Why does an orbit increase in altitude with more velocity?

[Fez]

Also, why does the altitude decrease by decreasing velocity?

[livefree75]

Simply explained, if you increase your velocity, it will take longer for gravity to slow you down. allowing you to coast higher. Vice versa for decreasing velocity.

[Fez]

What do you mean it will take longer for gravity to slow the craft down?

[Yourself]

How else would you expect it to work?  If you don't move at all, you fall down and hit the planet.  If you move fast enough you still fall down, but miss the planet.  The faster you go, the farther you travel in the time it takes gravity to pull you down, so you end up reaching higher altitudes the faster you go.

[Fez]

Is that because the earth curves away or something like that? That's really hard for me to wrap my brain around

[legoclone09]

5 minutes ago, Fez said:

Is that because the earth curves away or something like that? That's really hard for me to wrap my brain around

Yes, the Earth curves away, here is a gif that shows it. The a is gravity and the v is the velocity. Gravity pulls the satellite down but the forward motion causes it to miss the Earth.

[livefree75]

Sorry, I didn't explain it very well.

Think of throwing a ball on Earth (or any celestial body). If you toss it at a vertical speed of, say, 10 m/s, it will go higher than if you threw the ball at 5 m/s. This is because, while the ball is still accelerating at roughly the same rate (9.8 m/s^2), the faster the ball is traveling upward, the longer it will take to accelerate to a vertical speed of zero. 

Here's the equation if you're interested:

t = Vi/g

where t represents the time to apogee, Vi represents the initial vertical speed in m/s, and g is the acceleration due to gravity (9.8 m/s^2 on Earth/Kerbin).

In space it's a lot more complicated, but hopefully this answers your question.

[Fez]

Bit in orbit the craft isn't going vertically up, its going horizontally...

[Dman979]

That's right. Imagine it this way:

You have a table. You roll a ball off that table. It's moving slowly, so it falls to the ground about 5 feet from the edge of the table.

Now you roll another ball off the table, a bit faster. It falls, too, but it falls about 10 feet from the table, in the same amount of time (because gravity is the same on each of them).

You keep doing this until you roll the ball off the table, and it's moving so fast that gravity pulls it down, but the earth has become further away from the starting point. This keeps happening.

If you were using a mountain and a cannonball it would look like this:

C is a perfect orbit.

D is the orbit you are talking about. Because the cannonball has a higher initial velocity, the Earth curves away more than the cannonball falls. Then, as the cannonball reaches the highest point away from Earth, it comes down, just like if it were thrown straight up. The difference is, it has vertical velocity combined with the horizontal velocity (using physics, you could work this out, but I don't want to ), so it's moving faster.

It will return to its starting point, and repeat this orbit forever.

[Fez]

Thank you for your responses, I understand the concept, unfortunately I can't seem to visualize it in my head, which is really frustrating

[lajoswinkler]

If you throw upwards a rock with more force, it will reach a greater altitude. That's basically it.

[Bill Phil]

It's because the Periapsis is the point with the fastest velocity. Increasing that velocity increases the kinetic orbital energy at that point, so the opposite point ( in this case the apoapsis) has a higher altitude, increasing its potential energy, so the net energy at any point is the same, just divided among kinetic and potential.

Well, actually, it's just how the Vis Viva equation says it works. If you play around with it, it'll change the values. Like if you change the velocity at the same radius, you can solve for the semi major axis, and if you're at an Apsis, then you can use the SMA to find the altitude of the other one, and then you can solve for it's velocity.

[Lukaszenko]

As everyone is saying, if you throw a rock faster straight up, it goes higher up. At the top, it's velocity is the lowest (zero, in fact, if you throw it straight up).

Ok, so a satellite goes faster sideways, not up. Imagine a swing then. In order to higher, you push yourself harder at the bottom, sideways. The swing rope then curves your sideways path and converts it into height. So sideways speed and height are interconnected, and affect each other. In the case of a satellite, gravity acts like the swing rope to curve your path. 

