Transit times between L4 and Moon

Spaceship A is at L4.

Spaceship B is at L5.

They are racing to reach the Moon. Each has the same engines, and
will go at the same speed.

Question #1: which will arrive first? Question #2: if I didn't have
much energy (and these ships weren't the supersleek dragsters they
undoubtedly are), what would be the optimal/energy-efficient orbital
"route" from each libration point to the Moon?

I.e., what I'm trying to figure out here is whether the fact that L4
is "ahead" of the Moon's position in orbit is an advantage or
disadvantage vis-a-vis L5's position "behind" the Moon's position in
orbit. My first thought was that Spaceship A will win easily (vis-a-
vis Question #1), because while it moves toward the Moon, the Moon is
moving toward it. But then I reflected that Spaceship A, in going
"backward", still has to compensate for the forces that are propelling
it "forward." And then I reflected that Spaceship A, in entering a
retrograde orbit, will actually start to move in toward the Earth.

And then I decided to put the question to all your brainiacs out there
in the hopes that someone will actually know the answer to this #$#
thing.

Just so we're all on the same page, this is the libration point
topography. (This map has the Sun at the center, but substitute the
Earth for the Sun, and the Moon for the Earth, and we're golden.)

http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg

thanks!

FA

On Jan 17, 8:08*am, Aztec50 wrote:
Spaceship A is at L4.

Spaceship B is at L5.

They are racing to reach the Moon. *Each has the same
engines, and will go at the same speed.

L4 and L5 for the Earth-Moon system.
http://www.freemars.org/l5/aboutl5.html

Question #1: *which will arrive first?

Since they both start out at "zero", in orbit around the Earth,
staying away from the Moon... they will arrive on the surface
together, given not having to negotiate to some point on the surface
that might not be equidistant.

*Question #2: *if I didn't have much energy (and these
ships weren't the supersleek dragsters they undoubtedly
are), what would be the optimal/energy-efficient orbital
"route" from each libration point to the Moon?

For the one leading the Moon, boost out, let the Moon catch up, then
brake in.
Opposite for the one trailing the Moon.

...
And then I decided to put the question to all your brainiacs
out there in the hopes that someone will actually know the
answer to this #$# thing.

I'm no brainiac. I used to analyze sewer networks.

David A. Smith

"Aztec50" wrote in message
...
| Spaceship A is at L4.
|
| Spaceship B is at L5.
|
| They are racing to reach the Moon. Each has the same engines, and
| will go at the same speed.
|
| Question #1: which will arrive first? Question #2: if I didn't have
| much energy (and these ships weren't the supersleek dragsters they
| undoubtedly are), what would be the optimal/energy-efficient orbital
| "route" from each libration point to the Moon?
|
| I.e., what I'm trying to figure out here is whether the fact that L4
| is "ahead" of the Moon's position in orbit is an advantage or
| disadvantage vis-a-vis L5's position "behind" the Moon's position in
| orbit. My first thought was that Spaceship A will win easily (vis-a-
| vis Question #1), because while it moves toward the Moon, the Moon is
| moving toward it. But then I reflected that Spaceship A, in going
| "backward", still has to compensate for the forces that are propelling
| it "forward." And then I reflected that Spaceship A, in entering a
| retrograde orbit, will actually start to move in toward the Earth.
|
| And then I decided to put the question to all your brainiacs out there
| in the hopes that someone will actually know the answer to this #$#
| thing.
|
| Just so we're all on the same page, this is the libration point
| topography. (This map has the Sun at the center, but substitute the
| Earth for the Sun, and the Moon for the Earth, and we're golden.)
|
| http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg
|
| thanks!

Seeing the situation from the Moon, each ship has the same distance
to "fall" to the lunar surface and will take the same time.
Neither has any advantage over the other.
Mentally switching frames of reference is sometimes
difficult, this may help:
http://faculty.ifmo.ru/butikov/Proje...llection1.html
The checkbox labelled "Geo frame" shows all the same orbits
as seen Earth.
L4 can be seen in example 7 and L5 by running the model
"backwards".

I read an old magasine from the early 80's where a nobel prize
winner,Burton Richter,was complaining that mathematicians were
beginning to thing that these non geometric differential equaltions
known as Langrangians were 'reality'.Twenty five years later it
appears that his prediction is now official policy !

