saying, speeding up the asteroid might actually work?

And you raise the other elephant in the room, if the asteroid doesn't hit the earth (she wins), it's still out there, ready to be a problem again...

Any other solutions to that, besides let it hit the earth? Or is there a way to hit the earth safely? Or build a parachute for it? or wings to land it like a shuttle?

I don't think she can drill it fast enough or disolve it with her pico-printer-gel (think my version of nano-tech, but smaller)

 

[Eltab]

Flying up to the Really Big Rock and doing a Superman trick sounds like a bit of a cliché. (Let her best friend tell her so.) Let's make her smart and clever as well as tough.

She wants to plant a motor on the asteroid and let THAT push it off collision course. This could be a solar sail (very fragile thing provides very low-G push over a very long time) or a Saturn V moon rocket (tough robust structure provides high-G push over a short time). Either way, she does the math and realizes she must go NOW. Her friends, the parts suppliers, &c all think there's plenty of time no hurry. If she proposes the solar sail and shows the physics but everybody blows her off because they watched Armageddon as kids and now they think a moon rocket full of nukes will do the job, we set up that everybody acknowledges the seriousness of the situation but not the urgency. That allows some people to change their minds and help her out once they think it through.

"Victory" for Our Heroine may be that she breaks up the Really Big Rock into several smaller parts that mere mortals can handle, plus a lot of gravel and fragments that make a very spectacular meteor shower as they burn up on re-entry. This may look too much like that old movie, though...

As the writer you can align everything as you want. The asteroid is arriving from a direction such that, if you push it to one side enough, the Moon's gravity does some more of the work for her. (Hmmm, her computer simulations account for the Moon's gravity but the official simulation doesn't; she finds out the Asteroid is going to hit THIS time, not NEXT time, it crosses Earth's orbit. Must hurry!)

Or … the incoming Really Big Rock is actually a Really Big Iceball (comet). If you can make only one side melt, the natural jets (which normally create the tail and halo) will push it off its original course. The solar sail can perform double duty IF it is in place early enough and can be installed in the right position.

Our Heroine may have to hack NASA's supercomputers along the way, to figure out how to place the sail so all the physics tricks can work together.