Orbital Speed/Altitude
 

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.

what brand of beer do you have?

The deal is that when in orbit, you're not actually weightless, you're actually in freefall, so you're hurtling towards the earth. The only thing that keeps you from slamming into the earth is that you're also hurtling in a direction that's perpendicular to the earth's surface. If you are closer to the earth, you have to go much faster sideways to keep from going down. So, yes, to catch a guy on a lower orbit, you would eventually have to speed up (to manage to stay in the lower orbit). You might slow down in order to reduce your orbit and then fire rockets again to speed up and readjust to a new orbit, or I suppose, you could accelerate down to the new orbit.

It's my understanding that when the astronauts are in the shuttle or ISS orbiting earth, they actually weight something like 98% as much as they do on earth, but because they are in freefall, it feels to them like they are weightless. So their weightlessness is created the same way as it is in the vomit comet.

I don't know if this will help you visualize...

http://scienceblogs.com/dotphysics/w...1/orbit-23.jpg

You might know of it. Inversion IPA.

This is the part I have a hard time getting my mind around. Accelerate to a lower orbit? But to get closer to the Earth, I would slow down? Huh?

So.....a rocket with a satellite wouldn't need to accelerate as much as the Space Shuttle, since it will go into a higher orbit? Doesn't make sense to me.

Perhaps after one more beer, I will have it.

one of my favorites!
http://forums.pelicanparts.com/uploa...1328161661.jpg

If you've ever worked in a corp environment or had a badge hanging of of one of these, you may have played with it by spinning it around.
http://www.crobike.de/en/werbemittel...5000/27116.jpg

You start swinging the thing around in a circle.
http://www.westlake.k12.oh.us/lbmste...s/image002.jpg

As the badge gets farther away from your hand, you can spin it slower and it will stay extended, if you slow the rotation down, the badge will start to pull in closer to your hand. If at some point you want to stop it from getting closer to your hand, you have to speed up the rotation. If you speed it up too much, then the badge will start getting farther away.

It's a delicate balancing act of having the right amount of speed. If you increase speed, that will usually cause the orbit to increase, and then when you've gotten far enough out that you don't want it to increase any more, you can slow it down a bit. If you want to bring it in closer, then you need to slow it down a bit, but then if you want it to stop getting closer, then you need to speed it up just enough to keep it where it is.

I don't know how many you have to drink in order to get tired of it, but I've spent these past few years trying to find out. Still don't know.

Being in an orbit means you are not falling or rising relative to the earth. To achieve this you have to match gravity pulling you down with centrifugal force pushing you away from the earth.

Gravity increases if you are getting closer to earth, so you have to go faster to make up for it.

Your rocket slowing will reduce the speed of the spaceship which will make it fall - its centrifugal force is now lower than gravity.

To get from a higher orbit to a lower, you would have to first slow your spaceship to make it fall, but then speed up to get back to equal forces!

Hope this helps? I sure wonder why you'd worry about such a thing at 10 pm ...

G

I think the big problem is that direction of acceleration is the big factor to consider. Everything in one of these situations is in 2 directions, one is towards the earth (vertical if you will), the other is perpendicular to the surface(horizontal). If you slow down the horizontal, then that will allow the vertical to pull you towards the earth (you'd accelerate due to gravity in the vertical). As you approach a new closer orbit, you would have to start accelerating the horizontal again to get you up to the right speed.

If you wanted to accelerate to the lower orbit, then you would have to have rockets that fired to accelerate you towards the earth (vertical) and in the horizontal. This would be a silly inefficient way to do it because you'd need to use a LOT of rocket to force you towards the earth because centripetal force would be trying to pull you outward. It would be much better to slow down, let gravity pull you down and then as you approached your new orbit, speed back up to the right speed to maintain that orbit.

Right. So....higher orbits required faster speeds. That is what makes sense. And faster periods for lower orbits. But the data matches the period thing, but not the speed thing. In reality, if I believe the graphs, higher orbits mean lower speeds. WTF?

The badge example leads to confusion central.

The force of the badge being pulled out on the line is at best linear. This means the force grows with distance between the badge and the person spinning it.

The gravitational force is going DOWN with distance of the spaceship from the earth and it drops of with 1/distance^2.

So, the badge thing is not the same. Don't use it to explain a gravitational force and space orbit.

George

I guess the trick for telco satelites is to be in that sweet spot where your orbital speed gives you a period of 24hrs - it revolves around the earth once a day, as the earth rotates on it's axis once a day with the effect that the satelite remains in a constant position relative to a point on the earth.

geosynchronous orbit

Two words Implicit Differentiation

Supe,

Think of the energy required to lift something.

Anything which rises above the earth's surface has to have energy input to allow it to get up there, whether it be getting your car on jack stands or a satellite into orbit. The higher it rises, the more energy it took.

Once it is up there, as mentioned in other posts, it is in free fall. If you want to get down, you have to degrade the energy level to decay the orbit. Some of that energy may be recaptured to establish the new (lower) orbit, but you will have to add more energy to sustain the orbit (free fall) at a lower altitude.

The energy required to (re)establish the orbit is nothing like the amount of energy required just to lift the thing in the first place. Imagine the difference between lifting your car and giving it a push across a frictionless surface.

Hope this hasn't muddied the waters.

Best
Les

Geosynchronous orbit. Ground speed may be 0, but at 22000 miles high, you are still going over 6800mph to maintain that one spot.

Low earth orbit is what is used by the shuttle and ISS. "The International Space Station is in a LEO that varies from 320 km (199 mi) to 400 km (249 mi) above the Earth's surface.

While a majority of artificial satellites are placed in LEO, where they travel at about 7.8 km/s (28,080 km/h or 17440mph), making one complete revolution around the Earth in about 90 minutes"

The math and numbers aren't the same, but the concepts are similar.

Well there's no real discussion, it's math and physics, and they are not open for debate really

"The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy."


Eg if you drop to his orbit, you are trading potential energy (altitude) for speed
There's no way you can simply slow down to his orbit, cause you got all that energy to deal with. Unless you have enough energy to counter it, which frankly is not going to happen, energy stores up there are limited by what you can take up (weight you have to lift in the first place).
So realistically, the only way to meet up, is to calculate the exact time of your decent burn, so just a minimal burn is required to slow you down from high orbit, and end up at the right speed in his orbit (at which point you will probably need another burn to match his speed again.

EDIT, that doesn't sound right now that i read it back.

EDIT again..

i think it's about relative speed to the ground.. Eg If you are on a lower orbit, your relative speed to the ground will appear faster, but your absolute speed will not differ as much.

So doing 30 0000 km / hour , at 200 km altitude, will appear really fast at ground level
But the same speed at 600 km altitude will appear a lot slower at ground level
The craft is doing the exact amount of distance in both scenarios, but lower orbit will look faster from the ground.

Final EDIT :
So to drop from flight level 300 km to 200 km, all they have to do is slightly slow down, so the orbit decays
And time it right, so by the time it arrives at 200km, it is timed to happen so they both are at the same point at the same time..
At that time the descending craft has to undo the slowing down bit, and match speed with the craft at lower level, eg, speed up a bit.

not enough info.

does your imaginary spaceship weigh the same as your friend's imaginary spaceship?

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.