andy-nimmo wrote:
> Whether or not a NEA may collide with us is a matter of the
relative trajectories of its orbit and ours.
> The amount of delta V required to reach and return from an
asteroid is a matter of relative velocity change required.
> Accordingly, the fact that an asteroid may or may not have
similar orbital trajectories to Earth does not mean it needs less
delta V than one further away.

Quite the contrary: Its orbit is very like ours (definition of NEA).
Similar mean distance from the Sun necessarily means that its
velocity around the Sun is similar to ours around the Sun. Hence,
low Delta-V requirement.

> The fact that any particular NEA might hit us does not mean it
necessarily needs a low delta V to reach it.

The 2 are interconnected -one factor depends on another. If it
didn't have an orbit very similar to ours (which would make it less
of a threat) then it would have a larger velocity difference (which
would make it a poor prospect for mining).

The other class of threatening asteroids, the Earth Crossers,
are not such good prospects. The fact that they have more
elliptical orbits, and that they go farther out from the Sun, means
that when they are in closer (and nearer to us) they are moving at
their fastest (Back to Kepler: when an elliptically orbiting body is
closest to its primary, it moves faster). Incidently, this also
means that it would hit Earth's atmosphere with higher velocity,
thus less likely to survive aeroentry (this doesn't apply to the big
ones, though, which makes these Earth crosser elliptical orbit
asteroids very dangerous).

It has been suggested that since many of these go out to 2 or 3
AU, and are sweeping through the main belt, it would be helpful
to hitch a ride on one out to the main belt.
This does not follow. While they are close to us, they are moving
fast, so we'd need a lot of delta-V to match them. If you've got the
delta-V to do this, you can get out to the belt on your own.
Similarly, if you did ride one out to the belt, you would be moving
at the same speed as your taxi: too slow for that orbital distance.
You would fall back in if you didn't expend propellants to
circularise at that distance from the Sun.
The only possible help is that they could supply volatiles to the
ship during the trip out -either for life support or for refueling.
In such a case, it doesn't make sense to go out to the belt, since
your taxi has what you need -unless you were going to the belt
anyway, and you had the rockets to do the required velocity
changes, but for some reason needed to resupply on the way.

Another option is for later.
EM rails could be attached to the taxi, so that a properly
equipped ship could engage these rails, to get boosted to the
asteroid's speed as it swept past. Similarly, the rails could shoot
you off the asteroid taxi with the required speed to let you stay out
there. Tethers could also do the same thing.
In this case, you're adopting the 'Cycling Station" concept.
Entirely likely, and useful, if the needed EM rail or tether
capability exists.
Note that this follows along with Moravec's concept for rotating
tether momentum exchange stations throughout the solar
system. Sheffield & Clarke also used this in fiction.

>> Al Globus wrote:
>>> A lot of asteroids are found these days because of concerns
about a collision with earth. I haven't checked the data for
awhile, but I'm sure many asteroids with very low delta-v have
been found.
>>
>> John F. wrote:
>>... The Earth-crossers include many of those with an elliptical
orbit, some of which take them out to 2.5AU+.
>>The term NEA is more specific to those which are not so
elliptical, and spend more of their time very near 1AU.
>> The very same fact that they have low delta-V requirements is
what makes them so dangerous: They would enter our
atmosphere with low relative velocity, and they would not build up
a tremendous pressure wave of super-heated air. The higher the
pressure of this bow-wave, the more likely that it will exceed the
crush strength of the body, thus a lower velocity means it's more
likely to hit the ground!

Hi John,

You say, "Quite the contrary: Its orbit is very like ours (definition of
NEA). Similar mean distance from the Sun necessarily means that its
velocity around the Sun is similar to ours around the Sun. Hence, low
Delta-V requirement." This is simply untrue. For its velocity to be
similar to ours in a similar orbit it would have to have similar mass to
us, and none of these do. Accordingly, there will be major velocity
differences between any such object and us. The delta V required to
match velocities will be relatively high.

