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Elliptical orbit question



 
 
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  #1  
Old September 9th 18, 08:40 AM posted to sci.space.policy
Stuf4
external usenet poster
 
Posts: 554
Default Elliptical orbit question

From Alain Fournier:
On Sep/6/2018 at 19:23, JF Mezei wrote :
I know this is likely a newbie question but...

Say I have a satellite in elliptical orbit of 10,000km at apogee and
400km perigee.

At 400km, the satellite is going way too fast to stay at that altitude
and goes up. At 10,000km the satellite doesn't have enough speed to
remain at that altitude and will drop back in altitude.

So far correct?


Is it correct to state that the satellite's energy level is simular to
one with a circular orbit somewhere between 400km and 10,000? ( lets
say 5000 for sake of disussion).


Yes. The 5000km figure isn't right, but you have the right idea.

If, between 5000 and 400, the satellite has more speed than needed to be
in orbit, how come it continues to drop all the way down to 400km before
rising?

Or is this a case of the innertia gained falling from 10,000 to 5000
will make the satellite w3ant to continue in the same direction towards
earth until the "slinghot" cause it to change direction and turn around
and rise up in altitude again?


I'm not sure exactly what you mean by slingshot, but for the rest you
have the right idea. Somewhere between 400km and 10,000km the satellite
will have enough speed to achieve a circular orbit at that altitude, but
that speed will not be in the right direction. Therefore as you said
because of inertia, it will continue in that direction. Earth will
slowly change its direction, Earth pulling it always towards Earth. But
because it is going too fast, Earth will not be pulling it fast enough
to compensate the fact that it isn't going straight towards Earth. So as
it gets closer to Earth it will be pointing less and less towards Earth
(I'm simplifying a little here) until it reaches perigee at which point
it will actually start going further away from Earth.


It might help to think of two-body orbit dynamics in a way that most people don't think of it:

A satellite going around a planet acts like a mass hanging on the end of a spring.

Basic diagram:
https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg

Gravity pulls down on the mass, but the mass can move down and up in an oscillation. The spring is pulling up on the mass, and this is how the centripetal force works, pulling the satellite up and away from the Earth. The centripetal force is a manifestation of the inertial property of the satellite's mass.

When gravity and the centripetal force are in equilibrium, the mass remains at a constant altitude from the Earth. Circular orbits are static in this respect, in a reference frame that rotates at the same rate as the satellite is orbiting. And this is why you can bolt your DirecTV dish pointing to one point in the sky and the geometry does not change. The satellite is as still as the mass hanging on the end of the spring.

Elliptical orbits are not still. They have a continual tradeoff of Potential Energy & Kinetic Energy.

This is the situation you have in the lab, with the mass bobbing up and down on the end of the spring.

Hopefully this makes it clear exactly what is causing the altitude changes with the satellite. When the mass moves down past what would be the static equilibrium point, it has plenty of kinetic energy. And that is getting packed into "the spring" of inertia. It bottoms out at perigee when the spring force finally overcomes the motion from the gravitational force, and the direction reverses.

So yes, it is the inertia of the velocity that has built up during this downward part of the cycle that causes the altitude reversal. You can think of it as a spring that has been pulling on this satellite. You stretch the spring all the way down to perigee, and then its force will finally reverse the direction that the force of gravity was pulling in.

But from every moment that the mass was below the point of equilibrium - the altitude of the circular orbit - that spring force was greater than the force of gravity. The satellite's velocity toward the Earth was decelerating the entire time since it had passed that equilibrium point.

That equates to a flight path angle, gamma, with respect to the horizon, that was continually shallowing ever since passing that circular altitude equilibrium point. And upon passing perigee, the satellite's flight path angle goes through zero and turns from negative to positive and it starts climbing again.

Just like the mass on the spring.

~ CT
  #2  
Old September 9th 18, 08:59 AM posted to sci.space.policy
Stuf4
external usenet poster
 
Posts: 554
Default Elliptical orbit question

Oops. I misspoke. I had said "centripetal force", but I meant centrifugal force. The spring in the diagram represents the centripetal force acting on the satellite, again just a manifestation of inertia.


(And of course, the bigger picture of physics is that inertia itself is just a manifestation of a more fundamental property. As is gravity. And the biggest clue to that is in how inertial mass is indistinguishable from gravitational mass. So it is helpful to keep in mind when speaking about things like inertia, centripetal force, centrifugal force, and gravity, that these are constructs. Useful and consistent. Like in how everybody uses the terms "sunrise" & "sunset" while when we stop to think about it, we know that the phenomenon we are actually referring to is "Earth spin". The Sun is only rising from the perspective of our non-inertial reference frame of standing on the surface of the spinning planet.)

