I'm assuming that's one of the things that NASA engineers are calculating for. But if it doesn't come close enough to any other massive objects to affect its orbit (meaning that changing its orbit won't negate those effects and cause changes that weren't planned for), don't you still have to consider the orbit itself?
In other words, if you make a change to the object's path on the shortest end of its orbit, does that not have a completely different effect than if you make the change at the longest point?
I'm guessing it would, but I don't know... that's why I'm asking.
And I realize we're talking about pretty small changes here, relative to the massive scale of the system. But the amount of change we're looking for is also only about 400 meters.
asteroid strike 100% likely, but... (warning - physics post)
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[xeno]Julios
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Good question - i figure that there are two possibilities:R00k wrote:I'm assuming that's one of the things that NASA engineers are calculating for. But if it doesn't come close enough to any other massive objects to affect its orbit (meaning that changing its orbit won't negate those effects and cause changes that weren't planned for), don't you still have to consider the orbit itself?
1) the orbit is so fucking large that even at the timescale of decades you can treat it as a straight line.
2) curved motion or straight motion, it may not matter - necessary deflection may be the same.
It's clear from the calculations they used in their paper that they were generalizing across all asteroids, so either they assume a straight path, or 2) is correct.
ah, I should clear something up - apophis, yes - that's a 400m keyhole thing, but the nature paper in question, which is co-authored by the Nasa astronaut (i quoted some of the actual paper on page 3) is discussing general impact diversion, not just apophis.And I realize we're talking about pretty small changes here, relative to the massive scale of the system. But the amount of change we're looking for is also only about 400 meters.
Nevertheless, to address your point:
What do you mean by longest and shortest point here? You may be onto something interesting here, but i'm trying to grasp what you mean.In other words, if you make a change to the object's path on the shortest end of its orbit, does that not have a completely different effect than if you make the change at the longest point?
Can you elaborate?
In elliptical orbits, the central body (the sun in this case) is usually at one end of the ellipse. Therefore, as the satellite is heading back toward that focal point of the ellipse, it is constantly accelerating until it passes the the central body. Conversely, when the satellite is moving the other direction as it returns, it is constantly decelerating until it reaches its farthest point and begins to return. (I say accelerate and decelerate meaning in relative position to the sun).
So, if you were to apply a force to the satellite when it is furthest away from the sun and moving slowly, would that not have a different effect than if you applied the force when the object is closest to the sun and moving at its highest velocity? You'd have to take into account the direction of the force applied as well, because if it were closer to the central object, you would need a greater force in order to overcome the stronger pull of gravity that comes with proximity.
So, if you were to apply a force to the satellite when it is furthest away from the sun and moving slowly, would that not have a different effect than if you applied the force when the object is closest to the sun and moving at its highest velocity? You'd have to take into account the direction of the force applied as well, because if it were closer to the central object, you would need a greater force in order to overcome the stronger pull of gravity that comes with proximity.
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[xeno]Julios
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ah - interesting.
One way of asking the question is this:
Imagine you had two "central" bodies on each end of a very long elipse.
Now imagine you applied a very large instantanous force orthogonal to the instantaneous direction of the satellite (tangent to the curve at that point). The question is: would that same force deviate the path by the same amount if you applied this force at different points along the ellipse.
That's a really interesting question, and my intuitions go both ways:
Perhaps at the tight end, there would be less deflection, since you're working against an active gravitational pull (the thing responsible for the slingshot at either end).
On the other hand, perhaps it all cancels out in the end somehow, and deviation is proportional to applied force by the same amount no matter where in the path you apply it. While it is true that the velocity changes during an elliptical orbit, and thus a given force will perturb the satellite less than during slower parts of the path, perhaps those high velocity areas are somehow more sensitive, in the sense that small pertubations in high speed areas end up changing the overall path by a larger amount.
Keep in mind the timescales here though - they're talking about tugging for a whole year, 20 years before impact, so during those "straights" the satellite might be treatable as one moving along a straight line.
That reference (4) which I quoted may give insight into this question.
One way of asking the question is this:
Imagine you had two "central" bodies on each end of a very long elipse.
Now imagine you applied a very large instantanous force orthogonal to the instantaneous direction of the satellite (tangent to the curve at that point). The question is: would that same force deviate the path by the same amount if you applied this force at different points along the ellipse.
That's a really interesting question, and my intuitions go both ways:
Perhaps at the tight end, there would be less deflection, since you're working against an active gravitational pull (the thing responsible for the slingshot at either end).
On the other hand, perhaps it all cancels out in the end somehow, and deviation is proportional to applied force by the same amount no matter where in the path you apply it. While it is true that the velocity changes during an elliptical orbit, and thus a given force will perturb the satellite less than during slower parts of the path, perhaps those high velocity areas are somehow more sensitive, in the sense that small pertubations in high speed areas end up changing the overall path by a larger amount.
Keep in mind the timescales here though - they're talking about tugging for a whole year, 20 years before impact, so during those "straights" the satellite might be treatable as one moving along a straight line.
That reference (4) which I quoted may give insight into this question.
The mean change in velocity required to deflect an asteroid from an Earth impact trajectory is about 3.5x10^-2/t m/s , where t is the lead time in years(4). So a 20-tonne gravitational tractor hovering for one year can deflect a typical asteroid of about 200m diameter given a lead time of roughly 20 years.
...
4.Chesley, S. R. & Spahr, T. B. in Mitigation of Hazardous Comets and Asteroids(eds Belton, M. J. S.et al.)22–37 (Cambridge Univ. Press, Cambridge, 2004).
Yes, but as I mentioned earlier, the asteroid's orbit is 323 days. So if the tractor were applied for a full year, it would be working at all points of the orbit at least once. Which means that the position/direction of the tractor at any given point along the ellipse may be very important.
If it turns out that it is important, then - as menkent said - it would be a logistical nightmare.
If it turns out that it is important, then - as menkent said - it would be a logistical nightmare.
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[xeno]Julios
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[xeno]Julios
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If it leaps out at me, I can't imagine the NASA guys wouldn't have taken it into account. Maybe it's negligible or irrelevant.
It's interesting that they use a general formula for something like this though, and not something that takes into account the specifics of the object's orbit.
But what do I know, I've never worked for NASA, or even studied space or aeronautics.
It's interesting that they use a general formula for something like this though, and not something that takes into account the specifics of the object's orbit.
But what do I know, I've never worked for NASA, or even studied space or aeronautics.