Author Topic: Change satellite speed without changing its trajectory  (Read 2140 times)

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
If a satellite is on a circular orbit, is it possible to increase its speed (by the mean of its engine) by keeping it on the same circualr orbit ? If so, what should be the direction of the engine thrust ?
Some references of the litterature explaining this possibility, or impossibility, will be welcome.

Thanks

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #1 on: 08/05/2017 12:57 PM »
No, any change in the speed of satellite is going to change the orbital altitude. 

However, one can change the velocity of a satellite with thrust and not change the altitude.  The key is that velocity is a vector quantity (speed and direction). The inclination of the orbit can be changed by thrusting at the proper angles to keep orbit at the same altitude (and same speed)

Offline imfan

  • Member
  • Full Member
  • *
  • Posts: 179
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #2 on: 08/05/2017 01:12 PM »
If you increase spacecraft velocity above circular orbital velocity the orbit changes to eliptical one and the spacraft would start climbing towards apogee. This could  be countered by applying thrust radialy towards body it is orbiting. However to do this would require constant fuel expenditure.
« Last Edit: 08/05/2017 01:13 PM by imfan »

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #3 on: 08/05/2017 01:50 PM »
No, any change in the speed of satellite is going to change the orbital altitude. 

However, one can change the velocity of a satellite with thrust and not change the altitude.  The key is that velocity is a vector quantity (speed and direction). The inclination of the orbit can be changed by thrusting at the proper angles to keep orbit at the same altitude (and same speed)

Actually only the same orbital plane interest me.

Do you mean that if I stay in the same orbital plane, any speed change will change the orbit for an ellipse (or parabola or hyperbola), but if I want to change the orbital plane I can make it with an appropriate thrust ?

Would you have a reference in the litterature that explicitely states this (for the same plane) ?

Thanks


Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #4 on: 08/05/2017 01:51 PM »
If you increase spacecraft velocity above circular orbital velocity the orbit changes to eliptical one and the spacraft would start climbing towards apogee. This could  be countered by applying thrust radialy towards body it is orbiting. However to do this would require constant fuel expenditure.

Would you have a reference in the litterature that explicitely states this ?

Thanks

Offline imfan

  • Member
  • Full Member
  • *
  • Posts: 179
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #5 on: 08/05/2017 02:07 PM »
If you increase spacecraft velocity above circular orbital velocity the orbit changes to eliptical one and the spacraft would start climbing towards apogee. This could  be countered by applying thrust radialy towards body it is orbiting. However to do this would require constant fuel expenditure.

Would you have a reference in the litterature that explicitely states this ?

Thanks

No, but it cen be easily derived. Since circular orbit is a result from balancing gravitational and centrifugal force, by adding force (thrust) in direction of the gravity force you have to also increase velocity to increase the centrifugal force to maintain the balance

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #6 on: 08/05/2017 03:41 PM »
No, any change in the speed of satellite is going to change the orbital altitude. 

However, one can change the velocity of a satellite with thrust and not change the altitude.  The key is that velocity is a vector quantity (speed and direction). The inclination of the orbit can be changed by thrusting at the proper angles to keep orbit at the same altitude (and same speed)

Actually only the same orbital plane interest me.

Do you mean that if I stay in the same orbital plane, any speed change will change the orbit for an ellipse (or parabola or hyperbola), but if I want to change the orbital plane I can make it with an appropriate thrust ?

Would you have a reference in the litterature that explicitely states this (for the same plane) ?

Thanks

No, just knowledge of orbital mechanics

Offline Proponent

  • Senior Member
  • *****
  • Posts: 5063
  • Liked: 751
  • Likes Given: 511
Re: Change satellite speed without changing its trajectory
« Reply #7 on: 08/06/2017 05:25 AM »
With continuous thrust, it would be possible to increase speed while remaining on the same circular trajectory.  An initial impulse along the direction of motion would accelerate the satellite, and sustained thrust toward the center of the planet would keep it on the original trajectory.

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #8 on: 08/07/2017 02:47 PM »
With continuous thrust, it would be possible to increase speed while remaining on the same circular trajectory.  An initial impulse along the direction of motion would accelerate the satellite, and sustained thrust toward the center of the planet would keep it on the original trajectory.
You use a conditional sentence, so is it an opinion or would you have a reference in the litterature that explains this possibility ?