~ CT



On Sunday, September 9, 2018 at 2:40:49 AM UTC-5, Stuf4 wrote:
From Alain Fournier:
On Sep/6/2018 at 19:23, JF Mezei wrote :
I know this is likely a newbie question but...

Say I have a satellite in elliptical orbit of 10,000km at apogee and
400km perigee.

At 400km, the satellite is going way too fast to stay at that altitude
and goes up. At 10,000km the satellite doesn't have enough speed to
remain at that altitude and will drop back in altitude.

So far correct?


Is it correct to state that the satellite's energy level is simular to
one with a circular orbit somewhere between 400km and 10,000? ( lets
say 5000 for sake of disussion).


Yes. The 5000km figure isn't right, but you have the right idea.

If, between 5000 and 400, the satellite has more speed than needed to be
in orbit, how come it continues to drop all the way down to 400km before
rising?

Or is this a case of the innertia gained falling from 10,000 to 5000
will make the satellite w3ant to continue in the same direction towards
earth until the "slinghot" cause it to change direction and turn around
and rise up in altitude again?


I'm not sure exactly what you mean by slingshot, but for the rest you
have the right idea. Somewhere between 400km and 10,000km the satellite
will have enough speed to achieve a circular orbit at that altitude, but
that speed will not be in the right direction. Therefore as you said
because of inertia, it will continue in that direction. Earth will
slowly change its direction, Earth pulling it always towards Earth. But
because it is going too fast, Earth will not be pulling it fast enough
to compensate the fact that it isn't going straight towards Earth. So as
it gets closer to Earth it will be pointing less and less towards Earth
(I'm simplifying a little here) until it reaches perigee at which point
it will actually start going further away from Earth.


It might help to think of two-body orbit dynamics in a way that most people don't think of it:

A satellite going around a planet acts like a mass hanging on the end of a spring.

Basic diagram:
https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg

Gravity pulls down on the mass, but the mass can move down and up in an oscillation. The spring is pulling up on the mass, and this is how the centripetal force works, pulling the satellite up and away from the Earth. The centripetal force is a manifestation of the inertial property of the satellite's mass.

When gravity and the centripetal force are in equilibrium, the mass remains at a constant altitude from the Earth. Circular orbits are static in this respect, in a reference frame that rotates at the same rate as the satellite is orbiting. And this is why you can bolt your DirecTV dish pointing to one point in the sky and the geometry does not change. The satellite is as still as the mass hanging on the end of the spring.

Elliptical orbits are not still. They have a continual tradeoff of Potential Energy & Kinetic Energy.

This is the situation you have in the lab, with the mass bobbing up and down on the end of the spring.

Hopefully this makes it clear exactly what is causing the altitude changes with the satellite. When the mass moves down past what would be the static equilibrium point, it has plenty of kinetic energy. And that is getting packed into "the spring" of inertia. It bottoms out at perigee when the spring force finally overcomes the motion from the gravitational force, and the direction reverses.

So yes, it is the inertia of the velocity that has built up during this downward part of the cycle that causes the altitude reversal. You can think of it as a spring that has been pulling on this satellite. You stretch the spring all the way down to perigee, and then its force will finally reverse the direction that the force of gravity was pulling in.

But from every moment that the mass was below the point of equilibrium - the altitude of the circular orbit - that spring force was greater than the force of gravity. The satellite's velocity toward the Earth was decelerating the entire time since it had passed that equilibrium point.

That equates to a flight path angle, gamma, with respect to the horizon, that was continually shallowing ever since passing that circular altitude equilibrium point. And upon passing perigee, the satellite's flight path angle goes through zero and turns from negative to positive and it starts climbing again.

Just like the mass on the spring.

~ CT


  #3  
Old September 9th 18, 09:04 AM posted to sci.space.policy
Stuf4
external usenet poster
 
Posts: 554
Default Elliptical orbit question

I wrote:
Oops. I misspoke. I had said "centripetal force", but I meant centrifugal
force. The spring in the diagram represents the centripetal force acting on
the satellite, again just a manifestation of inertia.


DAMN. I misspoke two posts in a row.
Correction to the correction:

The spring in the diagram represents the _centrifugal force_ acting on the satellite, again just a manifestation of inertia.

