Science > Physics > Total Energy of Rocket Increasing in Earth-Moon System
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Science > Physics |
| User: |
"Matt" |
| Date: |
18 Apr 2007 09:12:51 AM |
| Object: |
Total Energy of Rocket Increasing in 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 its 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: "Phineas T Puddleduck" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 09:36:20 AM |
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In article <1176905571.255496.110900@b58g2000hsg.googlegroups.com>,
Matt <mattb95@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 its 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?
Your system is the Earth and moon and rocket. Are you accurately modelling the
potential to include both for r? Don't forget that the rocket is gaining ke
from the decrease in pe from the moon.
--
Sacred keeper of the Hollow Sphere, and the space within. Coffee boy to the
rich and famous
COOSN-174-07-82116: alt.astronomy's favourite poster (from a survey taken
of the saucerhead high command).
.
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 10:47:44 AM |
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Your system is the Earth and moon and rocket. Are you accurately modelling the
potential to include both for r? Don't forget that the rocket is gaining ke
from the decrease in pe from the moon.
My gravitiational potential term includes both the Earth and Moon.
It's given as follows:
U = - G(M1)m/(Re) - G(M2)m/(Rm)
Where U is the gravtiational potential of the rocket at that location,
M1 is the mass of the Earth, M2 is the mass of the Moon, Re is the
rocket-Earth distance and Rm is the rocket-Moon distance.
Does this seem correct?
Kind Regards,
Matt
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| User: "CWatters" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 02:20:07 PM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176911264.404730.163960@y80g2000hsf.googlegroups.com...
My gravitiational potential term includes both the Earth and Moon.
It's given as follows:
U = - G(M1)m/(Re) - G(M2)m/(Rm)
Where U is the gravtiational potential of the rocket at that location,
M1 is the mass of the Earth, M2 is the mass of the Moon, Re is the
rocket-Earth distance and Rm is the rocket-Moon distance.
Does this seem correct?
I'm no expert but... What happens when Re is zero? U becomes very large so
it looks like somethings wrong.
Try the equation after this paragraph..
"With this simplifying assumption, integrating force over distance leads to
the following general expression for the gravitational potential energy, Ug,
of a system of two masses"
on this page...
http://en.wikipedia.org/wiki/Potential_energy
Regarding h1....(h1 is the reference level the separation at which potential
energy is considered to be zero) ...
When working out the contribution due to the earth use h1 = radius of the
earth.
Then working out the contribution due to the moon h1 = (earth moon
seperation - radus of the earth)
or something like that.
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| User: "Greg Neill" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 02:47:28 PM |
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"CWatters" <colin.watters@turnersNOSPAMoak.plus.com> wrote in message
news:46266f61$0$8744$ed2619ec@ptn-nntp-reader02.plus.net...
"Matt" <mattb95@hotmail.com> wrote in message
news:1176911264.404730.163960@y80g2000hsf.googlegroups.com...
My gravitiational potential term includes both the Earth and Moon.
It's given as follows:
U = - G(M1)m/(Re) - G(M2)m/(Rm)
Where U is the gravtiational potential of the rocket at that location,
M1 is the mass of the Earth, M2 is the mass of the Moon, Re is the
rocket-Earth distance and Rm is the rocket-Moon distance.
Does this seem correct?
I'm no expert but... What happens when Re is zero? U becomes very large so
it looks like somethings wrong.
No, it's fine. In the real world the Earth and Moon are not
point masses, so the distances between mass m and either of
M1 or M2 can never be less than their respective radii. If
somehow m were to be able to burrow into either one, then
progressively less mass would be between it and the center,
so you'd end up with a situation where you'd need to start
considering limits (mass approaches zero as radius approaches
zero).
Matt might want to inform us what kind of model he's
using to perform his calculations. Perhaps he's performing
a simple integration of the trajectory and something's
amiss with his implementation.
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:07:52 PM |
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Matt might want to inform us what kind of model he's
using to perform his calculations. Perhaps he's performing
a simple integration of the trajectory and something's
amiss with his implementation.
