Gravity assist to Mars by retrograde comets?

I'm thinking in regards to shortening the travel time for a manned
Mars mission. There is a nice article here on gravity assist or the
gravitational slingshot effect:

Gravity assist.
http://en.wikipedia.org/wiki/Gravity_assist#Explanation

This show the greatest effect is when the spacecraft is traveling in
an opposite direction to the gravitating body. You get twice the
velocity of the body added to the spacecraft's velocity, both measured
with respect to the Sun.
Then this could be especially useful if a retrograde comet near its
perihelion is rendezvoused by the spacecraft. You would make the
rendezvous when the comet is near Earth's orbit to cut the travel time
to the comet. If we can get an initial velocity off the Earth of say
30 km/sec, and added to the Earth's orbital velocity of 30 km/sec,
this would result in a tangential velocity of 60 km/sec.
The problem of just using this tangential velocity to get to Mars is
that it turns out the increased distance of the tangential direction
to intersect Mars orbit over just the radial direction cancels out the
improvement of the increased speed. And even traveling at an optimal
angle only shortens the travel time slightly.(*)
However, when a comet is close to the Earth's orbit it will have an
orbital velocity close to that of the Earth, about 30 km/sec. Then
when the slingshot effect is applied to the spacecraft on close flyby
of the comet, its speed will be increased from 60 km/sec to 60 +
2*(30) = 120 km/sec. Now this would result in a significant reduction
in the travel time to Mars even with an increased tangential distance.
A key problem though would be finding a retrograde comet that is
close to the Earth when Mars is also near its perihelion, not a
trivial matter. After a web search I found this sci.astro.amateur post
that discusses retrograde comets:

======================================
Newsgroups: sci.astro.amateur
From: (Paul Schlyter)
Date: 1997/04/18
Subject: Why no retrograde asteroid orbits?
....
Not one single asteroid has been found in a retrograde orbit around
the Sun. Therefore not merely "most" asteroids move in prograde
orbits, but ALL known asteroids do. Of course there may be some
unknown asteroid moving in a retrograde orbit, but since not a single
one has been found so far, they must be very few - if they exist at
all.

another line of evidence that they all came from the same source in the
solar nebula that formed the solar system, if you don't believe in the
planet explosion theory.

Another thing to consider: any asteroid in a retrograde orbit would
run a much much greater risk of colliding with other asteroids.
Therefore their lifetimes would probably be quite short -- and this
may have wiped all of them out by now.

The only known celestial objects in retrograde orbits are comets, and
almost all retrograde comets are long-period comets. Almost all short-
period comets move in prograde orbits: of all the 124 short-period
comets catalogued so far, only three move in a retrograde orbit: 1P
Halley, 55P Tempel-Tuttle, and 109P Swift-Tuttle. A few additional
ones have quite high inclinations (122P de Vico 85 degrees, 12P Pons-
Borrks 75 degrees, 35P Herschel-Rigollett 64 degrees, 96P Machholz 1
60 degrees, 8P Tuttle 55 degrees, 13P Olbers 44 degrees) - but all the
remaining 115 short-period comets have inclinations lower than 32
degrees.
=========================================

So according to this there are only three (!) short-period retrograde
comets. Tempel-Tuttle is the only one that has its next perihelion at
a reasonably close to time now, on May 20, 2031. I don't know if its
perihelion corresponds to a close approach of Mars.
However, it turns out most long period comets have retrograde orbits.
So it may be possible out of this large population to find one whose
perihelion occurs near the time when Mars is at its closest approach.

Another key fact to consider is that for using the comet gravity
assist for shortening the Mars travel time, the optimal angle might
not be tangential. This is because of the shortness of the radial
distance to Mars and to the comet. In this case as shown in the
"Gravity assist" article you would still get an increase in velocity
though a smaller one from using vector addition of the velocities.
Note in this case you might not even need the comet to be retrograde
which would greatly increase the population of comets that might be
used such their closest approach and Mars closest approach are near
the same time.


Bob Clark

(*)Newsgroups: sci.astro, sci.physics, sci.space.policy, sci.math
From: Robert Clark
Date: Wed, 9 Jul 2008 13:29:06 -0700 (PDT)
Local: Wed, Jul 9 2008 4:29 pm
Subject: Short Mars travel times at high speed.
http://groups.google.com/group/sci.a...2aa4c9666ef2ef

You've said it all in this one sentence:

"A key problem though would be finding a retrograde comet that is
close to the Earth when Mars is also near its perihelion, not a
trivial matter."