As far as I know, and read for instance here :
"An Introduction to Vectors, Vector Operators and Vector Analysis", paragraph 12.4.3, p473,https://books.google.fr/books?id=sQlQDQAAQBAJ&pg=PA474&lpg=PA474&dq=change+satellite+speed&source=bl&ots=UwFb8eWC1R&sig=GOICxdgdOZp_Bb60OCVSIn0mqgA&hl=en&sa=X&ved=0ahUKEwisj9Dw-L_VAhVjF8AKHSfeD604FBDoAQhKMAc#v=onepage&q=change%20satellite%20speed&f=false
It is not possible to give a thrust an a circular orbit by staying on this orbit, which is automatically changed in an ellipse. And this aplies to an impulsional as well as a low thrust problem.

So can you give me a reference in the literature about what you said ?

Thanks

Online meberbs

  • Full Member
  • ****
  • Posts: 1133
  • Liked: 1052
  • Likes Given: 273
Re: Change satellite speed without changing its trajectory
« Reply #9 on: 08/07/2017 03:02 PM »
With continuous thrust, it would be possible to increase speed while remaining on the same circular trajectory.  An initial impulse along the direction of motion would accelerate the satellite, and sustained thrust toward the center of the planet would keep it on the original trajectory.
You use a conditional sentence, so is it an opinion or would you have a reference in the litterature that explains this possibility ?
You keep asking for literature references for things that are simply basic facts about orbital mechanics that people familiar with orbital mechanics clearly understand. If you continuously fire a thruster directly towards the Earth, this adds to the force of gravity, meaning you need a faster velocity to stay in the same circular orbit. Combined with an initial impulse to increase your velocity, you could travel faster while maintaining the same orbit at least until you run out of fuel.

This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Offline ejb749

  • Member
  • Posts: 33
  • Troy, MI
  • Liked: 24
  • Likes Given: 3
Re: Change satellite speed without changing its trajectory
« Reply #10 on: 08/07/2017 03:24 PM »
Looks like someone has never played with the Kerbel Space Program!

https://kerbalspaceprogram.com

A few hours of playing this, and you'll know enough about orbital dynamics to be dangerous!

Offline laszlo

  • Full Member
  • *
  • Posts: 136
  • Liked: 153
  • Likes Given: 25
Re: Change satellite speed without changing its trajectory
« Reply #11 on: 08/07/2017 03:34 PM »
hclatomic,

You wouldn't be trying to get us to do your homework for you, would you?  :)

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #12 on: 08/07/2017 03:36 PM »
You keep asking for literature references for things that are simply basic facts about orbital mechanics that people familiar with orbital mechanics clearly understand. If you continuously fire a thruster directly towards the Earth, this adds to the force of gravity, meaning you need a faster velocity to stay in the same circular orbit. Combined with an initial impulse to increase your velocity, you could travel faster while maintaining the same orbit at least until you run out of fuel.

This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Sorry to ask for references but the answers above are contradictory, and the link that I give above says that you can not stay on the circular orbit by thrusting in any direction. So who should I believe ?
As far as I know in science any statement has to be proven, with either a demonstration or a reference of the literature. Do you think that I could refere to your post in a scientific paper that only says "meberbs, at forum.nasaspaceflight.com, stated so" ? I would be very happy if I could but I figure out that it won't do it.
This is why I am looking for references. Sorry for that.


Online meberbs

  • Full Member
  • ****
  • Posts: 1133
  • Liked: 1052
  • Likes Given: 273
Re: Change satellite speed without changing its trajectory
« Reply #13 on: 08/07/2017 03:47 PM »
Sorry to ask for references but the answers above are contradictory, and the link that I give above says that you can not stay on the circular orbit by thrusting in any direction. So who should I believe ?
Both, there is no contradiction. In the case I described, as soon as you turn off the thrust (run out of fuel) you end up in an elliptical orbit.

You wouldn't cite anything for this in a scientific paper. If you felt for some reason just stating it as a fact isn't enough (your audience for a typical paper shouldn't need this explained) you could write down
F = m*a
mu*m/r^2 + T = m*v^2/r
where mu is the gravitational parameter, m is the satellite mass, r is the orbit radius, T is the continuous applied thrust, and v is the orbital speed.