Let me bring you all back down to Earth -

http://astro.berkeley.edu/~imke/Infr..._2001_2005.jpg

You probably notice that the moons of Uranus have a motion which
follows the unique Eqiuatorial oreintation of Uranus.You probably even
notice the seperate motion where the moons also follow a path
perpendicular to the planetary axis of rotation,it is not that
difficult,you see the change in the Equatorial ring signifying a
change in orbital orientation of the planet.

The moons of Uranus travel off a common radius for both fixed axial
orientation/rotation and changing orbital orientation,I would not
expect you to know why the dual motions of the moons,and subsequently
our moon makes calculating orbital trajectories a far more difficult
task than the poor two dimensional view but it would be a good start
if astronomers recognised the major orbital component of changing
orientation -

http://space.newscientist.com/data/i...2529-1_800.jpg

Everybody remembers the names of Rheticus,Maestlin,Kepler,Galileo for
supporting recognition of the axial and orbital motions of the Earth
and nobody remembers those who opposed it.The additional orbital
component is there waiting for those who have the intelligence and the
courage to bring astronomy up to speed with modern imaging and modern
imaging as a tool for exquisite reasoning.

Differential equations cannot compete witn the sequence of images
showing an overlooked motion !.


On Jan 17, 4:08*pm, Aztec50 wrote:
Spaceship A is at L4.

Spaceship B is at L5.

They are racing to reach the Moon. *Each has the same engines, and
will go at the same speed.

Question #1: *which will arrive first? *Question #2: *if I didn't have
much energy (and these ships weren't the supersleek dragsters they
undoubtedly are), what would be the optimal/energy-efficient orbital
"route" from each libration point to the Moon?

I.e., what I'm trying to figure out here is whether the fact that L4
is "ahead" of the Moon's position in orbit is an advantage or
disadvantage vis-a-vis L5's position "behind" the Moon's position in
orbit. *My first thought was that Spaceship A will win easily (vis-a-
vis Question #1), because while it moves toward the Moon, the Moon is
moving toward it. *But then I reflected that Spaceship A, in going
"backward", still has to compensate for the forces that are propelling
it "forward." * *And then I reflected that Spaceship A, in entering a
retrograde orbit, will actually start to move in toward the Earth.

And then I decided to put the question to all your brainiacs out there
in the hopes that someone will actually know the answer to this #$#
thing.

Just so we're all on the same page, this is the libration point
topography. *(This map has the Sun at the center, but substitute the
Earth for the Sun, and the Moon for the Earth, and we're golden.)

http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg

thanks!

FA

oriel36 wrote:
I read an old magasine from the early 80's where a nobel prize
winner,Burton Richter,was complaining that mathematicians were
beginning to thing that these non geometric differential equaltions
known as Langrangians were 'reality'.Twenty five years later it
appears that his prediction is now official policy !

Let me bring you all back down to Earth -

http://astro.berkeley.edu/~imke/Infr..._2001_2005.jpg

You probably notice that the moons of Uranus have a motion which
follows the unique Eqiuatorial oreintation of Uranus.You probably even
notice the seperate motion where the moons also follow a path
perpendicular to the planetary axis of rotation,it is not that
difficult,you see the change in the Equatorial ring signifying a
change in orbital orientation of the planet.

The moons of Uranus travel off a common radius for both fixed axial
orientation/rotation and changing orbital orientation,I would not
expect you to know why the dual motions of the moons,and subsequently
our moon makes calculating orbital trajectories a far more difficult
task than the poor two dimensional view but it would be a good start
if astronomers recognised the major orbital component of changing
orientation -

http://space.newscientist.com/data/i...2529-1_800.jpg

Everybody remembers the names of Rheticus,Maestlin,Kepler,Galileo for
supporting recognition of the axial and orbital motions of the Earth
and nobody remembers those who opposed it.The additional orbital
component is there waiting for those who have the intelligence and the
courage to bring astronomy up to speed with modern imaging and modern
imaging as a tool for exquisite reasoning.

Differential equations cannot compete witn the sequence of images
showing an overlooked motion !.


On Jan 17, 4:08 pm, Aztec50 wrote:
Spaceship A is at L4.

Spaceship B is at L5.

They are racing to reach the Moon. Each has the same engines, and
will go at the same speed.