What would you do, wait a thousand years for the right comet to
come by through happenstance, or travel to Mars the slow way
and get there in a human lifetime?

Where I live there is a bus every 10 minutes except on Sundays
when there is a bus every hour. Given that I have to find somewhere
to park in town, I drive on Sundays and get to town much faster
than the bus - if I wait a week. But when I'm hungry for ham and
eggs on Wednesday and the fridge is empty I take the slow bus.





"Robert Clark" wrote in message
...
| I'm thinking in regards to shortening the travel time for a manned
| Mars mission. There is a nice article here on gravity assist or the
| gravitational slingshot effect:
|
| Gravity assist.
| http://en.wikipedia.org/wiki/Gravity_assist#Explanation
|
| This show the greatest effect is when the spacecraft is traveling in
| an opposite direction to the gravitating body. You get twice the
| velocity of the body added to the spacecraft's velocity, both measured
| with respect to the Sun.
| Then this could be especially useful if a retrograde comet near its
| perihelion is rendezvoused by the spacecraft. You would make the
| rendezvous when the comet is near Earth's orbit to cut the travel time
| to the comet. If we can get an initial velocity off the Earth of say
| 30 km/sec, and added to the Earth's orbital velocity of 30 km/sec,
| this would result in a tangential velocity of 60 km/sec.
| The problem of just using this tangential velocity to get to Mars is
| that it turns out the increased distance of the tangential direction
| to intersect Mars orbit over just the radial direction cancels out the
| improvement of the increased speed. And even traveling at an optimal
| angle only shortens the travel time slightly.(*)
| However, when a comet is close to the Earth's orbit it will have an
| orbital velocity close to that of the Earth, about 30 km/sec. Then
| when the slingshot effect is applied to the spacecraft on close flyby
| of the comet, its speed will be increased from 60 km/sec to 60 +
| 2*(30) = 120 km/sec. Now this would result in a significant reduction
| in the travel time to Mars even with an increased tangential distance.
| A key problem though would be finding a retrograde comet that is
| close to the Earth when Mars is also near its perihelion, not a
| trivial matter. After a web search I found this sci.astro.amateur post
| that discusses retrograde comets:
|
| ======================================
| Newsgroups: sci.astro.amateur
| From: (Paul Schlyter)
| Date: 1997/04/18
| Subject: Why no retrograde asteroid orbits?
| ...
| Not one single asteroid has been found in a retrograde orbit around
| the Sun. Therefore not merely "most" asteroids move in prograde
| orbits, but ALL known asteroids do. Of course there may be some
| unknown asteroid moving in a retrograde orbit, but since not a single
| one has been found so far, they must be very few - if they exist at
| all.
|
| another line of evidence that they all came from the same source in the
| solar nebula that formed the solar system, if you don't believe in the
| planet explosion theory.
|
| Another thing to consider: any asteroid in a retrograde orbit would
| run a much much greater risk of colliding with other asteroids.
| Therefore their lifetimes would probably be quite short -- and this
| may have wiped all of them out by now.
|
| The only known celestial objects in retrograde orbits are comets, and
| almost all retrograde comets are long-period comets. Almost all short-
| period comets move in prograde orbits: of all the 124 short-period
| comets catalogued so far, only three move in a retrograde orbit: 1P
| Halley, 55P Tempel-Tuttle, and 109P Swift-Tuttle. A few additional
| ones have quite high inclinations (122P de Vico 85 degrees, 12P Pons-
| Borrks 75 degrees, 35P Herschel-Rigollett 64 degrees, 96P Machholz 1
| 60 degrees, 8P Tuttle 55 degrees, 13P Olbers 44 degrees) - but all the
| remaining 115 short-period comets have inclinations lower than 32
| degrees.
| =========================================
|
| So according to this there are only three (!) short-period retrograde
| comets. Tempel-Tuttle is the only one that has its next perihelion at
| a reasonably close to time now, on May 20, 2031. I don't know if its
| perihelion corresponds to a close approach of Mars.
| However, it turns out most long period comets have retrograde orbits.
| So it may be possible out of this large population to find one whose
| perihelion occurs near the time when Mars is at its closest approach.
|
| Another key fact to consider is that for using the comet gravity
| assist for shortening the Mars travel time, the optimal angle might
| not be tangential. This is because of the shortness of the radial
| distance to Mars and to the comet. In this case as shown in the
| "Gravity assist" article you would still get an increase in velocity
| though a smaller one from using vector addition of the velocities.
| Note in this case you might not even need the comet to be retrograde
| which would greatly increase the population of comets that might be
| used such their closest approach and Mars closest approach are near
| the same time.
|
|
| Bob Clark
|
| (*)Newsgroups: sci.astro, sci.physics, sci.space.policy, sci.math
| From: Robert Clark
| Date: Wed, 9 Jul 2008 13:29:06 -0700 (PDT)
| Local: Wed, Jul 9 2008 4:29 pm
| Subject: Short Mars travel times at high speed.
| http://groups.google.com/group/sci.a...2aa4c9666ef2ef