~ CT



..



..



..





(And of course, the bigger picture of physics is that inertia itself is just
a manifestation of a more fundamental property. As is gravity. And the
biggest clue to that is in how inertial mass is indistinguishable from
gravitational mass. So it is helpful to keep in mind when speaking about
things like inertia, centripetal force, centrifugal force, and gravity, that
these are constructs. Useful and consistent. Like in how everybody uses the
terms "sunrise" & "sunset" while when we stop to think about it, we know that
the phenomenon we are actually referring to is "Earth spin". The Sun is only
rising from the perspective of our non-inertial reference frame of standing
on the surface of the spinning planet.)

~ CT



On Sunday, September 9, 2018 at 2:40:49 AM UTC-5, Stuf4 wrote:
From Alain Fournier:
On Sep/6/2018 at 19:23, JF Mezei wrote :
I know this is likely a newbie question but...

Say I have a satellite in elliptical orbit of 10,000km at apogee and
400km perigee.

At 400km, the satellite is going way too fast to stay at that altitude
and goes up. At 10,000km the satellite doesn't have enough speed to
remain at that altitude and will drop back in altitude.

So far correct?


Is it correct to state that the satellite's energy level is simular to
one with a circular orbit somewhere between 400km and 10,000? ( lets
say 5000 for sake of disussion).

Yes. The 5000km figure isn't right, but you have the right idea.

If, between 5000 and 400, the satellite has more speed than needed to be
in orbit, how come it continues to drop all the way down to 400km before
rising?

Or is this a case of the innertia gained falling from 10,000 to 5000
will make the satellite w3ant to continue in the same direction towards
earth until the "slinghot" cause it to change direction and turn around
and rise up in altitude again?

I'm not sure exactly what you mean by slingshot, but for the rest you
have the right idea. Somewhere between 400km and 10,000km the satellite
will have enough speed to achieve a circular orbit at that altitude, but
that speed will not be in the right direction. Therefore as you said
because of inertia, it will continue in that direction. Earth will
slowly change its direction, Earth pulling it always towards Earth. But
because it is going too fast, Earth will not be pulling it fast enough
to compensate the fact that it isn't going straight towards Earth. So as
it gets closer to Earth it will be pointing less and less towards Earth
(I'm simplifying a little here) until it reaches perigee at which point
it will actually start going further away from Earth.


It might help to think of two-body orbit dynamics in a way that most people don't think of it:

A satellite going around a planet acts like a mass hanging on the end of a spring.

Basic diagram:
https://i.ytimg.com/vi/lZPtFDXYQRU/maxresdefault.jpg

Gravity pulls down on the mass, but the mass can move down and up in an oscillation. The spring is pulling up on the mass, and this is how the centripetal force works, pulling the satellite up and away from the Earth. The centripetal force is a manifestation of the inertial property of the satellite's mass.

When gravity and the centripetal force are in equilibrium, the mass remains at a constant altitude from the Earth. Circular orbits are static in this respect, in a reference frame that rotates at the same rate as the satellite is orbiting. And this is why you can bolt your DirecTV dish pointing to one point in the sky and the geometry does not change. The satellite is as still as the mass hanging on the end of the spring.

Elliptical orbits are not still. They have a continual tradeoff of Potential Energy & Kinetic Energy.

This is the situation you have in the lab, with the mass bobbing up and down on the end of the spring.

Hopefully this makes it clear exactly what is causing the altitude changes with the satellite. When the mass moves down past what would be the static equilibrium point, it has plenty of kinetic energy. And that is getting packed into "the spring" of inertia. It bottoms out at perigee when the spring force finally overcomes the motion from the gravitational force, and the direction reverses.

So yes, it is the inertia of the velocity that has built up during this downward part of the cycle that causes the altitude reversal. You can think of it as a spring that has been pulling on this satellite. You stretch the spring all the way down to perigee, and then its force will finally reverse the direction that the force of gravity was pulling in.

But from every moment that the mass was below the point of equilibrium - the altitude of the circular orbit - that spring force was greater than the force of gravity. The satellite's velocity toward the Earth was decelerating the entire time since it had passed that equilibrium point.

That equates to a flight path angle, gamma, with respect to the horizon, that was continually shallowing ever since passing that circular altitude equilibrium point. And upon passing perigee, the satellite's flight path angle goes through zero and turns from negative to positive and it starts climbing again.

Just like the mass on the spring.

~ CT


 




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