John Frazer wrote:

> andy-nimmo wrote:
> > Whether or not a NEA may collide with us is a matter of the
> relative trajectories of its orbit and ours.
> > The amount of delta V required to reach and return from an
> asteroid is a matter of relative velocity change required.
> > Accordingly, the fact that an asteroid may or may not have
> similar orbital trajectories to Earth does not mean it needs less
> delta V than one further away.
>
> Quite the contrary: Its orbit is very like ours (definition of NEA).
> Similar mean distance from the Sun necessarily means that its
> velocity around the Sun is similar to ours around the Sun. Hence,
> low Delta-V requirement.
>
> > The fact that any particular NEA might hit us does not mean it
> necessarily needs a low delta V to reach it.
>
> The 2 are interconnected -one factor depends on another. If it
> didn't have an orbit very similar to ours (which would make it less
> of a threat) then it would have a larger velocity difference (which
> would make it a poor prospect for mining).
>
> The other class of threatening asteroids, the Earth Crossers,
> are not such good prospects. The fact that they have more
> elliptical orbits, and that they go farther out from the Sun, means
> that when they are in closer (and nearer to us) they are moving at
> their fastest (Back to Kepler: when an elliptically orbiting body is
> closest to its primary, it moves faster). Incidently, this also
> means that it would hit Earth's atmosphere with higher velocity,
> thus less likely to survive aeroentry (this doesn't apply to the big
> ones, though, which makes these Earth crosser elliptical orbit
> asteroids very dangerous).
>
> It has been suggested that since many of these go out to 2 or 3
> AU, and are sweeping through the main belt, it would be helpful
> to hitch a ride on one out to the main belt.
> This does not follow. While they are close to us, they are moving
> fast, so we'd need a lot of delta-V to match them. If you've got the
> delta-V to do this, you can get out to the belt on your own.
> Similarly, if you did ride one out to the belt, you would be moving
> at the same speed as your taxi: too slow for that orbital distance.
> You would fall back in if you didn't expend propellants to
> circularise at that distance from the Sun.
> The only possible help is that they could supply volatiles to the
> ship during the trip out -either for life support or for refueling.
> In such a case, it doesn't make sense to go out to the belt, since
> your taxi has what you need -unless you were going to the belt
> anyway, and you had the rockets to do the required velocity
> changes, but for some reason needed to resupply on the way.
>
> Another option is for later.
> EM rails could be attached to the taxi, so that a properly
> equipped ship could engage these rails, to get boosted to the
> asteroid's speed as it swept past. Similarly, the rails could shoot
> you off the asteroid taxi with the required speed to let you stay out
> there. Tethers could also do the same thing.
> In this case, you're adopting the 'Cycling Station" concept.
> Entirely likely, and useful, if the needed EM rail or tether
> capability exists.
> Note that this follows along with Moravec's concept for rotating
> tether momentum exchange stations throughout the solar
> system. Sheffield & Clarke also used this in fiction.
>
> >> Al Globus wrote:
> >>> A lot of asteroids are found these days because of concerns
> about a collision with earth. I haven't checked the data for
> awhile, but I'm sure many asteroids with very low delta-v have
> been found.
> >>
> >> John F. wrote:
> >>... The Earth-crossers include many of those with an elliptical
> orbit, some of which take them out to 2.5AU+.
> >>The term NEA is more specific to those which are not so
> elliptical, and spend more of their time very near 1AU.
> >> The very same fact that they have low delta-V requirements is
> what makes them so dangerous: They would enter our
> atmosphere with low relative velocity, and they would not build up
> a tremendous pressure wave of super-heated air. The higher the
> pressure of this bow-wave, the more likely that it will exceed the
> crush strength of the body, thus a lower velocity means it's more
> likely to hit the ground!
>
[www.newaydirect.com]

andy-nimmo wrote:

> Hi John,
>
> You say, "Quite the contrary: Its orbit is very like ours (definition
> of NEA). Similar mean distance from the Sun necessarily means that its
> velocity around the Sun is similar to ours around the Sun. Hence, low
> Delta-V requirement." This is simply untrue. For its velocity to be
> similar to ours in a similar orbit it would have to have similar mass
> to us, and none of these do.

