Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: thedoc on 16/01/2014 14:38:05
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If you had been riding through space on the asteroid that killed the dinosaurs, would you have been able to jump off it, before it hit the Earth?
Asked by Gavin Francis
Visit the webpage for the podcast in which this question is answered. (http://www.thenakedscientists.com/HTML/podcasts/naked-scientists/show/20131224/)
[chapter podcast=1000582 track=13.12.24/Naked_Scientists_Show_13.12.24_1001803.mp3](https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.thenakedscientists.com%2FHTML%2Ftypo3conf%2Fext%2Fnaksci_podcast%2Fgnome-settings-sound.gif&hash=f2b0d108dc173aeaa367f8db2e2171bd) ...or Listen to the Answer[/chapter] or [download as MP3] (http://nakeddiscovery.com/downloads/split_individual/13.12.24/Naked_Scientists_Show_13.12.24_1001803.mp3)
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Assuming the asteroid was travel at 50KM/s you would have to accelerate to that speed in the reverse direction in the second or so when it reaches the fringes of the atmosphere so that you can deploy your parachute.
To accelerate at such a high rate would be rather stressful !!
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If one plans ahead, then YES.
As one's space ship passes Jupiter, the difference between a fraction of a degree would mean the difference between hitting Earth, and missing Earth. One could even get much closer before jumping off, such as getting as close as the moon.
Aerobraking maneuvers are apparently complex.
Too steep, and one smacks into Earth.
Too shallow and one misses Earth, or bounces off the atmosphere.
Just right, and one can loose the desired velocity, and come in for a soft landing.
Timing might be tough. Would one wish to hit the atmosphere at the same time (but a different place) as a large asteroid or comet? With very precise control, one might be able to do aerobraking + orbital insertion, then wait a while before making the final descent.
The atmosphere impact of the asteroid/comet might create disrupting shock waves, but one may be ok with a simultanous aerobraking maneuver a few thousand miles away.
Is the goal for the comet or asteroid to impact Earth (causing a partial purge of life)? Or to miss earth? There has been some debate about redirecting asteroids. The angle required to change the direction of the comet a few decades, or perhaps a century before hitting Earth would be very small. Or, one could apply constant thrust for a century, and perhaps safely direct the asteroid into any other planet, then hop off and head to Earth.
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Jumping off an asteroid is no big deal as its gravitational pull would be small. But in the absence of any other heavenly bodies your combined center of mass would continue to accelerate earthwards, so in order not to participate in the extinction event, you would have to jump away from the earth at or above escape speed. Whilst this would exonerate you from the evolution of mankind in your own mind, it would however bring forward the date of extinction by accelerating the asteroid earthwards, and incur the wrath of treehuggers.
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Jumping off an asteroid is no big deal as its gravitational pull would be small. But in the absence of any other heavenly bodies your combined center of mass would continue to accelerate earthwards, so in order not to participate in the extinction event, you would have to jump away from the earth at or above escape speed. Whilst this would exonerate you from the evolution of mankind in your own mind, it would however bring forward the date of extinction by accelerating the asteroid earthwards, and incur the wrath of treehuggers.
While a good fantasy, it isn't really true.
The asteroid must arrive at earth's orbit around the sun at the precise date and time.
Push it faster, and it will arrive too soon, and miss earth.
Slow it down, and it will arrive too late and miss earth.
Push it right or left, and it will miss earth.
Would changing the asteroid's mass also affect its trajectory?
One would likely already be in a solar orbit, and traveling at at least the escape velocity for earth. The best way to reach a solar escape velocity would be to do gravity assist flybys (https://en.wikipedia.org/wiki/Gravity_assist) of the major planets, possibly including Earth like the Voyager probe. (https://en.wikipedia.org/wiki/File:Voyager_2_velocity_vs_distance_from_sun.svg)
Also, essentially all of our rockets to date have been chemical rockets. While one might give a slight nudge to the asteroid at takeoff, the majority of the rocket's gain in velocity is from the discharge of gas in space, independent from the asteroid.
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The gravity of a 10km asteroid would be very low. It should be possible for an unassisted human to reach escape velocity away from this asteroid, at 1-2 meters/second.
However, you will still be following the same general path towards the Earth, at some 10-30 km/s.
For a dramatised version of what you might find when you arrive, see: (Full video: 51 minutes. High-speed video: starts around 11:00 minutes)
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While a good fantasy, it isn't really true.
The asteroid must arrive at earth's orbit around the sun at the precise date and time.
I did state "in the absence of other heavenly bodies", which class includes the sun, I believe. You might argue that dinosaurs would have been extinct if the sun was absent, but you might also note that the entire initial proposition was absurd anyway.
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I finally had time to run the numbers (always a mistake to do it after writing an answer!).
Assuming I've done the calculations correctly: it should be almost possible to reach escape velocity from a 10km diameter spherical comet (mostly water), if you had a very light and flexible space suit.
It would be easier if the radius were smaller (much less mass), or if the density were lower (interior open spaces rather than stone or iron composition), or if the comet were already rotating at almost escape velocity. Its also easier for taller people (not the ideal candidates for astronauts).
Calculations (corrections are welcome!):
Density of Water 1000 kg/m^3
Density of asteroid 1 times water
G (Constant) 6.67E-11 Nm^2kg^-2
Radius 5000 m
Volume 5.23599E+11 m^3
Mass 5.23599E+14 kg
Human Mass 70 kg
Human Weight on asteroid 9.78E-02 N
Human Weight 0.01 kg
Escape Velocity 3.74 m/s
Leg force 1372 N
Leg extension 0.6 m
Acceleration 19.6 m/s^2
Duration of jump 0.17 s
Jump Speed 3.4 m/s
Of course, the final result will be similar - your light and flexible spacesuit would run out of air before you got very far from the comet on your record-breaking high-jump. Your corpse would then be flash-vapourised by the impact with Earth.
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Escaping from the asteroid isn't a problem. The trouble is that you are already accelerating towards earth in the earth's gravitational field, so you need to escape from that too.
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To slow down sufficiently to enter the Earths atmosphere at such a speed that you could deploy a parachute you would have to accelerate away from the asteroid at something like 5000g which would be neither practical or healthy.
Also this high acceleration would alter where the asteroid lands which may well lead to litigation.
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Dominic does say in his answer that, although you'd be travelling in an Earth-bound direction and at a velocity of some kilometres per second, if you jumped off far enough from Earth, you'd also have a vector at ninety degrees to the asteroid trajectory, so you could, theoretically time your jump so you'd sail past Earth rather than hit it. How you'd stop again, or avoid disappearing off into outer space, is another matter...!