Orbital Speed/Altitude

[Flieger]

Irrotational fluid flow speeds up on the inside of a turn in order to conserve angular momentum. Pressure also reduces as a result. The outside fluid slows down and pressure increases. The velocity thing (inverse relationship to radius) is opposite to a rigid body and happens with systems of particles.

[Tervuren]

Originally Posted by Superman

Let's say I am in a stable orbit at a certain speed, altitude and period. If I fire my rockets in exactly the same direction as I am moving, I will go faster. Obviously. Now, I'm going too fast to maintain my previous stable orbit. What happens? Viscerally, I would expect to go into a higher altitude orbit, but that runs contrary to the graphs. Higher orbits require LOWER speeds, and my speed is now increased increased. Increased sufficient to maintain a lower-altitude orbit. In other words, if I am to believe the graphs, and if I fire my rockets to increase speed, since I am now traveling too fast for my previous orbit, my centrifugal force would take me to a higher orbit where I am still going too fast. And so......it would seem that ANY increase in speed beyond what is required for a stable orbit at that altitude would take me to a higher and higher and higher orbit, all of which would require my speed to be slower. In other words, any firing of my rockets to propel me faster in the direction I am heading.......would cause me to escape the Earth's gravity.

Doesn't make sense.

I have the missing piece to your puzzle.

You have a table of orbital velocities. When you are in orbit, the moment you change speed, you are no longer in orbit!

If you accelerate in a forwards direction, you are over escape velocity - your object starts moving away from the earth. The farther from gravities pull, the less velocity is required to get away from the earths gravitational pull.

Orbit is a stable environment where your speed keeps you from falling back to the earth, speed up, in a direction not towards the earth while in orbit, and you move away.

[Superman]

So........if I am in a stable orbit and I speed up, in the same direction of my travel, then I will no longer be in orbit. Right? I will move further away from the Earth because of my increased velocity and inertia. Right? And as I move away, I will be moving to altitudes that require less speed for stable orbit. Since I am going faster, I will continue moving away from Earth until I deliberately accelerate in a direction toward it. Right? In other words, as you say, any acceleration in any direction that is not toward Earth will cause me to be in an 'escape' trajectory and velocity. Right?

[red-beard]

Close.

If you are in a stable orbit, and you increase velocity, you are adding energy. This will put you into a higher orbit.

See here:

Escape velocity - Wikipedia, the free encyclopedia

Because of the atmosphere it is not useful and hardly possible to give an object near the surface of the Earth a speed of 11.2 km/s (40,320 km/h), as these speeds are too far in the hypersonic regime for most practical propulsion systems and would cause most objects to burn up due to atmospheric friction or be torn apart by atmospheric compression. For an actual escape orbit a spacecraft is first placed in low Earth orbit (160–2,000 km) and then accelerated to the escape velocity at that altitude, which is a little less — about 10.9 km/s. The required change in speed, however, is far less because from a low Earth orbit the spacecraft already has a speed of approximately 8 km/s

So, if you're going 8 km/s in low earth orbit, you need to increase your speed by about 40% to 10.9 km/s to escape earth orbit. Anything less and all you do is put yourself into a different orbit.

[oldE]

Originally Posted by Superman

So........if I am in a stable orbit and I speed up, in the same direction of my travel, then I will no longer be in orbit. Right? I will move further away from the Earth because of my increased velocity and inertia. Right? And as I move away, I will be moving to altitudes that require less speed for stable orbit. Since I am going faster, I will continue moving away from Earth until I deliberately accelerate in a direction toward it. Right? In other words, as you say, any acceleration in any direction that is not toward Earth will cause me to be in an 'escape' trajectory and velocity. Right?

Almost,

If you expend enough energy to achieve escape velocity. Otherwise, Earth's gravity will do its thing and you will 'fall' into a new orbit.

Isn't this fun?
Les

[red-beard]

Supe, maybe we CAN teach on old dog a new trick!

[GH85Carrera]

What is the old line. I guess ya gotta be a rocket surgeon to understand.

[red-beard]

From Roxanne:

Chris McConnell: What am I afraid of her for? She's no rocket scientist.
C.D. Bales: Well, actually, she is a rocket scientist.

[tcar]

Originally Posted by Superman

Here's a question for all the guys here who are smarter than me. Maybe I should post this over on PARF, where the geniuses are.

A body in orbit around the Earth would need to travel at a certain speed in order to maintain a certain altitude. They're kinda like this:

......................................Alt .........................Speed...................P eriod
Moon.......................385,000 km.................1.0 km/s...................27 days
Satellite ....................30,000 km................3.2 km/s ...................20 hours
Space Station................380 km ...................7.68 km/s ...............92 minutes

Apparently, lower orbits mean faster speeds and quicker periods, and vice versa.