What matters is the ratio between the mass of the Sun and the object
orbiting about it. If the masses are reasonably similar they each orbit
about.in between them. As long as the sun's mass is sufficiently
dominant, the satellite effectively orbits around the center of the sun
regardless of its mass.

The equation is: GmM/r^2. So if m <<<< M variations in m don't matter
much.

> --

Al Globus
aglobus@..., (650) 604-4404
http://www.nas.nasa.gov/~globus/home.html

The dinosaurs weren't spacefaring. We are. I don't think that's an
accident.
Maybe we are life's taxi to the stars.

I think we should:

1. Devote half of NASA's budget ($7 billion) to reaching NASA's 2020
goal of
reducing launch costs to Low-Earth-Orbit to $220/kg with a 0.01% failure
rate.
This should enable space tourism. The resulting orbital hotels will need
to
develop efficient orbital life support and other necessary technologies.

2. Build orbital space colonies. The materials in the largest asteroid
are
sufficient for orbital colonies with a combined surface area about 500
times
greater than Earth's. Eros alone could make over ten thousand space
colonies,
each with about about 10 square kilometers of 1g living area.

3. After a few generations of orbital living, people won't need their
colony
to be near Sol. Then small groups of colonies with populations in the
tens-of-thousands can set out on multi-decade journeys to nearby stars.

Except the launch goals, none of this is even a little bit official.

--- In spacesettlers@y..., andy-nimmo wrote:
> Hi John,
>
> You say, "Quite the contrary: Its orbit is very like ours
(definition of
> NEA). Similar mean distance from the Sun necessarily means that its
> velocity around the Sun is similar to ours around the Sun. Hence,
low
> Delta-V requirement." This is simply untrue. For its velocity to be
> similar to ours in a similar orbit it would have to have similar
mass to
> us, and none of these do.

Not so. The sun is so massive that any tug on it produced by an
earth-sized object or smaller is negligible. Any object in a very
similar orbit to the earth's (in both eccentricity and mean radius)
will be moving at a similar speed. There should be trojan asteroids
in the earth-sun L4 and L5 libration orbits whose delta-vee from the
top of the earth-moon gravity well is nearly zero.