A couple of "peanut gallery" questions on using gravity assist from a
comet:

*) Is the ratio of the mass of the comet to that of the spacecraft
still such that the effect on the comet's orbit is epsilon?

*) How much extra shielding if any might be required to protect the
spacecraft's vital bits from the stuff spewing from the comet?

rick jones
--
Wisdom Teeth are impacted, people are affected by the effects of events.
these opinions are mine, all mine; HP might not want them anyway...
feel free to post, OR email to rick.jones2 in hp.com but NOT BOTH...

On Mon, 14 Jul 2008 17:12:34 -0700 (PDT), Robert Clark
wrote:

I'm thinking in regards to shortening the travel time for a manned
Mars mission. There is a nice article here on gravity assist or the
gravitational slingshot effect:

Gravity assist.
http://en.wikipedia.org/wiki/Gravity_assist#Explanation

This show the greatest effect is when the spacecraft is traveling in
an opposite direction to the gravitating body. You get twice the
velocity of the body added to the spacecraft's velocity, both measured
with respect to the Sun.
Then this could be especially useful if a retrograde comet near its
perihelion is rendezvoused by the spacecraft. You would make the
rendezvous when the comet is near Earth's orbit to cut the travel time
to the comet. If we can get an initial velocity off the Earth of say
30 km/sec, and added to the Earth's orbital velocity of 30 km/sec,
this would result in a tangential velocity of 60 km/sec...

There is a problem with this. A comet simply doesn't have enough mass to
significantly slingshot a probe. At 30 km/s, even if you graze the
surface of the nucleus, you're only going to get a tiny deflection. You
aren't going to swing around at all. And if a comet is near the Earth,
it's probably active, so getting close is very risky.
_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Jul 14, 4:12*pm, Robert Clark wrote:

[...]

Well thought out, but is unfortunately DOA given that comets simply do
not mass enough to give the impulse you require.

On Jul 14, 9:10 pm, Rick Jones wrote:
A couple of "peanut gallery" questions on using gravity assist from a
comet:

*) Is the ratio of the mass of the comet to that of the spacecraft
still such that the effect on the comet's orbit is epsilon?

*) How much extra shielding if any might be required to protect the
spacecraft's vital bits from the stuff spewing from the comet?

rick jones
--
Wisdom Teeth are impacted, people are affected by the effects of events.
these opinions are mine, all mine; HP might not want them anyway...
feel free to post, OR email to rick.jones2 in hp.com but NOT BOTH...

Both good questions. For massive manned craft you might not want to
use the same comet repeatedly for the perturbation they might have on
the comet. However comets are such long period anyway I don't think
you could even if you wanted to.
About protecting the craft from ejected matter from the comet perhaps
the Deep Impact and Stardust missions could give an idea of how much
dust we could expect to encounter on close approach to the comet.

Bob Clark

On Mon, 14 Jul 2008 19:14:12 -0700 (PDT), Robert Clark
wrote:

Both good questions. For massive manned craft you might not want to
use the same comet repeatedly for the perturbation they might have on
the comet. However comets are such long period anyway I don't think
you could even if you wanted to.

I don't think you need to worry much about even the most massive craft
we're likely to build having much effect on a body a few kilometers
across.