I'm having a hard time getting my mind around this and I'll tell you why. When the space shuttle prepares for re-entry, it turns around and fires some gentle 'retrorockets', slowing it down just a bit (about 200 mph). This causes its orbit to reduce, if you will. In this case, the orbit is decayed sufficiently to cause imminent re-entry but the point is that the object's orbit does not increase with its decreased speed. Here, a lower speed causes a lower orbit. At launch, higher speeds are necessary in order to achieve orbit. Am I to believe a "slower" rocket would achieve a higher orbit?

Okay.......here's my real question: Pretend you are in a high orbit, watching me pilot another spacecraft in a lower orbit. You'd see me going around the Earth more quickly than you. If you wanted to get together me, perhaps have a beer and a bite to eat, would you really speed up in order to do so? Wouldn't it rather be a matter of slowing down....in order to catch a lower orbit?

discuss.

Flaw: You are confusing orbital time with absolute speed.

The higher orbit vehicles are traveling a hugely greater distance per revolution, hence the longer orbital time. They are also traveling at a much faster speed

Every foot in distance from the Earth increase results in the orbit length increase of 3.14 feet.

Any time you decrease speed, you decrease altitude (shuttle re-entry).

[Superman]

Originally Posted by red-beard

Close.

If you are in a stable orbit, and you increase velocity, you are adding energy. This will put you into a higher orbit. ......

........So, if you're going 8 km/s in low earth orbit, you need to increase your speed by about 40% to 10.9 km/s to escape earth orbit. Anything less and all you do is put yourself into a different orbit.

Now you're confusing me again. LOWER speeds are required for higher orbits. I can understand how increasing speed will move you further from Earth, but your speed will then be too great for those higher orbits.

[red-beard]

Originally Posted by tcar

The higher orbit vehicles are traveling a hugely greater distance per revolution, hence the longer orbital time.

True

They are also traveling at a much faster speed

Not true.

They are indeed traveling slower. Read through the rest of my posts above.

[Superman]

Originally Posted by tcar

Any time you decrease speed, you decrease altitude (shuttle re-entry).

This I understand.

Originally Posted by tcar

The higher orbit vehicles are traveling a hugely greater distance per revolution, hence the longer orbital time. They are also traveling at a much faster speed

This disagrees with the principle that higher orbits require lower speeds.

[red-beard]

Originally Posted by Superman

This disagrees with the principle that higher orbits require lower speeds.

You increase energy to get to a higher orbit, but the speed in that orbit is lower. When you manuver, you increase speed, but over time you swing out to a higher orbit, which will in the end be a lower speed.

Again, think of the ball you through in the air. You have increased its speed with your arm and hand. But as it goes up in the air, it loses speed. At the top of the arc, it is going slowest. As it comes back down, it increases speed.

[Tervuren]

Originally Posted by Superman

So........if I am in a stable orbit and I speed up, in the same direction of my travel, then I will no longer be in orbit. Right? I will move further away from the Earth because of my increased velocity and inertia. Right? And as I move away, I will be moving to altitudes that require less speed for stable orbit. Since I am going faster, I will continue moving away from Earth until I deliberately accelerate in a direction toward it. Right? In other words, as you say, any acceleration in any direction that is not toward Earth will cause me to be in an 'escape' trajectory and velocity. Right?

Gravity's force diminishes with the square of the distance, so 100K miles away, vs 50K miles away, gravity has 4X the force at 50K miles.

This is why a slower speed is needed to stay in an orbit at a longer distance. If you accelerate forwards in orbit, this will cause you to "climb", as you now have more force than gravity.

However, to get to that farther orbit, requires fighting the pull of gravity to get there, so it takes either a longer period of thrust, or a higher initial velocity. From the earths surface, a cannon would have to scream along at IIRC somewhere near 27,000MPH to get away from the earth, and not fall back. From 4,000 miles out from the surface of the earth, it would take 1/4 of that.(Earth 4,000 miles radius + 4,000 miles above surface = 2X the distance from gravities center, so 1/4 the pull of gravity)

The satellites, space stations, etc, are mostly in somewhat circular, or mild ellipses. If you added velocity, depending on the direction, you would get a non circular orbit, with part of it being higher.

My food is done, my second incomplete post may leave you more confused than before I wrote it. :\

[Superman]

My understanding of these principles is increasing, and I think I may have gotten to where I wanted to be. In a nutshell, here is what I had hoped to verify, that I think is now verified:

The principle of slowing down to speed up (in the case of moving from a higher orbit to a lower one) and of speeding up to slow down (in the reverse case). A vehicle in a higher orbit watching a vehicle in a lower orbit, will perceive that the lower orbit vehicle is going faster. Its period will be quicker, giving the impression of higher speed and in fact, the lower orbit vehicle will indeed be going faster. Faster km/s and faster period.