:) ed

> Accordingly, there will be major velocity
> differences between any such object and us. The delta V required to
> match velocities will be relatively high.
>
> John Frazer wrote:
>
> > andy-nimmo wrote:
> > > Whether or not a NEA may collide with us is a matter of the
> > relative trajectories of its orbit and ours.
> > > The amount of delta V required to reach and return from an
> > asteroid is a matter of relative velocity change required.
> > > Accordingly, the fact that an asteroid may or may not have
> > similar orbital trajectories to Earth does not mean it needs less
> > delta V than one further away.
> >
> > Quite the contrary: Its orbit is very like ours (definition of
NEA).
> > Similar mean distance from the Sun necessarily means that its
> > velocity around the Sun is similar to ours around the Sun. Hence,
> > low Delta-V requirement.
> >
> > > The fact that any particular NEA might hit us does not mean it
> > necessarily needs a low delta V to reach it.
> >
> > The 2 are interconnected -one factor depends on another. If it
> > didn't have an orbit very similar to ours (which would make it
less
> > of a threat) then it would have a larger velocity difference
(which
> > would make it a poor prospect for mining).
> >
> > The other class of threatening asteroids, the Earth Crossers,
> > are not such good prospects. The fact that they have more
> > elliptical orbits, and that they go farther out from the Sun,
means
> > that when they are in closer (and nearer to us) they are moving at
> > their fastest (Back to Kepler: when an elliptically orbiting body
is
> > closest to its primary, it moves faster). Incidently, this also
> > means that it would hit Earth's atmosphere with higher velocity,
> > thus less likely to survive aeroentry (this doesn't apply to the
big
> > ones, though, which makes these Earth crosser elliptical orbit
> > asteroids very dangerous).
> >
> > It has been suggested that since many of these go out to 2 or 3
> > AU, and are sweeping through the main belt, it would be helpful
> > to hitch a ride on one out to the main belt.
> > This does not follow. While they are close to us, they are moving
> > fast, so we'd need a lot of delta-V to match them. If you've got
the
> > delta-V to do this, you can get out to the belt on your own.
> > Similarly, if you did ride one out to the belt, you would be
moving
> > at the same speed as your taxi: too slow for that orbital
distance.
> > You would fall back in if you didn't expend propellants to
> > circularise at that distance from the Sun.
> > The only possible help is that they could supply volatiles to the
> > ship during the trip out -either for life support or for
refueling.
> > In such a case, it doesn't make sense to go out to the belt, since
> > your taxi has what you need -unless you were going to the belt
> > anyway, and you had the rockets to do the required velocity
> > changes, but for some reason needed to resupply on the way.
> >
> > Another option is for later.
> > EM rails could be attached to the taxi, so that a properly
> > equipped ship could engage these rails, to get boosted to the
> > asteroid's speed as it swept past. Similarly, the rails could
shoot
> > you off the asteroid taxi with the required speed to let you stay
out
> > there. Tethers could also do the same thing.
> > In this case, you're adopting the 'Cycling Station" concept.
> > Entirely likely, and useful, if the needed EM rail or tether
> > capability exists.
> > Note that this follows along with Moravec's concept for rotating
> > tether momentum exchange stations throughout the solar
> > system. Sheffield & Clarke also used this in fiction.
> >
> > >> Al Globus wrote:
> > >>> A lot of asteroids are found these days because of concerns
> > about a collision with earth. I haven't checked the data for
> > awhile, but I'm sure many asteroids with very low delta-v have
> > been found.
> > >>
> > >> John F. wrote:
> > >>... The Earth-crossers include many of those with an elliptical
> > orbit, some of which take them out to 2.5AU+.
> > >>The term NEA is more specific to those which are not so
> > elliptical, and spend more of their time very near 1AU.
> > >> The very same fact that they have low delta-V requirements is
> > what makes them so dangerous: They would enter our
> > atmosphere with low relative velocity, and they would not build up
> > a tremendous pressure wave of super-heated air. The higher the
> > pressure of this bow-wave, the more likely that it will exceed the
> > crush strength of the body, thus a lower velocity means it's more
> > likely to hit the ground!
> >
> [www.newaydirect.com]
>
Service.

Hi Al,

No argument re your physics, but a major one with your interpretation of
the result. If Earth's mass is as domininant re the asteroid's mass as
the Sun's is to ours, then as far as we humans' rocket engineering and
fuel are concerned the velocity differences will indeed amount to a high
delta V - even if for general astronomical puposes there may seem little
difference.

Best wishes, Andy.

Al Globus wrote:

