### Author Topic: Change satellite speed without changing its trajectory  (Read 5515 times)

#### hclatomic

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##### Change satellite speed without changing its trajectory
« on: 08/05/2017 10:54 AM »
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

#### Jim

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##### 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)

#### imfan

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##### 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 »

#### hclatomic

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##### 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

#### hclatomic

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##### 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

#### imfan

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##### 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

#### Jim

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##### 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

#### Proponent

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##### 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.

#### hclatomic

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##### 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

#### meberbs

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##### 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.

#### ejb749

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##### 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!

#### laszlo

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##### 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?

#### hclatomic

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##### 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.

#### meberbs

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##### 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.

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##### 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 »

#### Jim

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##### 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.

#### hclatomic

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##### 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.

#### Idur

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##### 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.

#### meberbs

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##### 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 »

#### Jim

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##### 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.

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