Question #1: which will arrive first? Question #2: if I didn't have
much energy (and these ships weren't the supersleek dragsters they
undoubtedly are), what would be the optimal/energy-efficient orbital
"route" from each libration point to the Moon?

I.e., what I'm trying to figure out here is whether the fact that L4
is "ahead" of the Moon's position in orbit is an advantage or
disadvantage vis-a-vis L5's position "behind" the Moon's position in
orbit. My first thought was that Spaceship A will win easily (vis-a-
vis Question #1), because while it moves toward the Moon, the Moon is
moving toward it. But then I reflected that Spaceship A, in going
"backward", still has to compensate for the forces that are propelling
it "forward." And then I reflected that Spaceship A, in entering a
retrograde orbit, will actually start to move in toward the Earth.

And then I decided to put the question to all your brainiacs out there
in the hopes that someone will actually know the answer to this #$#
thing.

Just so we're all on the same page, this is the libration point
topography. (This map has the Sun at the center, but substitute the
Earth for the Sun, and the Moon for the Earth, and we're golden.)

http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg

thanks!

FA


What is with you and whacky theories about your anus? Jeeze...

Given that ship A and ship B start from stable orbits in the precise
center of the L4 and L5 gravitational pockets (i.e. their motion in
orbit around the sun is in a precise 1:1 frequency with Earth) and have
precisely the same mass, engines, fuel, etc. - they would arrive at a
theoretical point perpendicular to Earth's orbital trajectory at the
precise same time. This is due to conservation of angular momentum and
relativistic orbital velocity of the three bodies.
However, if they are in a theoretical "dead motion" state (relative
to the Sun) at the beginning of this conjectured model, they would not
only experience free-falling toward the sun, but would also experience
perturbations from the L4 and L5 points around them respectively that
would likely launch them into any number of potentially chaotic paths,
requiring careful compensation by any engines and navigation systems in
order to reach Earth. Since you're speaking purely hypothetically, we
may as well get really crazy.
The other consideration you failed to pay notice to when you were
thinking about the moon's orbit and one ship approaching the moon sooner
than the other due to the time it takes them to move toward it, the
moon's orbit is changing is: the ships may take more than one lunar
orbit to arrive, and therefore the advantage could be given to EITHER of
the ships depending on the time it takes them to travel to the general
vicinity of Earth. Without knowing the precise chronology that this
"race" begins and the precise details of the mass, thrust and
capabilities of these craft, it's impossible to guess which will arrive
first. Flip a coin. =)

- Timothy Partee


Aztec50 wrote:
Spaceship A is at L4.

Spaceship B is at L5.

They are racing to reach the Moon. Each has the same engines, and
will go at the same speed.

Question #1: which will arrive first? Question #2: if I didn't have
much energy (and these ships weren't the supersleek dragsters they
undoubtedly are), what would be the optimal/energy-efficient orbital
"route" from each libration point to the Moon?

I.e., what I'm trying to figure out here is whether the fact that L4
is "ahead" of the Moon's position in orbit is an advantage or
disadvantage vis-a-vis L5's position "behind" the Moon's position in
orbit. My first thought was that Spaceship A will win easily (vis-a-
vis Question #1), because while it moves toward the Moon, the Moon is
moving toward it. But then I reflected that Spaceship A, in going
"backward", still has to compensate for the forces that are propelling
it "forward." And then I reflected that Spaceship A, in entering a
retrograde orbit, will actually start to move in toward the Earth.

And then I decided to put the question to all your brainiacs out there
in the hopes that someone will actually know the answer to this #$#
thing.

Just so we're all on the same page, this is the libration point
topography. (This map has the Sun at the center, but substitute the
Earth for the Sun, and the Moon for the Earth, and we're golden.)

http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg

thanks!

FA

" They are racing to reach the Moon. "

"Flip a coin" doesn't enter into it, the result is a tie. :-)

Always amusing when someone wants to sound knowledgeable when they
babble "relativistic orbital velocity", but then say "likely", and funnier
still when they say:
"The other consideration you failed to pay notice to..."


