Orbital velocity relationship to altitude

[Fez]

So using the orbital velocity equation, I can figure out that the orbital velocity for a circular orbit at 100 km around Kerbin is 2245.8 m/s. However, say a spacecraft is orbiting in an elliptical orbit, and at one particular point on that orbit, it's travelling at 2245.8 m/s.  But since it's an elliptical orbit, the spacecraft is climbing/descending. How does that work? If a spacecraft climbs because it's going fast enough, or descends because it's too slow, how is the spacecraft staying at the same altitude in the first example, but climbing/descending in the second example?

[Steel]

Because in the first example you're moving at the right velocity for that orbit at the correct height. 

In an elliptical orbit you'd be going at that speed, but you wouldn't be at 100km, so you'd climb/fall depending on whether the speed at that point was above or below the speed for a circular orbit at that altitude.

 

Hope that makes sense!

Edited September 21, 2016 by Steel

[Fez]

Is that because gravity would be stronger/weaker at the different altitudes? Would the small difference in gravity account for that?

[Steel]

There's actually very little difference in the force of gravity at that height, even to the force on the ground. It's to do with the fact that in circular motion, the further you are from the centre point of the rotation, the slower you can go and still stay there.

You can see for yourself if you calculate the difference in circular orbital velocity at 90 km and at 110 km and compare those to the number for 100 km. That will show you the effect of being further away or closer, despite the fact that the gravitational force is almost exactly the same.

Edited September 21, 2016 by Steel
Got mixed up with faster/slower!

[Fez]

Did you mean that the further you are from the centre point in a circular motion, the slower you have to go to maintain? Since higher orbits are slower. And is there a reason for this? Thanks.

[Steel]

Yes I did, I've edited the post so I don't look like so much of an idiot!

[Fez]

No problem  Is there a reason though, that you can maintain a higher orbit at a slower speed, but need more speed for a lower orbit?

[kerbiloid]

Energy conservation law. Potential + kinetic energy = const
It climbs the hill loosing the speed, then it rolls down faster and faster.

[Steel]

Yeah, going back to gravity. You weren't wrong when you talked about gravity changing. It to do with the fact that at higher altitudes, the force needed to balance gravity gets less and less, and since centripetal force depends mainly on velocity squared, it means that the velocity in a circular orbit lower the higher you go.

[Fez]

This doesn't make sense to me though. According to that argument, there is no one velocity that accounts for a particular altitude.  You just lose some speed as you climb, and gain some speed as you descend. Also, is there a physical way to imagine it?

[Steel]

There is a particular velocity that accounts for an altitude, but only for circular orbits, due to the balance of the forces. The closer you are, the stronger the gravitational force and so the stronger the centripetal force has to be to balance it, hence a greater velocity.

[Fez]

Actually, nevermind, I see how energy conservation would work. Bit is there a physical way to imagine it?

[Steel]

What sort of physical situation exactly is it that you want to picture?

[Fez]

That makes sense, thanks. The way I always imagined orbits working was that gravity pulls the spacecraft down a bit, but the spacecraft moves tangentially at the same time. This combination of movements creates a curved trajectory. If the tangential velocity is fast enough, it will climb, since it's travelling so far horizontallybin the time it takes to fall a little

[Steel]

That's exactly how it does work!

[Fez]

Thanks so much for the help!!

[Fez]

Hey, sorry to revive this, but I've got another question  I was in an elliptical orbit, and I calculated the speed i would've needed to be in a circular orbit at the altitude I was at. I found that the speed i was at in the elliptical orbit, while climbing to apoapsis, was slower than the speed needed for a circular orbit.  How can that be, if a faster speed means I'll climb, but I was going slower than if I had been in a circular orbit? It's been bugging me, thanks.

[Dman979]

8 minutes ago, Fez said:

Hey, sorry to revive this, but I've got another question  I was in an elliptical orbit, and I calculated the speed i would've needed to be in a circular orbit at the altitude I was at. I found that the speed i was at in the elliptical orbit, while climbing to apoapsis, was slower than the speed needed for a circular orbit.  How can that be, if a faster speed means I'll climb, but I was going slower than if I had been in a circular orbit? It's been bugging me, thanks.

Basically, your vector is not in the tangential direction, it's missaligned.

If I throw a ball horizontally at 10 m/s, and one at a 45deg angle at 5 m/s, which one will go higher?

[Fez]

But isn't that outward radial velocity caused by the faster tangential velocity? In other words, you climb because you go fast

Edited September 23, 2016 by Fez

[Shpaget]

It can happen.

Remember, velocity is a vector, the direction of your movement is just as important as the speed.

Imagine if velocity x is needed for circular orbit at height y, and then you make a small turn "up" (not straight up, just not tangential to your previous orbit). In that manoeuvre you lose a small amount of speed. You now are in an elliptical orbit and your speed is lower that the one needed for circular orbit at your altitude.

Edited September 23, 2016 by Shpaget

[Fez]

Butbi calculated the speed needed for that elliptical orbit I was in, and got the speed i was traveling at, so it was accurate. But how does that equation account for different vectors of velocity?  

[Fez]

Would that also explain why a spacecraft starts climbing faster and faster while losing speed, while going towards the apoapsis? Because the vector is facing out? Still kinda confused...   

[magnemoe]

2 hours ago, Fez said:

Would that also explain why a spacecraft starts climbing faster and faster while losing speed, while going towards the apoapsis? Because the vector is facing out? Still kinda confused...   

You gain attitude slower and slower until it stop and you start falling back again. 
Orbit is basically falling while moving so fast forward you miss the planet, at minmus its just take a few 100 m/s to kill all orbital velosity and you fall straight down. 

[mikegarrison]

7 hours ago, Fez said:

Hey, sorry to revive this, but I've got another question  I was in an elliptical orbit, and I calculated the speed i would've needed to be in a circular orbit at the altitude I was at. I found that the speed i was at in the elliptical orbit, while climbing to apoapsis, was slower than the speed needed for a circular orbit.  How can that be, if a faster speed means I'll climb, but I was going slower than if I had been in a circular orbit? It's been bugging me, thanks.

Imagine you are in a circular orbit at height X. There is a certain amount of speed you need to be in that orbit. Now you take some of that speed away, by burning retrograde. What happens? The other side of your orbit drops in altitude.

Why? Two reasons. 1) Your orbit always goes through your position. So when you take energy away from it or add energy to it, you affect every other part of your orbit except the place you are at. 2) If you take energy away from your orbit, it has to go down somewhere. Since it can't go down where you are, it goes down on the other side.

Now what have you done? You have slowed down. You were at the speed for a circular orbit at height X, and you slowed down, putting yourself in an elliptical orbit with an apapsis of X. So it follows that when you are in an elliptical orbit and you reach apoapsis, your speed will be less that what it would take to stay there on a circular orbit at the same height.

[Fez]

That definitely makes sense, but what about when in other parts of hr orbit, besides apoapsis? Like when you're climbing to apoapsis, but you're speed is below the amount necessary for a circular orbit. Sincerely Rita slower, shouldn't it be descending?