Offline Nomadd

  • Senior Member
  • *****
  • Posts: 2552
  • Boca Chica, Texas
  • Liked: 3058
  • Likes Given: 211
Re: Change satellite speed without changing its trajectory
« Reply #14 on: 08/07/2017 03:48 PM »
You keep asking for literature references for things that are simply basic facts about orbital mechanics that people familiar with orbital mechanics clearly understand. If you continuously fire a thruster directly towards the Earth, this adds to the force of gravity, meaning you need a faster velocity to stay in the same circular orbit. Combined with an initial impulse to increase your velocity, you could travel faster while maintaining the same orbit at least until you run out of fuel.

This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Sorry to ask for references but the answers above are contradictory, and the link that I give above says that you can not stay on the circular orbit by thrusting in any direction. So who should I believe ?
As far as I know in science any statement has to be proven, with either a demonstration or a reference of the literature. Do you think that I could refere to your post in a scientific paper that only says "meberbs, at forum.nasaspaceflight.com, stated so" ? I would be very happy if I could but I figure out that it won't do it.
This is why I am looking for references. Sorry for that.


You're in a circular orbit right now, maintained by the earth thrusting (wrong term, I know) on your feet. No difference 200 miles up if you use an engine instead of the ground. With constant thrust, you can do anything you want.
« Last Edit: 08/07/2017 03:52 PM by Nomadd »

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #15 on: 08/07/2017 03:50 PM »

Sorry to ask for references but the answers above are contradictory, and the link that I give above says that you can not stay on the circular orbit by thrusting in any direction. So who should I believe ?


No, they aren't.  You never made a distinction between constantly thrusting and a short thruster burn.

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #16 on: 08/07/2017 04:13 PM »
I need solid references to include into a paper. I am ready to believe anything you tell me here, but my belief won't be enough. I am searching everywhere on the internet but I can not find nowhere a scientific description of a thrusted satellite that remains on its circular orbit.
At the contrary all the books and paper are describing thrusts that change the orbit, wether the thrust is impulsional or low and continuous. Here is an other example :
Fundamentals of Astrodynamics, Karel F. Wakker, paragraph 19.3 and 19.4
https://www.researchgate.net/publication/272507882_Fundamentals_of_Astrodynamics

This is why I ask you here if you can drive me to formal scientific evidences and demonstrations of how to perform a satellite acceleration by staying on the same circular orbit. My aim is not to offence any one, but just to get some solid scientific evidences.

Offline Idur

  • Member
  • Posts: 1
  • Liked: 1
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #17 on: 08/07/2017 04:18 PM »
I think laszlo is on to something:

hclatomic,

You wouldn't be trying to get us to do your homework for you, would you?  :)

If this is homework, you can ask for help, of course. The key thing is that you ask questions about "Orbital Mechanics".
A quick search turned up this: http://space.au.af.mil/au-18-2009/au-18_chap06.pdf
It explains how you can change orbits.

The answer for your original question depends: can you/are you allowed to use your engine after you changed the speed of your satellite, so you keep changing the velocity without changing the speed (so you change only the direction of your velocity vector). If you can't keep using the engine, Jim's anwer is final. If you can, you should work out the details of imfan's proposal.

You say you cannot change the orbit. Since using your engine like imfan proposes is, in a way, constantly changing your orbit, I'd say Jim's answer is the best one.

Online meberbs

  • Full Member
  • ****
  • Posts: 1133
  • Liked: 1052
  • Likes Given: 273
Re: Change satellite speed without changing its trajectory
« Reply #18 on: 08/07/2017 04:22 PM »
I need solid references to include into a paper. I am ready to believe anything you tell me here, but my belief won't be enough. I am searching everywhere on the internet but I can not find nowhere a scientific description of a thrusted satellite that remains on its circular orbit.
At the contrary all the books and paper are describing thrusts that change the orbit, wether the thrust is impulsional or low and continuous.

That would be because there is basically no reason to bother wasting fuel doing this. Even ion thrusters couldn't keep doing it for long, and the existing ones are too low thrust to make a significant difference anyway.

This is why I ask you here if you can drive me to formal scientific evidences and demonstrations of how to perform a satellite acceleration by staying on the same circular orbit.
That would be the basic physics equation I wrote down. Math is the most fundamental of ways to get scientific evidence. It is based equations found in any intro to physics textbook, so it needs no citations, and neither does any simple mathematical derivations based on it. If you can't derive this equation yourself, you really shouldn't be writing a paper on orbital mechanics.