"Timothy Partee" wrote in message
t...
|
| Given that ship A and ship B start from stable orbits in the precise
| center of the L4 and L5 gravitational pockets (i.e. their motion in
| orbit around the sun is in a precise 1:1 frequency with Earth) and have
| precisely the same mass, engines, fuel, etc. - they would arrive at a
| theoretical point perpendicular to Earth's orbital trajectory at the
| precise same time. This is due to conservation of angular momentum and
| relativistic orbital velocity of the three bodies.
| However, if they are in a theoretical "dead motion" state (relative
| to the Sun) at the beginning of this conjectured model, they would not
| only experience free-falling toward the sun, but would also experience
| perturbations from the L4 and L5 points around them respectively that
| would likely launch them into any number of potentially chaotic paths,
| requiring careful compensation by any engines and navigation systems in
| order to reach Earth. Since you're speaking purely hypothetically, we
| may as well get really crazy.
| The other consideration you failed to pay notice to when you were
| thinking about the moon's orbit and one ship approaching the moon sooner
| than the other due to the time it takes them to move toward it, the
| moon's orbit is changing is: the ships may take more than one lunar
| orbit to arrive, and therefore the advantage could be given to EITHER of
| the ships depending on the time it takes them to travel to the general
| vicinity of Earth. Without knowing the precise chronology that this
| "race" begins and the precise details of the mass, thrust and
| capabilities of these craft, it's impossible to guess which will arrive
| first. Flip a coin. =)
|
| - Timothy Partee


|
|
| Aztec50 wrote:
| Spaceship A is at L4.
|
| Spaceship B is at L5.
|
| They are racing to reach the Moon. Each has the same engines, and
| will go at the same speed.
|
| Question #1: which will arrive first? Question #2: if I didn't have
| much energy (and these ships weren't the supersleek dragsters they
| undoubtedly are), what would be the optimal/energy-efficient orbital
| "route" from each libration point to the Moon?
|
| I.e., what I'm trying to figure out here is whether the fact that L4
| is "ahead" of the Moon's position in orbit is an advantage or
| disadvantage vis-a-vis L5's position "behind" the Moon's position in
| orbit. My first thought was that Spaceship A will win easily (vis-a-
| vis Question #1), because while it moves toward the Moon, the Moon is
| moving toward it. But then I reflected that Spaceship A, in going
| "backward", still has to compensate for the forces that are propelling
| it "forward." And then I reflected that Spaceship A, in entering a
| retrograde orbit, will actually start to move in toward the Earth.
|
| And then I decided to put the question to all your brainiacs out there
| in the hopes that someone will actually know the answer to this #$#
| thing.
|
| Just so we're all on the same page, this is the libration point
| topography. (This map has the Sun at the center, but substitute the
| Earth for the Sun, and the Moon for the Earth, and we're golden.)
|
| http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg
|
| thanks!
|
| FA

Androcles wrote:
" They are racing to reach the Moon. "

"Flip a coin" doesn't enter into it, the result is a tie. :-)

Always amusing when someone wants to sound knowledgeable when they
babble "relativistic orbital velocity", but then say "likely", and funnier
still when they say:
"The other consideration you failed to pay notice to..."

To put it succinctly: you're wrong. =)

Racing to the moon means racing to an object with a dynamic
position. The only way the "race" would result in a tie is if the moon
just so happened to be precisely on the line of perpendicularity with
the sun at the time each rocket reached the moon. The odds of that are
pretty slim. This isn't even taking into account landing approaches,
which add another level of complexity that is likely to change the
outcome. Please think before you troll.

- Timothy Partee

"Timothy Partee" wrote in message
t...
| Androcles wrote:
| " They are racing to reach the Moon. "
|
| "Flip a coin" doesn't enter into it, the result is a tie. :-)
|
| Always amusing when someone wants to sound knowledgeable when they
| babble "relativistic orbital velocity", but then say "likely", and
funnier
| still when they say:
| "The other consideration you failed to pay notice to..."
|
| To put it succinctly: you're wrong. =)
|
| Racing to the moon means racing to an object with a dynamic
| position. The only way the "race" would result in a tie is if the moon
| just so happened to be precisely on the line of perpendicularity with
| the sun at the time each rocket reached the moon. The odds of that are
| pretty slim. This isn't even taking into account landing approaches,
| which add another level of complexity that is likely to change the
| outcome. Please think before you troll.
|
| - Timothy Partee

Pity you snipped the context. Fortunately I happen to know that if
Androcles has put something in quotation marks then he is quoting
someone else.