That is essentially all I'm doing. I was thinking the problem may be
due to the finite nature of numerical integration accuracy, however
the increase in total energy is from -3 x 10^8 J to -2.5 x 10^8 J, so
it's an appreciable difference and I don't think my Fourth Order
Method could cause that alone.
Kind Regards,
Matt
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| User: "Greg Neill" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:17:08 PM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176926872.189310.249090@p77g2000hsh.googlegroups.com...
Matt might want to inform us what kind of model he's
using to perform his calculations. Perhaps he's performing
a simple integration of the trajectory and something's
amiss with his implementation.
That is essentially all I'm doing. I was thinking the problem may be
due to the finite nature of numerical integration accuracy, however
the increase in total energy is from -3 x 10^8 J to -2.5 x 10^8 J, so
it's an appreciable difference and I don't think my Fourth Order
Method could cause that alone.
How detailed is your model? Are the Earth and Moon
in orbit too or are they fixed in place? What's the
frame of reference? The barycenter?
Next, what is the nature of your integrator? Is it
a simple Euler method, or perhaps a Verlet (leapfrog)
method?
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:34:02 PM |
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How detailed is your model? Are the Earth and Moon
in orbit too or are they fixed in place? What's the
frame of reference? The barycenter?
Next, what is the nature of your integrator? Is it
a simple Euler method, or perhaps a Verlet (leapfrog)
method?
The Earth and Moon are engaged in a circular orbit about their common
barycentre, both orbiting at the same angular velocity with an orbital
time period of 27.321582 days (i.e. the siderial period). Both have
the correct orbital radius from the barycentre at all times.
Therefore, the barycentre is my reference frame.
As for the integration method, I am using the 4th Order Runge-Kutta
Method.
Kind Regards,
Matt
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| User: "Greg Neill" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 04:13:34 PM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176928442.812560.30470@y80g2000hsf.googlegroups.com...
How detailed is your model? Are the Earth and Moon
in orbit too or are they fixed in place? What's the
frame of reference? The barycenter?
Next, what is the nature of your integrator? Is it
a simple Euler method, or perhaps a Verlet (leapfrog)
method?
The Earth and Moon are engaged in a circular orbit about their common
barycentre, both orbiting at the same angular velocity with an orbital
time period of 27.321582 days (i.e. the siderial period). Both have
the correct orbital radius from the barycentre at all times.
Therefore, the barycentre is my reference frame.
Ah. So you're using explicit functions of time for the
positions of the Earth and Moon, and integrating the
projectile trajectory.
As for the integration method, I am using the 4th Order Runge-Kutta
Method.
That should be accurate enough not to be able to see
any large fluctuations in the total mechanical energy
of the system. Are you using a fixed or variable time
step?
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 04:18:13 PM |
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That should be accurate enough not to be able to see
any large fluctuations in the total mechanical energy
of the system. Are you using a fixed or variable time
step?
A fixed timestep of 1 second.
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| User: "Greg Neill" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 04:25:44 PM |
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"Matt" <mattb95@hotmail.com> wrote in message
news:1176931092.969403.155950@l77g2000hsb.googlegroups.com...
That should be accurate enough not to be able to see
any large fluctuations in the total mechanical energy
of the system. Are you using a fixed or variable time
step?
A fixed timestep of 1 second.
Is this your own coded algorithm or a packaged
product you're using for the integrator?
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 06:19:19 PM |
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Is this your own coded algorithm or a packaged
product you're using for the integrator?
It is my own, but I've been given instructions on how the Runge-Kutta
method should be implemented
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| User: "" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
19 Apr 2007 09:55:25 AM |
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In article <1176928442.812560.30470@y80g2000hsf.googlegroups.com>, Matt <mattb95@hotmail.com> writes:
The Earth and Moon are engaged in a circular orbit about their common
barycentre,
*BINGO*
There's your problem. (Or at least one of your problems).