Edit: As Idur suggested above, if you are trying to learn orbital mechanics, you can ask questions so that you learn how to derive the relevant equations for yourself.
« Last Edit: 08/07/2017 04:26 PM by meberbs »

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #19 on: 08/07/2017 04:40 PM »
I remember doing a problem where somebody wanted a halo orbit at GSO altitude over the north pole. The propellant usage was unreal for no matter what the ISP was.

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #20 on: 08/07/2017 04:43 PM »
I need solid references to include into a paper. I am ready to believe anything you tell me here, but my belief won't be enough. I am searching everywhere on the internet but I can not find nowhere a scientific description of a thrusted satellite that remains on its circular orbit.


You haven't given us enough data or purpose.  What are you trying to do with this "thrusted satellite that remains on its circular orbit."? 

Offline Stan-1967

  • Full Member
  • ****
  • Posts: 457
  • Denver, Colorado
  • Liked: 236
  • Likes Given: 160
Re: Change satellite speed without changing its trajectory
« Reply #21 on: 08/07/2017 04:46 PM »
I need solid references to include into a paper. I am ready to believe anything you tell me here, but my belief won't be enough. I am searching everywhere on the internet but I can not find nowhere a scientific description of a thrusted satellite that remains on its circular orbit.
At the contrary all the books and paper are describing thrusts that change the orbit, wether the thrust is impulsional or low and continuous. Here is an other example :
Fundamentals of Astrodynamics, Karel F. Wakker, paragraph 19.3 and 19.4
https://www.researchgate.net/publication/272507882_Fundamentals_of_Astrodynamics

This is why I ask you here if you can drive me to formal scientific evidences and demonstrations of how to perform a satellite acceleration by staying on the same circular orbit. My aim is not to offence any one, but just to get some solid scientific evidences.

Here is a "proof" for you:

Your condition of a satellite accelerating ( increasing/decreasing velocity) over a planetary surface, while also maintaining a given altitude only work out in a system where the planet surface is an infinitely long, & massless flat plate. 

If you can find a condition like that in the universe, what you are proposing is possible.


edit:  The rest of the "universe" in which this happens must also contain zero mass, so as to not perturb your satellites trajectory.
« Last Edit: 08/07/2017 04:48 PM by Stan-1967 »

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #22 on: 08/07/2017 04:56 PM »
May be I should precise that I am not looking for help with a homework but that I have some skills about orbital mechanics. See here for instance : http://vixra.org/pdf/1504.0128v2.pdf, and this work led to the building of an impulsional space transfer simulator, here : http://www.hclatom.net/transferSimulator/

From the theorem of the keplerian kinematics (theorem, not theory), it is very simple to prove that thrusting on a circular orbit can not leave the satellite into its circular orbit, in no way at all. What I am interesting in is to have this demonstration done from the newtonian mechanics, instead of the kinematics, if it is possible.

Offline DarkenedOne

  • Full Member
  • ****
  • Posts: 930
  • Liked: 48
  • Likes Given: 6
Re: Change satellite speed without changing its trajectory
« Reply #23 on: 08/07/2017 04:57 PM »
You keep asking for literature references for things that are simply basic facts about orbital mechanics that people familiar with orbital mechanics clearly understand. If you continuously fire a thruster directly towards the Earth, this adds to the force of gravity, meaning you need a faster velocity to stay in the same circular orbit. Combined with an initial impulse to increase your velocity, you could travel faster while maintaining the same orbit at least until you run out of fuel.

This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Sorry to ask for references but the answers above are contradictory, and the link that I give above says that you can not stay on the circular orbit by thrusting in any direction. So who should I believe ?
As far as I know in science any statement has to be proven, with either a demonstration or a reference of the literature. Do you think that I could refere to your post in a scientific paper that only says "meberbs, at forum.nasaspaceflight.com, stated so" ? I would be very happy if I could but I figure out that it won't do it.
This is why I am looking for references. Sorry for that.


You're in a circular orbit right now, maintained by the earth thrusting (wrong term, I know) on your feet. No difference 200 miles up if you use an engine instead of the ground. With constant thrust, you can do anything you want.

