Destroying asteroids shown to be very difficult

[mfb]

In general Earth is a small target. If you can avoid a predicted impact it is likely that the object won't be a threat for hundreds of years or longer.

 

[TeethWhitener]

Possibly of relevance--some experiments scheduled for 2-4 years from now:
https://en.wikipedia.org/wiki/AIDA_(mission)

 

[LURCH]

To get the object away from Earth permanently you need a much larger trajectory change (~1000 times larger) than a simple impact avoidance maneuver needs. Moving it by a few thousand kilometers vs. moving it by a few million kilometers

I think this may not be true in all instances. I’m hoping somebody will check my reasoning here, but if the deflection is away from the ecliptic, then only two changes, each of equal magnitude, would be required. I’ll describe the plan and see if it meets with reason:

Let me start by observing that earth-crossing asteroids generally have elliptical orbits with eccentricities around 2.5-2.75 or so, and orbital periods of around 2.5-3 years. The only part of this orbit we need to address is the two points at which that ellipse crosses the line of 1AU distance from the Sun.

If a potential impactor is spotted, a slight deflection at an early enough moment will turn a “possible hit” into a “near miss.” On the object’s next approach, probably about three years later, it will miss by a slightly wider margin, and so on for each successive orbit.

If the initial acceleration is at 90° to the ecliptic plane, then the orbit will become progressively more inclined as time goes by. Once the orbit is inclined to a high enough degree, the two points at which the orbit passes inside of the 1AU line will both occur well outside of the ecliptic, at which time a second acceleration, equal and opposite to the first, will stop the continuous change, making the new, highly inclined orbit permanent (more or less), right?

 

[jbriggs444]

If the initial acceleration is at 90° to the ecliptic plane, then the orbit will become progressively more inclined as time goes by.

What effect would be responsible for increasing the tilt of an elliptical orbit over time?

If such an effect existed, one would expect all of the planets to be orbiting at 90 degrees relative to Jupiter.

 

[LURCH]

What effect would be responsible for increasing the tilt of an elliptical orbit over time?

If such an effect existed, one would expect all of the planets to be orbiting at 90 degrees relative to Jupiter.

Thank you @jbriggs444, that’s exactly the sort of double-checking I was hoping to get. If the tilt were started with a push, would it not continue until another force stopped it? Or would it require continuous thrust to keep going.? My impression is that, once the motion is begun, it will continue until some force makes it cease.

 

[mfb]

If a potential impactor is spotted, a slight deflection at an early enough moment will turn a “possible hit” into a “near miss.” On the object’s next approach, probably about three years later, it will miss by a slightly wider margin, and so on for each successive orbit.

Why would the closest approach follow such a pattern? Most likely it will jump around wildly.

Thank you @jbriggs444, that’s exactly the sort of double-checking I was hoping to get. If the tilt were started with a push, would it not continue until another force stopped it? Or would it require continuous thrust to keep going.? My impression is that, once the motion is begun, it will continue until some force makes it cease.

Orbits are closed (neglecting three-body interactions and general relativity). A simple push just changes the orientation of the orbit a bit but then it orbits stably in this new orientation.

 

[sophiecentaur]

What effect would be responsible for increasing the tilt of an elliptical orbit over time?

I was wondering about that too. The orbital period would change a bit but that's all I can imagine happening. If the orbital plane were tilted away from that of the Earth's and then the eccentricity were increased, you could permanently remove the object from danger. But I think that (as with most useful manoeuvres) would require two 'burns'.

 

[jbriggs444]

If the tilt were started with a push, would it not continue until another force stopped it?

The effect of a force that stops is a change in the orbit -- to a new stable elliptical orbit.

 

[jbriggs444]

But I think that (as with most useful manoeuvres) would require two 'burns'.

A single burn is adequate. A pair of distinct elliptical orbits about the same primary can intersect in at most two points. With a single burn you can tilt one orbit so that its position near the one intersection point rises up out of the plane and its position near the other intersection point is depressed down out of the plane.

I believe that it is even easier than that. A random burn applied at a random time will, with probability 1, result in orbits that do not intersect.

This is in theory -- treating the two orbits as separate two-body solutions. In practice, the solar system is a many body system. There is no such thing as a stable orbit and almost everything you can do is temporary. Also, the probability 1 thing applies for point-like satellites. Real planets and asteroids have non-zero cross-sections.

 

[sophiecentaur]

With a single burn you can tilt one orbit so that its position near the one intersection point rises up out of the plane and its position near the other intersection point is depressed down out of the plane.

I can almost picture that in my mind. The ellipse is narrower than the circle where the planes coincide?

 

[mfb]

Or wider. Or just not aligned with Earth. Here is a sketch - while that object doesn't intersect Earth's orbit you can see how it would intersect an orbit somewhere between Earth and Mars - but only once. The other intersection with the plane of the planets is much farther away from the Sun.

Another 3D sketch

A different 2 D sketch but the color code indicates where the asteroid is "above"/"below" the plane of the planets.

 

[sophiecentaur]

The other intersection with the plane of the planets is much farther away from the Sun.

You will have to help me with this one. Doesn't the major axis of the ellipse pass through the Sun - so why isn't there symmetry about that axis? Is it the effect of other bodies?

 

[jbriggs444]

You will have to help me with this one. Doesn't the major axis of the ellipse pass through the Sun - so why isn't there symmetry about that axis? Is it the effect of other bodies?

There is no reason for the line that is the intersection of the orbital planes to align with the major axis of either ellipse.

 

[sophiecentaur]

Of course. . . . Tilt. Durrrr

 

[LURCH]

@mrb; thanks for the images, they make the concept much more clear. Also thanks @jbriggs444 for pointing out that changing the inclination takes only one acceleration, and not two. I now remember learning that, many years ago, and having difficulty accepting it. It was in relation to artificial satellites, and I couldn’t see how a vehicle in space could move to a new orbit and be expected to stop without executing a burn once it reached that new orbit. Now it seems obvious. Live and learn, I guess.

I believe this sort of inclination change used to be called an “orbital plane adjustment”, or something similar, and it was quite problematic. I’m off to search for what those problems were, because I can’t remember.

 

[mfb]

Inclination changes are routinely done for geostationary satellites. They need zero inclination but there is no launch site right at the equator. Kourou (Ariane/European Soyuz) is the closest one at 5 degree N. The rockets launch them into an orbit with the lowest inclination available from the launch site, afterwards they change their inclination with their own propulsion. They also need to raise their perigee, as nearly all satellites are released in an elliptic orbit. With chemical rockets that can be a single burn, with electric propulsion they do it slowly with continuous thrust over months.