If the Moon and the Earth are orbitting their barycenter then neither
is fixed in place. It follows that NEITHER ONE HAS A UNIQUELY DEFINED
STATIC GRAVITATIONAL POTENTIAL FIELD! The energy imparted by a
time-varying gravitational field is not trajectory-independent.
Gravitational slingshot is incompatible with static gravitational potential.
Gravitational slingshot works.
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| User: "Artimus Q Dufflebag" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 10:13:14 AM |
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Phineas T Puddleduck wrote:
In article <1176905571.255496.110900@b58g2000hsg.googlegroups.com>,
Matt <mattb95@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 its 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?
Your system is the Earth and moon and rocket. Are you accurately modelling
the potential to include both for r? Don't forget that the rocket is
gaining ke from the decrease in pe from the moon.
wow, you teach 6th grade physics too?
impressive.
--
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: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 09:52:57 AM |
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In article <2112933.leMgFpV67D@unixd0rk.com>,
Artimus Q Dufflebag <artimusdufflebag@gmail.com> wrote:
Your system is the Earth and moon and rocket. Are you accurately modelling
the potential to include both for r? Don't forget that the rocket is
gaining ke from the decrease in pe from the moon.
wow, you teach 6th grade physics too?
impressive.
Wow. You really are obsessed.
--
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: "John \C" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 10:18:03 AM |
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"Phineas T Puddleduck" <phineaspuddleduck@gmail.com> wrote in message
news:phineaspuddleduck-9BD8D9.15525718042007@news.octanews.com...
In article <2112933.leMgFpV67D@unixd0rk.com>,
Artimus Q Dufflebag <artimusdufflebag@gmail.com> wrote:
Your system is the Earth and moon and rocket. Are you accurately
modelling
the potential to include both for r? Don't forget that the rocket is
gaining ke from the decrease in pe from the moon.
wow, you teach 6th grade physics too?
impressive.
Wow. You really are obsessed.
Wow. You really are Gay.
HJ
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| User: "Artimus Q Dufflebag" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 10:27:32 AM |
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Phineas T Puddleduck wrote:
In article <2112933.leMgFpV67D@unixd0rk.com>,
Artimus Q Dufflebag <artimusdufflebag@gmail.com> wrote:
Your system is the Earth and moon and rocket. Are you accurately
modelling the potential to include both for r? Don't forget that the
rocket is gaining ke from the decrease in pe from the moon.
wow, you teach 6th grade physics too?
impressive.
Wow. You really are obsessed.
yeah. i perch way up above in the clouds and swoop down on alt.astronomy to
pounce on unsuspecting tards... oh wait... that's you.
--
Posted via a free Usenet account from http://www.teranews.com
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| User: "Starlord" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 11:50:52 AM |
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It's supper simple and any grade school kid would know it. When you past the
point where the weaker force of the moon takes over, you are falling towards
the moon faster. NASA userstands this very much as it had to be adjusted for
in each of the manned flights to the moon.
--
There are those who believe that life here, began out there, far across the
universe, with tribes of humans, who may have been the forefathers of the
Egyptians, or the Toltecs, or the Mayans. Some believe that they may yet be
brothers of man, who even now fight to survive, somewhere beyond the
heavens.