I think people are adding a great deal of confusion here.  If you have a satellite that is not currently thrusting then its motion will be governed strictly by orbital mechanics.  The only forces on the spacecraft the force of gravity and the centrifugal force.  I have linked to a nice tutorial on orbital mechanics below.  Kepler's 3rd law of orbital dynamics states that "the squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits."  Since orbital period (the time it takes to complete one orbit) is directly related to the velocity, you can easily deduce that any two objects with the same trajectory have to share the same velocity.  We can come to this conclusion assuming that no other forces are acting on the satellite.
http://www.braeunig.us/space/orbmech.htm
https://en.wikipedia.org/wiki/Orbital_mechanics#Laws_of_astrodynamics

Of course Proponent decided to complicate things, and say that this can be achieved if the spacecraft is continuously thrusting.  It is true because you have added this third force created by thrusting that will counter the forces of gravity and the centrifugal force.  The problem with this idea is that satellite operators practically never do so.  Fuel on satellites is a precious resource that can't be replenished.  Great time and care is taken to plan every satellite maneuver in order to conserve as much fuel as possible.  Realistically no satellite can maneuver like this for very long to any significant degree before running out of fuel.

So to answer your question the technically yes, but practically no.  A satellite that is thrusting can manage to do this for a short period of time until it runs out of fuel.  A satellite that is not powered cannot because you cannot have two unpowered objects on the same trajectory, but with a different velocity.

« Last Edit: 08/07/2017 05:01 PM by DarkenedOne »

Offline DarkenedOne

  • Full Member
  • ****
  • Posts: 930
  • Liked: 48
  • Likes Given: 6
Re: Change satellite speed without changing its trajectory
« Reply #24 on: 08/07/2017 05:22 PM »
May be I should precise that I am not looking for help with a homework but that I have some skills about orbital mechanics. See here for instance : http://vixra.org/pdf/1504.0128v2.pdf, and this work led to the building of an impulsional space transfer simulator, here : http://www.hclatom.net/transferSimulator/

From the theorem of the keplerian kinematics (theorem, not theory), it is very simple to prove that thrusting on a circular orbit can not leave the satellite into its circular orbit, in no way at all. What I am interesting in is to have this demonstration done from the newtonian mechanics, instead of the kinematics, if it is possible.

It is all newtonian physics.  Keplers laws of orbital dynamics describe the motion of an object when no forces other than gravity and the centrifugal force are operating on the object. 

In a circular orbit the force of gravity and the centrifugal force are perfectly balanced.  You can increase the velocity by thrusting forward.  Of course this will increase the centrifugal force since the centrifugal force is directly related to gravity.  Normally this would cause orbit to expand as the centrifugal force grows stronger than gravity, but if you were to simultaneously thrust into the gravity well you could essentially reinforce the force of gravity.  With thrusters you can make up the difference between the two forces, and keep the spacecraft  on the same trajectory. 

Like I said before thrusting this way would be considered a stupid waste of fuel, but technically it can be done.

Offline Donosauro

  • Full Member
  • *
  • Posts: 131
  • Liked: 40
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #25 on: 08/07/2017 05:45 PM »
This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Well, a gravity train could theoretically make the trip in about 42.2 minutes: https://en.m.wikipedia.org/wiki/Gravity_train
http://www.uh.edu/engines/epi2703.htm
You probably would want to stock up on a good supply of unobtanium before starting in on this bit of extreme engineering!

Edit: added second reference.
« Last Edit: 08/07/2017 05:51 PM by Donosauro »

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #26 on: 08/07/2017 06:04 PM »

It is all newtonian physics.  Keplers laws of orbital dynamics describe the motion of an object when no forces other than gravity and the centrifugal force are operating on the object. 

In a circular orbit the force of gravity and the centrifugal force are perfectly balanced.  You can increase the velocity by thrusting forward.  Of course this will increase the centrifugal force since the centrifugal force is directly related to gravity.  Normally this would cause orbit to expand as the centrifugal force grows stronger than gravity, but if you were to simultaneously thrust into the gravity well you could essentially reinforce the force of gravity.  With thrusters you can make up the difference between the two forces, and keep the spacecraft  on the same trajectory. 

Like I said before thrusting this way would be considered a stupid waste of fuel, but technically it can be done.
If I understand what you say, the phasing maneuver (http://ccar.colorado.edu/asen5050/projects/projects_2012/bartkowicz/website/orbital_mechanics_4.html or https://en.wikipedia.org/wiki/Orbit_phasing), which is finally at the center of my question, is performed presently by changing the orbit 2 times (see the above links), but it could be done in an other way : by accelerating the satellite on its circular orbit. This last solution being too expensive in fuel, we choose the first way.