>
> andy-nimmo wrote:
>
> > Hi John,
> >
> > You say, "Quite the contrary: Its orbit is very like ours
> (definition
> > of NEA). Similar mean distance from the Sun necessarily means that
> its
> > velocity around the Sun is similar to ours around the Sun. Hence,
> low
> > Delta-V requirement." This is simply untrue. For its velocity to be
> > similar to ours in a similar orbit it would have to have similar
> mass
> > to us, and none of these do.
>
> What matters is the ratio between the mass of the Sun and the object
> orbiting about it. If the masses are reasonably similar they each
> orbit
> about.in between them. As long as the sun's mass is sufficiently
> dominant, the satellite effectively orbits around the center of the
> sun
> regardless of its mass.
>
> The equation is: GmM/r^2. So if m <<<< M variations in m don't
> matter
> much.
>
> > --
>
> Al Globus
> aglobus@..., (650) 604-4404
> http://www.nas.nasa.gov/~globus/home.html
>
> The dinosaurs weren't spacefaring. We are. I don't think that's an
> accident.
> Maybe we are life's taxi to the stars.
>
> I think we should:
>
> 1. Devote half of NASA's budget ($7 billion) to reaching NASA's 2020
> goal of
> reducing launch costs to Low-Earth-Orbit to $220/kg with a 0.01%
> failure
> rate.
> This should enable space tourism. The resulting orbital hotels will
> need
> to
> develop efficient orbital life support and other necessary
> technologies.
>
> 2. Build orbital space colonies. The materials in the largest asteroid
>
> are
> sufficient for orbital colonies with a combined surface area about 500
>
> times
> greater than Earth's. Eros alone could make over ten thousand space
> colonies,
> each with about about 10 square kilometers of 1g living area.
>
> 3. After a few generations of orbital living, people won't need their
> colony
> to be near Sol. Then small groups of colonies with populations in the
> tens-of-thousands can set out on multi-decade journeys to nearby
> stars.
>
> Except the launch goals, none of this is even a little bit official.
>
[www.newaydirect.com]

Are you refereing to the dV required to get off this rock?

Because if you are then it is also a problem for the moon and anywhere else you
plan to go, once your in HEO your pretty much right next door in terms of dV.

--- andy-nimmo wrote:

Hi Ryan,

So far as I am aware, while there do appear to be literally thousands of
asteroids of various sizes in similar orbit to ours, only 3 of those
that have been found so far, need less delta V to get there and get
back, than our Moon does. This is due not so much to differences in
orbit as differences in orbital velocities. Indeed, some folk have tried
to use this as an argument for forgetting asteroids and going to Mars,
failing to realize that there are indeed many asteroids that need less
delta V to get to than even the Martian moons, let alone Mars itself.

Best wishes, Andy.

Ryan Healey wrote:

> Are you refereing to the dV required to get off this rock?
>
> Because if you are then it is also a problem for the moon and anywhere
> else you
> plan to go, once your in HEO your pretty much right next door in terms
> of dV.
>
> --- andy-nimmo wrote:
> > Hi Al,
> >
> > No argument re your physics, but a major one with your
> interpretation of
> > the result. If Earth's mass is as domininant re the asteroid's mass
> as
> > the Sun's is to ours, then as far as we humans' rocket engineering
> and
> > fuel are concerned the velocity differences will indeed amount to a
> high
> > delta V - even if for general astronomical puposes there may seem
> little
> > difference.
> >
> > Best wishes, Andy.
> >
> > Al Globus wrote:
> >
> > > andy-nimmo wrote:
> > >
> > > > Hi John,
> > > >
> > > > You say, "Quite the contrary: Its orbit is very like ours
> > > (definition
> > > > of NEA). Similar mean distance from the Sun necessarily means
> that
> > > its
> > > > velocity around the Sun is similar to ours around the Sun.
> Hence,
> > > low
> > > > Delta-V requirement." This is simply untrue. For its velocity to
> be
> > > > similar to ours in a similar orbit it would have to have similar
>
> > > mass
> > > > to us, and none of these do.
> > >
> > > What matters is the ratio between the mass of the Sun and the
> object
> > > orbiting about it. If the masses are reasonably similar they each
>
> > > orbit
> > > about.in between them. As long as the sun's mass is sufficiently
> > > dominant, the satellite effectively orbits around the center of
> the
> > > sun
> > > regardless of its mass.
> > >
> > > The equation is: GmM/r^2. So if m <<<< M variations in m don't
> > > matter
> > > much.
> > >
> > > > --
> > >
> > > Al Globus
> > > aglobus@..., (650) 604-4404
> > > http://www.nas.nasa.gov/~globus/home.html
> > >
> > > The dinosaurs weren't spacefaring. We are. I don't think that's an
>
> > > accident.
> > > Maybe we are life's taxi to the stars.
> > >
> > > I think we should:
> > >
> > > 1. Devote half of NASA's budget ($7 billion) to reaching NASA's
> 2020
> > > goal of
> > > reducing launch costs to Low-Earth-Orbit to $220/kg with a 0.01%
> > > failure
> > > rate.
> > > This should enable space tourism. The resulting orbital hotels
> will
> > > need
> > > to
> > > develop efficient orbital life support and other necessary
> > > technologies.
> > >
> > > 2. Build orbital space colonies. The materials in the largest
> asteroid
> > >
> > > are
> > > sufficient for orbital colonies with a combined surface area about
> 500
> > >
> > > times
> > > greater than Earth's. Eros alone could make over ten thousand
> space
> > > colonies,
> > > each with about about 10 square kilometers of 1g living area.
> > >
> > > 3. After a few generations of orbital living, people won't need
> their
> > > colony
> > > to be near Sol. Then small groups of colonies with populations in
> the
> > > tens-of-thousands can set out on multi-decade journeys to nearby
> > > stars.
> > >
> > > Except the launch goals, none of this is even a little bit
> official.
> > >
> > [www.newaydirect.com]
> >
> Service.
> >
[www.debticated.com]

From: andy-nimmo
To:
Sent: Saturday, March 31, 2001 9:00 AM
Subject: Re: [spacesettlers] NEA trajectory / relative velocity

> Hi Al,
>

Hi Al,

> No argument re your physics, but a major one with your interpretation of
> the result. If Earth's mass is as domininant re the asteroid's mass as
> the Sun's is to ours, then as far as we humans' rocket engineering and
> fuel are concerned the velocity differences will indeed amount to a high
> delta V - even if for general astronomical puposes there may seem little
> difference.
>

Sorry, Andy, but it seems that you're assuming results given by intuition
rather than the ones that are given by calculation. The center of mass of
the Earth-Sun system is only 449 Km away from the mass center of the Sun.
(For an object more than a *gigameter* in diameter, that basically means
that the mass center is the center of the Sun. Even for an intuitive guess,
I would assume that that is evidence enough that both Earth and asteroids
have negligible mass relatively to the sun for both astronomical *and*
delta-V purposes. But since you don't agree with this, let carry the
calculations to the end.)

Making a lot of calculations to get the translation velocity of Earth around
the Earth-Sun center of mass, you get the result 29821.6477 m/s (I'm using a
lot of decimals because we will need them to see that the difference is too
small). Now, lets do the same thing for an asteroid 1 Km in diameter
weighting a trillion kilograms (that is, a density of about 2000 Kg/m^3)
circling the Sun at the same distance. The mass center of the asteroid/Sun
system would be *so* close to the center of mass of Sun itself that my
calculator does not have enough precision to make it, so I'll assume that
the center is coincident with the Sun's mass center. Well, doing again all
the calculations, you see that your asteroid would be circling the Sun at
the speed of... 29821.69233 m/s.

That is, the difference of delta-v that you can get due to mass differences,
even if such differences are *huge* as in the case of Earth and an asteroid,
are in the order of a few *centimeters* per second. That is probably well
below even the error in measuring/calculating speed for a very reliable
spacecraft, and it is a delta-v that has less meaning in technical terms
than in astronomical ones.

So, we once again prove Frazer's point, that a orbit closely matching
Earth's orbit *has to* have low delta-v relatively to us. Probably because
of that, John Lewis estimates, in his article in the third edition of "The
High Frontier", that a quarter of the NEAs - that is, hundreds to thousands
of asteroids - are easier to reach (in terms of fuel consumption) than
Moon... And he wasn't even counting the huge difference in lifting something
from the lunar surface and from an asteroid surface at the point, if I
remember correctly.

> Best wishes, Andy.
[snikt]

Best wishes, Lucio.