The Lone Sidewalk Astronomer of Rosamond
Telescope Buyers FAQ
http://home.inreach.com/starlord
Sidewalk Astronomy
www.sidewalkastronomy.info
The Church of Eternity
http://home.inreach.com/starlord/church/Eternity.html
AD World
http://www.adworld.netfirms.com/
"Matt" <mattb95@hotmail.com> wrote in message
news:1176905571.255496.110900@b58g2000hsg.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 its 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: "Borked Pseudo Mailed" |
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| Title: Re: Total Energy of Dennis Bishop SPAM Increasing Up Your Black Arsehole |
18 Apr 2007 02:32:32 PM |
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mulatto boy niggertard <starlord@sidewalkastronomy.info> felched a gerbil:
Itss upper spam leand ayy grade spam scool smap wuld now it when you pust the
pong where the week the festering pustule on my arsehole got badly inflamed after our
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fawking arsehole my spam i stalk i am a barmy fawking drunken self pity thirty percent
cripple bum my butt ugly nappy headed neegriss crack ***** ex moved to watts
tard my godshite fuster NASA userstands i am the fawking spelling bee champion of
rosatard with my ickle red wagon shite my arsehole had to be adjusted for the
gerbil tube in each of the manned buggering up my full moon
I am shitetard i am a 70 iq spamming arsehole please donate to my lager fund
you fawking arsehole my bisexual daddy and crack ***** niger mum used to take turns
nursing my little johnson my mum used the strap on but my daddy used the real
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what no antelope valley trailer trash weather centre report today shitetard
now we know how your arsehole got so big
astronomers whip out their chubby telescopes and investigate uranus at night in the
dark at their nancy buggering poofter parties star parties because when they
felch dennis bishops gerbils at the end they see fawking stars ooh aah
"Matt" <mattb95@hotmail.com> wrote in message
news:1176905571.255496.110900@b58g2000hsg.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 its 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: "Sam Wormley" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 09:16:38 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 its 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: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 10:01:45 AM |
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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
I had trouble signing up, so I'd prefer a text response if possible.
Kind Regards,
Matt
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| User: "Randy Poe" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 11:55:49 AM |
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On Apr 18, 10:12 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 its 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.
When coasting (no boost) how are you determining changes
in rocket KE, if not getting them from calculating the change
in PE?
- Randy
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:08:33 PM |
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When coasting (no boost) how are you determining changes
in rocket KE, if not getting them from calculating the change
in PE?
By calculating the kinetic energy of the rocket from the rocket's
velocity at each point in time.
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| User: "Randy Poe" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:17:48 PM |
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On Apr 18, 4:08 pm, Matt <matt...@hotmail.com> wrote:
When coasting (no boost) how are you determining changes
in rocket KE, if not getting them from calculating the change
in PE?
By calculating the kinetic energy of the rocket from the rocket's
velocity at each point in time.
And you're getting the velocity at each point in time by...?
Perhaps by integrating the acceleration due to the gravitational
forces?
Perhaps it would help if you sketched out your entire calculation
once instead of having us try to guess at it line by line.
- Randy
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:40:26 PM |
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And you're getting the velocity at each point in time by...?
Perhaps by integrating the acceleration due to the gravitational
forces?
That is exactly what I'm doing :)
The acceleration formula I'm using is given as follows:
d2x/dt2 = - G * Me * [ (x-xe) / (de^3) ] - G * Mm * [ (x-xm) /
(dm^3) ]
where:
de = sqrt[ (x-xe)^2 + (y-ye)^2 ]
dm = sqrt[ (x-xm)^2 + (y-ym)^2 ]
xe is the x-axis distance between the Earth and the barycentre and ye
is the y-axis distance between the Earth and the barycentre. The same
applies for xm and ym, except it's the Moon-barycentre distance this
time.
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| User: "arvee" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 07:32:45 PM |
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On Apr 18, 1:40 pm, Matt <matt...@hotmail.com> wrote:
And you're getting the velocity at each point in time by...?
Perhaps by integrating the acceleration due to the gravitational
forces?
That is exactly what I'm doing :)
The acceleration formula I'm using is given as follows:
d2x/dt2 = - G * Me * [ (x-xe) / (de^3) ] - G * Mm * [ (x-xm) /
(dm^3) ]
where:
de = sqrt[ (x-xe)^2 + (y-ye)^2 ]
dm = sqrt[ (x-xm)^2 + (y-ym)^2 ]
xe is the x-axis distance between the Earth and the barycentre and ye
is the y-axis distance between the Earth and the barycentre. The same
applies for xm and ym, except it's the Moon-barycentre distance this
time.
So, are you integrating the coupled first-order system
dx/dt = vx,
dvx/dt = - G * Me * [ (x-xe) / (de^3) ] - G * Mm * [ (x-xm) /
(dm^3) ] ,
dy/dt = vy,
dvy/dt = - G * Me * [ (y-ye) / (de^3) ] - G * Mm * [ (y-ym) /
(dm^3) ] ?