About protecting the craft from ejected matter from the comet perhaps
the Deep Impact and Stardust missions could give an idea of how much
dust we could expect to encounter on close approach to the comet.

They did. Lots of dust, and lots of damage. Optics got pitted, and there
was always concern about a chunk large enough to do fatal damage. These
craft employed special shielding. You could do the same for a manned
mission, but I think we'd be a lot more conservative about safety-
enough that this wouldn't be attempted.

BTW, Stardust demonstrates something else (mentioned elsewhere in this
discussion): a comet doesn't have enough mass to be useful for providing
a gravity assist. The probe, massing just a few hundred kilograms, and
passing only 240 km from the nucleus of Comet Wild, was barely
deflected. It continued on in nearly the same orbit it had previously
been following.
_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Jul 14, 11:30 pm, Chris L Peterson wrote:
On Mon, 14 Jul 2008 19:14:12 -0700 (PDT), Robert Clark

wrote:
Both good questions. For massive manned craft you might not want to
use the same comet repeatedly for the perturbation they might have on
the comet. However comets are such long period anyway I don't think
you could even if you wanted to.

I don't think you need to worry much about even the most massive craft
we're likely to build having much effect on a body a few kilometers
across.

About protecting the craft from ejected matter from the comet perhaps
the Deep Impact and Stardust missions could give an idea of how much
dust we could expect to encounter on close approach to the comet.

They did. Lots of dust, and lots of damage. Optics got pitted, and there
was always concern about a chunk large enough to do fatal damage. These
craft employed special shielding. You could do the same for a manned
mission, but I think we'd be a lot more conservative about safety-
enough that this wouldn't be attempted.

BTW, Stardust demonstrates something else (mentioned elsewhere in this
discussion): a comet doesn't have enough mass to be useful for providing
a gravity assist. The probe, massing just a few hundred kilograms, and
passing only 240 km from the nucleus of Comet Wild, was barely
deflected. It continued on in nearly the same orbit it had previously
been following.
_________________________________________________

Chris L Peterson
Cloudbait Observatoryhttp://www.cloudbait.com

Yeah, this won't work. Here's a mathematical analysis:

Gravitational Slingshot.
http://www.mathpages.com/home/kmath114.htm

It shows the spacecraft receding from the gravitating body at the
same angle it approached, at which point you would get the high
increase in speed.
It doesn't say so, but this *assumes* the gravity is strong enough to
bend the spacecraft around into going in the reverse direction. It
would be true if the body was a point particle then you could get
close enough to it you wanted to get the high enough gravitational
field. But not for a real sized body.

Bob Clark

On Tue, 15 Jul 2008 09:16:54 -0700 (PDT), Robert Clark
wrote:

Yeah, this won't work. Here's a mathematical analysis:

Gravitational Slingshot.
http://www.mathpages.com/home/kmath114.htm

That's an incomplete treatment. A full analysis needs to include the
planetary mass and the slingshot radius (hyperbolic focus). I'm pretty
sure that the equations will simplify to just including a term for the
escape velocity, which scales with the square root of the mass and the
inverse square root of the radius.

Of course, it's a good thing that a gravitational assist is dependent on
escape velocity. Otherwise, we'd never get to any other planet, since
our probes would be slingshotting all over the place off of cosmic dust!
_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Tue, 15 Jul 2008 14:55:51 -0600, Chris L Peterson
wrote:
Yeah, this won't work. Here's a mathematical analysis:
Gravitational Slingshot.
http://www.mathpages.com/home/kmath114.htm

That's an incomplete treatment. A full analysis needs to include the
planetary mass and the slingshot radius (hyperbolic focus).

As I read it, the mass of the planet IS included in that web page
analysis, and then at the end it is simplified by noting that the mass
of the space probe is negligibly small compared with the mass of a
planet. Also it points out that the "radius" of the hyperbolic orbit
doesn't matter, provided the planet's radius is small enough that you
can pass close enough to get the desired angular deflection. As it
says on that page, the only limitation is the density of the planet
(and its atmosphere), which determines how closely you can loop around
the planet.

I'm pretty sure that the equations will simplify to just including a term for
the escape velocity...

What do you mean by this? What would equations look like if they "just
included a term for the escape velocity"?