In order to "catch up" with this lower orbit vehicle, I would initially slow my speed. Slightly. This will allow gravity to pull me closer to Earth. If my delta-v is low enough, this will take some time but will also allow me a shallow ellipse, giving me a shallower angle at that lower orbit. At the proper altitude I would need to change direction and perhaps speed up a bit, but most of my increased speed will have come from the force of gravity. Again, I have "slowed down" in order to "speed up."

Conversely, if I were in a low orbit hoping to connect with a vehicle in a higher orbit, I would initially speed up. This would take me outside my orbit, to a higher altitude. As I gain altitude, I will be in an ellipse during which gravity will slow me down. As I reach the desired altitude, I would then need to make a directional change into the new orbit, and may also need to slow down a bit.......if gravity has not already handled that for me. In this instance, I have "sped up" in order to "slow down."

This is what I have been trying to get at. The "speed up to slow down" and the "slow down to speed up."

Where are those PARF geniuses when we need them the most?

[Jim727]

Hi all. Poking my nose in after a long Pelican hatus; great thread to find on day one!

Supe, you're close.

James is telling it straight. Last time I did orbit calculations was even before James, but here goes:

There's clearly a tendency here to think in terms of circular orbits, but it's important to think in terms of elliptical orbits. It's also important to think in terms of adding (forward thrust) or removing ('retro' thrust) energy from the orbit and let that lead you to the 'faster' or 'slower', because it's obviously counter-intuitive.

Lower circular orbits are faster (yes) and higher circular orbits are slower (again, yes), but adding energy should make me go faster (yes) and removing energy should make me go slower (still yes). Sounds impossible, but it isn't. The point at which the effect of adding/removing energy is most obvious is not at the point where the energy change is applied, but at the point diametrically opposite in the orbit.

Consider a circular polar orbit. If you add energy over the north pole you expect to be going faster (and that would imply a lower circular orbit); however, what you have actually done is to increase the eccentricity of the orbit and raise the altitude of the orbit over the south pole while retaining the altitude over the north pole where you appled the energy change. Your perigee altitude over the north pole is unchanged - as is your speed - and your apogee altitude over the south pole is increased and the speed *there* is lower (Kepler worked all this out). If you want a circular orbit, such as a geosynchronous orbit, you would again add energy at the south pole to raise the altitude of the opposite point (north pole) until the orbit becomes circular and uniformly slower.

That's also how de-orbit burns work. Retro rocket firing reduces the energy of the orbit (increases eccentricity) except you are now at the apogee of the orbit and the perigee is lower - i.e., it intersects with the earth.

It also explains the Hohmann Transfer Ellipse. By definition, that is the elliptical orbit which tangentially intersects two other orbits. If you want to head to Mars, you add energy from the Earth's orbit to increase the eccentricity of your (solar) orbit such that the opposite point touches the orbit of Mars.

Jim

[red-beard]

Originally Posted by Superman

Where are those PARF geniuses when we need them the most?

What are you talking about? I'm HERE!!!

[Bill Verburg]

From Wikipedia

Orbital Mechanics

"Without applying thrust (such as firing a rocket engine), the height and shape of the satellite's orbit won't change, and it will maintain the same orientation with respect to the fixed stars.
A satellite in a low orbit (or low part of an elliptical orbit) moves more quickly with respect to the surface of the planet than a satellite in a higher orbit (or a high part of an elliptical orbit), due to the stronger gravitational attraction closer to the planet.
If thrust is applied at only one point in the satellite's orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change. Thus to move from one circular orbit to another, at least two brief applications of thrust are needed.
From a circular orbit, thrust in a direction which slows the satellite down will create an elliptical orbit with a lower periapse (lowest orbital point) at 180 degrees away from the firing point. If thrust is applied to speed the satellite, it will create an elliptical orbit with a higher apoapse 180 degrees away from the firing point.
The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster. This will change the shape of its orbit, causing it to gain altitude and miss its target. One approach is to actually fire a reverse thrust to slow down, and then fire again to re-circularize the orbit at a lower altitude. Because lower orbits are faster than higher orbits, the trailing craft will begin to catch up. A third firing at the right time will put the trailing craft in an elliptical orbit which will intersect the path of the leading craft, approaching from below."

[masraum]

Excellent, this thread has cleared it up for me. It's easy to think "apply thrust" and that's the end of the accel or decel, but then Gravity will have a hand as well. It makes sense realizing that you've got to apply thrush a couple of times.

This place is cool.

[red-beard]

Steve, where you live, you should have a hard time throwing a rock and missing a person who understands orbital mechanics...