Le sept./6/2018 Ã* 06:49, Jeff Findley a écritÂ*:
In article ,
ess says...

On 6/09/2018 11:37 AM, Alain Fournier wrote:

A small nudge a long way out can be enough to direct it towards the
Earth. But after the aerobraking, you don't have that option. You need
to raise its perigee quite a lot.

But you would probably want to nudge it millions of kilometres for it to
go towards Earth. You only need to raise perigee a few kilometres per
orbit.

Yes, you do have to know what you are doing. And make sure that you can
raise the perigee. But in most cases, raising the perigee should be
easier than sending it to Earth's atmosphere, maybe not all cases, but
most cases. And those who would do this are most likely people who
understand the difficulty of the task and the risks. You don't send an
asteroid towards Earth without understanding orbital mechanics and
rocketry.


Alain Fournier

That's really not how orbital mechanics work. It's not distances that
are a problem, but velocities. A small change in velocity for an object
a long way out can translate into a large change in distance by the time
the object arrives in the vicinity of Earth.

By contrast, raising the perigee requires a significant change in
velocity, and there's no getting around that. For a massive object, that
implies a correspondingly large rocket.

Putting a large rocket into space is difficult and expensive.

Sylvia is right. That's why this issue was mentioned early on in the
thread. Starting aerobraking is a lot easier, in terms of delta-V, than
raising the perigee such that you're no longer aerobraking. If you
can't raise the perigee fast enough, the orbit will decay turning your
asteroid into a meteorite.

The low thrust engine(s) originally used to nudge the asteroid onto an
intercept course with the earth's atmosphere would likely be woefully
undersized for the task. For example, you could use solar electric
propulsion to nudge the asteroid's orbit over many months or years to
get it on an intercept course. But when trying to raise the perigee,
you need orders of magnitude more thrust so you can perform the perigee
raising maneuver in much less time (i.e. a fraction of an orbit of
earth).

Raising the perigee in Earth orbit a few kilometres is much easier than
raising the perigee in Sun orbit by a few million kilometres (especially
that here, for Earth orbit, we are talking about a highly elliptical
orbit). And if you are going to make a plane change to move a few
million kilometres instead of raising perigee it isn't easier. It is
kind of true that you can use highly efficient low thrust engines to
make easier the change in Sun orbit. But keep in mind that ion engines
are fired for long periods of time to move spacecrafts weighing a few
tons. Are you going to fire an ion engine for centuries to move an asteroid?

Once again, it is possible that one would find an interesting asteroid
that would need only a very small push to do an Earth aerobraking
manoeuvre, it just isn't bloody likely. So if you plan on capturing an
asteroid, be prepared to give it some sizeable delta-V.

This is why I, only half jokingly, said that dropping Kuiper Belt
Objects directly onto Mars would be easier and safer.

I would assume that if something goes wrong while you send the KBO to
Mars, and it falls 100 km off its target, the consequences would be less
severe than if an asteroid intended for Earth aerocapture goes 100 km
too low into the atmosphere (lithosphere). So yes, I too would consider
it easier and safer to drop stuff on Mars.


Alain Fournier