If so, I would like to have the reference of the scientific work that demonstrates this difference of cost in fuel. Such a work would certainly contain the orbital mechanics equations that I am looking for.
Thanks for help.


Online meberbs

  • Full Member
  • ****
  • Posts: 1133
  • Liked: 1052
  • Likes Given: 273
Re: Change satellite speed without changing its trajectory
« Reply #27 on: 08/07/2017 06:08 PM »
This kind of idea is the only way to travel from one side of the Earth to the exact opposite in less than about 45 minutes.

Well, a gravity train could theoretically make the trip in about 42.2 minutes: https://en.m.wikipedia.org/wiki/Gravity_train
http://www.uh.edu/engines/epi2703.htm
You probably would want to stock up on a good supply of unobtanium before starting in on this bit of extreme engineering!

Edit: added second reference.
I almost mentioned that concept, although I didn't know it was the "gravity train" name for it.

The 45 minutes was approximate, the lower the orbit altitude the shorter the period. Because the semi-major axis of the orbit is the sole determinant of the period, the 42.2 minutes would also be half the period of a satellite orbiting at the Earth's surface (in a globe encircling vacuum tube :)).

Offline Jim

  • Night Gator
  • Senior Member
  • *****
  • Posts: 31158
  • Cape Canaveral Spaceport
  • Liked: 9397
  • Likes Given: 297
Re: Change satellite speed without changing its trajectory
« Reply #28 on: 08/07/2017 06:10 PM »

If so, I would like to have the reference of the scientific work that demonstrates this difference of cost in fuel.


You would have to do that yourself.  Because it is intuitive that constant burning is going to be more than two burns
« Last Edit: 08/07/2017 06:15 PM by Jim »

Online meberbs

  • Full Member
  • ****
  • Posts: 1133
  • Liked: 1052
  • Likes Given: 273
Re: Change satellite speed without changing its trajectory
« Reply #29 on: 08/07/2017 06:17 PM »
If so, I would like to have the reference of the scientific work that demonstrates this difference of cost in fuel. Such a work would certainly contain the orbital mechanics equations that I am looking for.
Thanks for help.
The difference in fuel is so huge that people with experience in this field usually would have no reason to calculate it, it is just obvious to them. As a result, there may not be any references, but it is any easy problem to solve. If someone else doesn't beat me to it, I could work an example later, but I don't have time now.

Offline hclatomic

  • Member
  • Posts: 14
  • France
  • Liked: 0
  • Likes Given: 0
Re: Change satellite speed without changing its trajectory
« Reply #30 on: 08/07/2017 06:42 PM »
If so, I would like to have the reference of the scientific work that demonstrates this difference of cost in fuel. Such a work would certainly contain the orbital mechanics equations that I am looking for.
Thanks for help.
The difference in fuel is so huge that people with experience in this field usually would have no reason to calculate it, it is just obvious to them. As a result, there may not be any references, but it is any easy problem to solve. If someone else doesn't beat me to it, I could work an example later, but I don't have time now.

Oh Don't. If the Nasa, the ESA and the russians have chosen a solution for the phasing, against an other, there is certainly a scientific paper giving the arguments for why doing so. They are not taking any decisions without scientific calculations, evidences and argumentation.

Because all the space agencies have chosen the same method for phasing, I figure out that it is a classic of orbital mechanics that we can find it in any good academic book. But so far, I searched in many of them, and found nothing.

 



Offline Lar

  • Fan boy at large
  • Global Moderator
  • Senior Member
  • *****
  • Posts: 8162
  • Saw Gemini live on TV
  • A large LEGO storage facility ... in Michigan
  • Liked: 4915
  • Likes Given: 3338
Re: Change satellite speed without changing its trajectory
« Reply #31 on: 08/07/2017 06:56 PM »
You won't find writeups on this because  no one that understands orbital mechanics would try to do this[1]. Some things are pretty intuitively obvious and don't get derived. This is one of them. Study orbital mechanics and you'll see why.

Locked.

1 - Arguably whoever asked Jim about doing this didn't understand orbital mechanics either.
"I think it would be great to be born on Earth and to die on Mars. Just hopefully not at the point of impact." -Elon Musk
"We're a little bit like the dog who caught the bus" - Musk after CRS-8 S1 successfully landed on ASDS OCISLY

Tags: