Science > Physics > Strange Increase in the Total Energy of a Rocket in the Earth-Moon system
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Science > Physics |
| User: |
"Matt" |
| Date: |
18 Apr 2007 09:07:24 AM |
| Object: |
Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
Kind Regards,
Matt
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| User: "Androcles" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 11:09:55 AM |
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"Matt" <mattb95@hotmail.com> wrote in message =
news:1176905244.556846.191010@n76g2000hsh.googlegroups.com...
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
It's been done, but new wheels are always being invented.
=20
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
=20
Does anyone have any ideas why this is happening?
Yes. You have to go a tad beyond the basics you learned in=20
high school. Energy is relative and can be negative.=20
Although KE =3D 1/2 mv^2 gives you the energy of a bullet fired from=20
a gun at the rocket, the rocket goes faster than the bullet and the=20
bullet can't catch it, so the energy (ability to do work) can do=20
no work on the rocket. The bullet's energy *relative to the rocket*=20
is negative, you have to give it MORE energy until it matches the=20
speed of the rocket (come to zero energy) and then even more than
that to catch the rocket and do work on it, punching a hole.=20
The potential energy of a rock at the top of a cliff (it's ability to
crack you skull) is more that the potential energy of a rock at your
feet, which has negative potential energy until you lift it to head =
height.
To put it another way, once your rocket has landed on the moon
you have to give it energy (relative to the Moon) to get off it again.=20
It already has all the energy it will ever need to get back to Earth.
Energy is relative.
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| User: "Uncle Al" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moonsystem |
18 Apr 2007 11:45:58 AM |
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Matt wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
You are falling into the moon's gravitational field as you are falling
out of the Earth's. 1/r^2 - things are not linear. Proximity
matters.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "Androcles" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 12:06:05 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message =
news:46264B46.F06F0B04@hate.spam.net...
[snip river of *****]
1) GPS works.
2) Sub-idiot.
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| User: "Sam Wormley" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moonsystem |
18 Apr 2007 09:18:27 AM |
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Matt wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
Kind Regards,
Matt
See Episode 24. Navigating in Space
Voyages to other planets use the same laws that guide planets around
the solar system.
http://www.learner.org/resources/series42.html
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| User: "Dwib" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 10:14:22 AM |
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On Apr 18, 9:07 am, Matt <matt...@hotmail.com> wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
Kind Regards,
Matt
Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 10:50:28 AM |
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Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
I hadn't thought about that. I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative? The mass of the
rocket is set at 30332 kg.
Kind Regards,
Matt
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| User: "Greg Neill" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 11:14:10 AM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176911428.872779.74420@q75g2000hsh.googlegroups.com...
Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
I hadn't thought about that. I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative? The mass of the
rocket is set at 30332 kg.
I think you mean that the total mechanical energy is
negative, rather than its absolute value. Absolute
values are always positive (or zero).
A negative energy means that the object is gravitationally
bound to the system. If it were positive it would be on
an escape trajectory away from the Earth-Moon system.
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 03:10:09 PM |
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I think you mean that the total mechanical energy is
negative, rather than its absolute value. Absolute
values are always positive (or zero).
Yes you're right, sorry to type something misleading :s
A negative energy means that the object is gravitationally
bound to the system. If it were positive it would be on
an escape trajectory away from the Earth-Moon system.
I don't know why I didn't realise that sooner! That expains it
perfectly
Kind Regards,
Matt
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| User: "Phineas T Puddleduck" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 11:25:20 AM |
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In article <1176911428.872779.74420@q75g2000hsh.googlegroups.com>,
Matt <mattb95@hotmail.com> wrote:
Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
I hadn't thought about that. I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative? The mass of the
rocket is set at 30332 kg.
Its gaining energy from the gravitational potential of the moon. Once you're
past the point where the forces of gravity balance...
Negative energy = bound.
--
Sacred keeper of the Hollow Sphere, and the space within. Coffee boy to the
rich and famous. Proud owner of the Mop Jockey.
COOSN-174-07-82116: alt.astronomy's favourite poster (from a survey taken
of the saucerhead high command).
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| User: "Artimus Q Dufflebag" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 12:13:58 PM |
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Phineas T Puddleduck wrote:
In article <1176911428.872779.74420@q75g2000hsh.googlegroups.com>,
Matt <mattb95@hotmail.com> wrote:
Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
I hadn't thought about that. I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative? The mass of the
rocket is set at 30332 kg.
Its gaining energy from the gravitational potential of the moon. Once
you're past the point where the forces of gravity balance...
Negative energy = bound.
it's like a fucking flashback to 7th grade.
don't forget about the van allen belt radiation in your calculations or else
you'll be to blame when this kid gets a red mark on his homework.
--
Posted via a free Usenet account from http://www.teranews.com
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| User: "Phineas T Puddleduck" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 11:55:50 AM |
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In article <29448774.3c3NFoGDqv@unixd0rk.com>,
Artimus Q Dufflebag <artimusdufflebag@gmail.com> wrote:
Phineas T Puddleduck wrote:
In article <1176911428.872779.74420@q75g2000hsh.googlegroups.com>,
Matt <mattb95@hotmail.com> wrote:
Just a speculation.. do you need to include Chemical Potential along
with the other two energies?
Kinetic + Grav. Pot + Chem. Pot.
I hadn't thought about that. I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative? The mass of the
rocket is set at 30332 kg.
Its gaining energy from the gravitational potential of the moon. Once
you're past the point where the forces of gravity balance...
Negative energy = bound.
it's like a fucking flashback to 7th grade.
don't forget about the van allen belt radiation in your calculations or else
you'll be to blame when this kid gets a red mark on his homework.
I apologise Matt, as it seems I have something stuck to my shoe.
--
Sacred keeper of the Hollow Sphere, and the space within. Coffee boy to the
rich and famous. Proud owner of the Mop Jockey.
COOSN-174-07-82116: alt.astronomy's favourite poster (from a survey taken
of the saucerhead high command).
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| User: "Steve Willner" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 03:35:57 PM |
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Matt wrote:
I'm not too worried about what happens to
the total energy when the boost is applied, the bigger concern is why
the value rises as it approaches the Moon.
My first thought was the same as others: the Moon's potential energy.
From a later post, though, you appear to have that right. Could the
problem be numerical inaccuracy? How are you doing the orbit
integration?
I've also noticed that the absolute value of the rocket's total energy
is around -3 x 10^10 J. Why is this value negative?
Think about what energy=0 would mean. Can the rocket escape the Earth-
Moon system?
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 03:42:23 PM |
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problem be numerical inaccuracy? How are you doing the orbit
integration?
Using a Fourth Order Runge-Kutta Method
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| User: "Timo A. Nieminen" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moonsystem |
18 Apr 2007 03:30:52 PM |
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On Thu, 18 Apr 2007, Matt wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
Are you doing this with a stationary moon, or an orbiting moon?
Consider what would happen if the rocket was in a circular orbit around
the moon. When moving in the same direction as the moon, it would be
moving faster relative to the earth than when moving in the opposite
direction about the moon. The KE varies around the orbit. Of course, the
PE will vary as well, since the distance from the earth changes, this
doesn't explain it (consider two different orbits about the moon, one
where the rocket and moon move in the same direction when the rocket is
furthest from the earth, and the other when it is closest to earth).
The moon and rocket interact - the moon will speed up and slow down
relative to the earth as the rocket orbits, and the moon's KE will change.
This is where the rocket's extra KE can be coming from.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "George Dishman" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 04:03:49 PM |
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"Timo A. Nieminen" <timo@physics.uq.edu.au> wrote in message
news:Pine.WNT.4.64.0704190626220.668@serene.st...
On Thu, 18 Apr 2007, Matt wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
You are getting some detailed answers to this from people
with far more experience but thinking laterally this isn't
just a "gravitational slingshot" effect is it? An extreme
case would be to eject the craft from the system so the
total energy can certainly increase.
George
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| User: "Randy Poe" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 07:33:59 PM |
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On Apr 18, 5:03 pm, "George Dishman" <geo...@briar.demon.co.uk> wrote:
"Timo A. Nieminen" <t...@physics.uq.edu.au> wrote in messagenews:Pine.WNT.4.64.0704190626220.668@serene.st...
On Thu, 18 Apr 2007, Matt wrote:
Hey guys. I am currently working on a project to model the trajectory
of a rocket traversing the Earth-Moon system. Basically it moves from
a circular orbit about the Earth to an intercept course with the Moon
by applying an impulse or boost to it's tangential velocity.
Basically, my problem is that the total energy of the rocket in this
system (i.e. Kinetic + Gravitational Potential) is not constant.
Naturally, there is an increase when the boost is applied, but there
is also an increase as the rocket approaches the Moon, which seems
bizarre because surely the gravitational potential should become more
negative as the rocket's velocity (and thus its kinetic energy)
increases, leading to no net increase in total energy.
Does anyone have any ideas why this is happening?
You are getting some detailed answers to this from people
with far more experience but thinking laterally this isn't
just a "gravitational slingshot" effect is it? An extreme
case would be to eject the craft from the system so the
total energy can certainly increase.
I think that's exactly what Timo is suggesting is happening.
- Randy
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
19 Apr 2007 09:14:55 AM |
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So to summarise, the increase in the total energy of the rocket as it
approaches the Moon is due to the Moon's kinetic and potential energy
not being considered. The thing I'm having a problem with is that the
*only* way the kinetic energy of a rocket in freefall can increase is
when there is a corresponding decrease in the gravitational potential
between the rocket and the body in question (i.e. the Moon).
Also, where does this extra kinetic energy come from? It can't be due
to a decrease in the Moon's kinetic energy, as the Moon is also being
gravitationally attracted to the rocket. The rocket's trajectory takes
it just ahead of where the Moon will be in its orbital path, so the
Moon's kinetic energy will increase rather then decrease.
Does this increase in kinetic energy for both the rocket and the Moon
come from a decrease in the Moon's gravitational potential?
Kind Regards,
Matt
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| User: "Greg Neill" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
19 Apr 2007 11:16:36 AM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176992095.555791.106350@b75g2000hsg.googlegroups.com...
So to summarise, the increase in the total energy of the rocket as it
approaches the Moon is due to the Moon's kinetic and potential energy
not being considered. The thing I'm having a problem with is that the
*only* way the kinetic energy of a rocket in freefall can increase is
when there is a corresponding decrease in the gravitational potential
between the rocket and the body in question (i.e. the Moon).
Also, where does this extra kinetic energy come from? It can't be due
to a decrease in the Moon's kinetic energy, as the Moon is also being
gravitationally attracted to the rocket. The rocket's trajectory takes
it just ahead of where the Moon will be in its orbital path, so the
Moon's kinetic energy will increase rather then decrease.
Does this increase in kinetic energy for both the rocket and the Moon
come from a decrease in the Moon's gravitational potential?
Consider a fixed point in space that happens to lie on the
Moon's trajectory. The frame of reference is the barycenter
and is not rotating. If you were to look at the gravitational
potential at that location over time you'd see it change as the
Earth and Moon move, heading towards infinity as the Moon bears
down on it (point mass simplification).
So the potential associated with a location can change without
there being any related change in total kinetic energy anywhere
in the system! A test mass fixed at that location can find its
potential energy change without a change in its kinetic energy.
If the test mass is free to move then it will respond to the
potential, changing the KE of the test mass according to the
usual laws of physics but without any guarantee that the
change in KE is strictly proportional to the change in PE
over time. Interestingly, the behavior of the energies might
be more intuitive if you were to switch to a rotating frame
of reference in which the Earth and Moon are fixed! You
would need to incorporate another potential term associated
with the rotation proportional to the distance from the
origin.
All this aside, if you believe that the kinetic energy of
the spacecraft is not in accord with what you think it
should be given the geometry of the situation you could
have a problem with the integration. In this case you
might want to investigate its properties. Another poster
has suggested a simplified situation in which the Earth and
Moon are fixed. I would also suggest varying the size of
the timestep to see if numerical error is creeping in. An
RK integrator should be able to tolerate a goodly sized
timestep. Try a timestep of an hour rather than a second
to see what happens.
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| User: "" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
19 Apr 2007 11:47:32 AM |
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In article <462795aa$0$30330$9a6e19ea@news.newshosting.com>, "Greg Neill" <gneillREM@VEsympatico.ca> writes:
over time. Interestingly, the behavior of the energies might
be more intuitive if you were to switch to a rotating frame
of reference in which the Earth and Moon are fixed! You
would need to incorporate another potential term associated
with the rotation proportional to the distance from the
origin.
I think you'll find that centrifugal potential goes as the square
of the radius.
force = m omega^2 r
PE = 1/2 m omega^2 r^2
As a sanity check, note that this PE matches the KE of
a "motionless" object viewed from the rotating frame.
Choose an appropriate sign convention, of course.
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| User: "Greg Neill" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
19 Apr 2007 11:53:33 AM |
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<briggs@encompasserve.org> wrote in message news:gpYnp$w$xwgj@eisner.encompasserve.org...
In article <462795aa$0$30330$9a6e19ea@news.newshosting.com>, "Greg Neill"
<gneillREM@VEsympatico.ca> writes:
over time. Interestingly, the behavior of the energies might
be more intuitive if you were to switch to a rotating frame
of reference in which the Earth and Moon are fixed! You
would need to incorporate another potential term associated
with the rotation proportional to the distance from the
origin.
I think you'll find that centrifugal potential goes as the square
of the radius.
force = m omega^2 r
PE = 1/2 m omega^2 r^2
As a sanity check, note that this PE matches the KE of
a "motionless" object viewed from the rotating frame.
Choose an appropriate sign convention, of course.
D'oh! Of course. I was writing faster than I was
thinking. Again.
Cheers.
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 03:47:23 PM |
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Are you doing this with a stationary moon, or an orbiting moon?
An orbiting Moon. It's in a circular orbit about the Earth-Moon
barycentre.
Consider what would happen if the rocket was in a circular orbit around
the moon. When moving in the same direction as the moon, it would be
moving faster relative to the earth than when moving in the opposite
direction about the moon. The KE varies around the orbit. Of course, the
PE will vary as well, since the distance from the earth changes, this
doesn't explain it (consider two different orbits about the moon, one
where the rocket and moon move in the same direction when the rocket is
furthest from the earth, and the other when it is closest to earth).
The moon and rocket interact - the moon will speed up and slow down
relative to the earth as the rocket orbits, and the moon's KE will change.
This is where the rocket's extra KE can be coming from.
An interesting thought. Does this still apply when we take the
barycentre as our reference frame?
Kind Regards,
Matt
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| User: "Timo Nieminen" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moonsystem |
18 Apr 2007 05:14:59 PM |
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On Thu, 18 Apr 2007, Matt wrote:
Are you doing this with a stationary moon, or an orbiting moon?
An orbiting Moon. It's in a circular orbit about the Earth-Moon
barycentre.
Consider what would happen if the rocket was in a circular orbit around
the moon. When moving in the same direction as the moon, it would be
moving faster relative to the earth than when moving in the opposite
direction about the moon. The KE varies around the orbit. Of course, the
PE will vary as well, since the distance from the earth changes, this
doesn't explain it (consider two different orbits about the moon, one
where the rocket and moon move in the same direction when the rocket is
furthest from the earth, and the other when it is closest to earth).
The moon and rocket interact - the moon will speed up and slow down
relative to the earth as the rocket orbits, and the moon's KE will change.
This is where the rocket's extra KE can be coming from.
An interesting thought. Does this still apply when we take the
barycentre as our reference frame?
Sure. Simplifying by considering the earth to be at rest is a convenient
approximation that preserves the basic behaviour of the rocket-moon
interaction. Since the mass of the rocket is so much smaller than the mass
of the moon, the change in speed of the moon is so small, even if its
change in KE is large, that you can assume the moon moves at constant
speed.
A coordinate system in which the barycentre is at rest is better, but
shouldn't be necessary to see the effect.
Of course, it could be numerical error - for an orbit about a single
object, Verlet works better than 4th order RK (and both much, much, better
than a naive Euler method) in my experience. Whether it's just the 4th
order RK failing to give you conservation of energy, I don't know, but
it's plausible. You can test this - try it with a stationary earth and
moon and see if it still happens.
On the other hand, if the rocket gains energy as it catches up to the
moon, this is exactly what you would expect. Calculate the work done by
the rocket on the moon and see if it equals the gain in energy by the
rocket.
Anyway, it works in practice as well as in theory - gravitational
slingshot, eg, a sun-planet-probe system where the probe gains KE, and the
planet loses it.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "Matt" |
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| Title: Re: Strange Increase in the Total Energy of a Rocket in the Earth-Moon system |
18 Apr 2007 06:25:37 PM |
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Sure. Simplifying by considering the earth to be at rest is a convenient
approximation that preserves the basic behaviour of the rocket-moon
interaction. Since the mass of the rocket is so much smaller than the mass
of the moon, the change in speed of the moon is so small, even if its
change in KE is large, that you can assume the moon moves at constant
speed.
I've ocme to realise that I am not taking the kinetic energy of the
Moon into consideration (perhaps I should?). This is likely to explain
the lack of energy conservation.
A coordinate system in which the barycentre is at rest is better, but
shouldn't be necessary to see the effect.
Thankfully that's exactly what I am modelling.
Of course, it could be numerical error - for an orbit about a single
object, Verlet works better than 4th order RK (and both much, much, better
than a naive Euler method) in my experience. Whether it's just the 4th
order RK failing to give you conservation of energy, I don't know, but
it's plausible. You can test this - try it with a stationary earth and
moon and see if it still happens.
In the initial stages that is exactly what I had. The same changes
still occured. I think I'm more comfortable with the idea of it being
that I'm not considering the kinetic energy of the Moon at this time,
as I've found the RK method to be very accurate so far, which makes up
for its lack of efficiency.
Kind Regards,
Matt
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