You yourself said
Timothy Partee: "they would arrive at a theoretical point perpendicular
to Earth's orbital trajectory at the precise same time. "

That is correct, although long-winded.
To put it succinctly: you contradict yourself. Only an idiot does that.
Please think before you troll.



"Timothy Partee" wrote in message
t...
|
| Given that ship A and ship B start from stable orbits in the precise
| center of the L4 and L5 gravitational pockets (i.e. their motion in
| orbit around the sun is in a precise 1:1 frequency with Earth) and have
| precisely the same mass, engines, fuel, etc. - they would arrive at a
| theoretical point perpendicular to Earth's orbital trajectory at the
| precise same time. This is due to conservation of angular momentum and
| relativistic orbital velocity of the three bodies.
| However, if they are in a theoretical "dead motion" state (relative
| to the Sun) at the beginning of this conjectured model, they would not
| only experience free-falling toward the sun, but would also experience
| perturbations from the L4 and L5 points around them respectively that
| would likely launch them into any number of potentially chaotic paths,
| requiring careful compensation by any engines and navigation systems in
| order to reach Earth. Since you're speaking purely hypothetically, we
| may as well get really crazy.
| The other consideration you failed to pay notice to when you were
| thinking about the moon's orbit and one ship approaching the moon sooner
| than the other due to the time it takes them to move toward it, the
| moon's orbit is changing is: the ships may take more than one lunar
| orbit to arrive, and therefore the advantage could be given to EITHER of
| the ships depending on the time it takes them to travel to the general
| vicinity of Earth. Without knowing the precise chronology that this
| "race" begins and the precise details of the mass, thrust and
| capabilities of these craft, it's impossible to guess which will arrive
| first. Flip a coin. =)
|
| - Timothy Partee


|
|
| Aztec50 wrote:
| Spaceship A is at L4.
|
| Spaceship B is at L5.
|
| They are racing to reach the Moon. Each has the same engines, and
| will go at the same speed.
|
| Question #1: which will arrive first? Question #2: if I didn't have
| much energy (and these ships weren't the supersleek dragsters they
| undoubtedly are), what would be the optimal/energy-efficient orbital
| "route" from each libration point to the Moon?
|
| I.e., what I'm trying to figure out here is whether the fact that L4
| is "ahead" of the Moon's position in orbit is an advantage or
| disadvantage vis-a-vis L5's position "behind" the Moon's position in
| orbit. My first thought was that Spaceship A will win easily (vis-a-
| vis Question #1), because while it moves toward the Moon, the Moon is
| moving toward it. But then I reflected that Spaceship A, in going
| "backward", still has to compensate for the forces that are propelling
| it "forward." And then I reflected that Spaceship A, in entering a
| retrograde orbit, will actually start to move in toward the Earth.
|
| And then I decided to put the question to all your brainiacs out there
| in the hopes that someone will actually know the answer to this #$#
| thing.
|
| Just so we're all on the same page, this is the libration point
| topography. (This map has the Sun at the center, but substitute the
| Earth for the Sun, and the Moon for the Earth, and we're golden.)
|
| http://en.wikipedia.org/wiki/Image:Lagrange_points.jpg
|
| thanks!
|
| FA

Pity you snipped the context. Fortunately I happen to know that if
Androcles has put something in quotation marks then he is quoting
someone else.

The context is the thread, if your NG reader doesn't have the whole
thread you need to change your settings or something, apparently. Next
time someone whines or bitches about "quoting the whole thread" I'll
point them to you...

You yourself said
Timothy Partee: "they would arrive at a theoretical point perpendicular
to Earth's orbital trajectory at the precise same time. "

Given the context that they were not trying to reach the moon but the
linear path from the Sun to Earth, yes.

That is correct, although long-winded.
To put it succinctly: you contradict yourself. Only an idiot does that.
Please think before you troll.

Appearances can be deceiving. The only reason I could have appeared to
contradict myself is due to giving multiple if-then-else scenarios due
to the parameters of the "problem" not being clearly enough defined to
come to a full answer to the initial question posted that started the
thread. Ironically it now appears that the sole point of that initial
question was to troll the NG to get people with half a brain to argue
over something so stupid and benign. So congratulations for feeding the
troll further. Idiot.