Since you are not allowing the satellite to alter the motions of the
Earth and Moon, your Earth and Moon are acting like external, moving
forces. Why should the total energy of the satellite (alone) remain
constant in such a case?
R.G. Vickson
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| User: "Matt" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
19 Apr 2007 09:16:00 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: "Steve Willner" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
25 Apr 2007 11:48:22 AM |
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Matt wrote:
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).
It's the _total_ energy of the Moon that compensates. (There's a tiny
contribution from the total energy of the Earth as well.) The
conserved quantity is the total energy of the system.
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.
It sounds as though the Moon's potential energy should increase and
its kinetic energy should decrease. This would make the rocket's
total energy decrease. It's hard to say for sure, though, without
knowing more details. Alternatively, I may simply be confused.
Orbits are tricky!
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| User: "arvee" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
19 Apr 2007 09:56:43 AM |
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On Apr 19, 7:16 am, Matt <matt...@hotmail.com> wrote:
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.
Your model does not account for this. If I understand correctly, your
Earth and Moon just go around in orbits determined by one another. At
that point (after fixing the orbits) you throw in the rocket. E and M
are just two moving sources. In a Hamiltonian formulation, the energy
H satisfies dH/dt = @H/@t (@ = partial derivative). Normally, H does
not contain t explicitly, so @H/@t = 0, hence dH/dt = 0, hence total
energy H is conserved. In your case, the E and M locations are
(xe(t),ye(t)) and (xm(t),ym(t)), so the potentials Ve and Vm are time-
dependent. You have @H/@t <> 0, so H is not constant.
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.
The Moon is not being affected at all by the rocket, at least, not in
the way you have told us your model works. If you allow the Moon and
the Earth to also be affected by the rocket, you have a true three-
body problem, and that's a lot harder. Even then, the total system
energy will be conserved, not that of the individual constituents such
as the rocket separately, etc.
Try this: make a modified model in which the Earth and the Moon are
stationary. See if the rocket gains or loses total energy after the
engine is shut down and it goes into 'free fall'. If you find non-
conservation, that would be an effect of discretizing the DE. Probably
_some_ energy non-conservation is to be expected, but you would hope
that it is small. If not small, that is something to be worried about.
This bring up an interesting research question: can one devise a
numerical DE solving method that accurately preserves quantities that
are supposed to be conserved? I have not seen any such. There's a good
Masters' or PhD topic for somebody to work on!
R.G. Vickson
Adjunct Professor, University of Waterloo
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: Total Energy of Rocket Increasing in Earth-Moon System |
19 Apr 2007 10:45:43 AM |
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"arvee" <C6L1V@shaw.ca> wrote in message
news:1176994603.122278.226980@b75g2000hsg.googlegroups.com...
This bring up an interesting research question: can one devise a
numerical DE solving method that accurately preserves quantities that
are supposed to be conserved? I have not seen any such. There's a good
Masters' or PhD topic for somebody to work on!
While no numerical integrator is perfect, there are some
that are 'symplectic' (google 'symplectic integrator')
and have the property that they conserve a quantity
that is very much like the total energy. More specifically,
they conserve a Hamiltonian that is slightly perturbed from
the original one that describes the given system.
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| User: "Randy Poe" |
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| Title: Re: Total Energy of Rocket Increasing in Earth-Moon System |
18 Apr 2007 03:27:29 PM |
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On Apr 18, 4:08 pm, Matt <matt...@hotmail.com> wrote:
When coasting (no boost) how are you determining changes
in rocket KE, if not getting them from calculating the change
in PE?
By calculating the kinetic energy of the rocket from the rocket's
velocity at each point in time.
Are you using distances from the center of each body in
all calculations?
You should be able to do a simple sanity check: At two
different neighboring points in your trajectory, give Re, Rm,
and both PE and force terms, as well as what you used
for velocity and acceleration at both times.
Force is supposed to be the gradient of PE. We could
check that. We could also validate F = ma and that
a = dv/dt.
- Randy
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