It's still not a perfect analogy because the path of a swing is usually fixed, so the faster you go the harder the rope pulls on you to curve your path. Gravity doesn't fix the path, but the force is fixed. The point is that sideways and up/ down are still interconnected.

I recommend playing around with some gravity simulators online, such as:

http://waowen.screaming.net/revision/force&motion/ncananim.htm

 

[KSK]

Like Bill Phil, I find it easiest to think about this in terms of energy.

At any point along an orbit you'll have a fixed amount of energy which is the sum of your kinetic energy (due to your speed) and gravitational potential energy (due to your altitude. Because that total is fixed, the lower you are (less potential energy), the faster you go (higher kinetic energy) to compensate. 

So the lowest point in your orbit (periapsis) is also the fastest. Likewise the highest point in your orbit  (apoapsis) is also the slowest.

Now what happens if I burn prograde at periapsis? I give myself more kinetic energy which I then have to exchange for more potential energy at apoapsis (highest point, therefore slowest, therefore least kinetic energy, therefore most potential energy) And the only way that can work is if my altitude at apoapsis increases.

The same logic applies at apoapsis (or anywhere in your orbit for that matter. Burn prograde, increase kinetic energy, exchange for more potential energy aka altitude on the opposite side of your orbit. Which is why you burn prograde at apoapsis to circularise your orbit.

The same logic in reverse explains why e.g burning retrograde at periapsis lowers your apoapsis.

Hope this helps.

 

 

[RizzoTheRat]

Put a weight on the end of a bit of elastic (I would say a conker on a bit of string but non Brits might now know what I'm talking about :D)

Spin it around your head.

The faster you spin it round the more it stretches the elastic and the longer it's orbit.

Completely different principal but it visualises it nicely

[Fez]

But what does kinetic energy have to do with it? That doesn't really explain why it would cause the orbit to increase in altitude, at least not to me

[tater]

As you accelerate at a tangent, you can visualize the craft moving in the straight path a very tiny amount, vs the circular orbit. As it does this, it is very slightly farther away from the planet, right? (the circular orbit is the place where it is equally far from the center of the planet, so any deviation at a tangent is higher)

Gravitational acceleration is then lowered due to this distance (and it's an inverse square). You've just changed the curve of the orbit because the craft is ever so slightly farther away so the force pulling the craft down is lower. Keep doing this, and the ellipse gets larger and larger.

 

Edited January 26, 2016 by tater

[0111narwhalz]

Kinetic energy comes from your speed, potential (at least in this case) from altitude.
Kinetic energy can be exchanged for potential energy.
Total energy is conserved.
When it's at the bottom of the orbit (PE), more of the total energy is kinetic than is potential. This point is lowest, therefore it has less potential energy. It must have more kinetic energy.
As the object reaches the top of the orbit (AP), more of the energy is potential. This point is highest, therefore it has more potential energy. It must have less kinetic energy.

When you add kinetic energy, it forces the point on the opposite side to rise, because you're adding potential energy (altitude) to that side. The faster you're going on one side, the higher you go on the other.

As has been discussed previously, there is an equation to discover the velocity at any point, given various other factors. You can manipulate it to find altitude instead, if you wish to. It's called the Vis-Viva equation, and it's quite useful.

[mikegarrison]

35 minutes ago, Fez said:

But what does kinetic energy have to do with it? That doesn't really explain why it would cause the orbit to increase in altitude, at least not to me

It has everything to do with it. You will never understand orbits if you don't understand conservation of energy. Seriously, you must get the physics understood first.

[mikegarrison]

There are only two things you really need to understand to know everything about orbits. 1) Conservation of energy: E=M*(1/2*V^2+gh), and 2) you are always in your orbit, so any burning you do can only move every other part of your orbit, not the place you are actually at.

So you always trade speed for height, any energy you add will increase your speed where you are and your height in other places, and mass is a separate factor so it doesn't affect the speed v. height trade but it does mean you need more energy to get a bigger mass into the same orbit as a smaller mass.

Edited January 26, 2016 by mikegarrison

[Fez]

I think I got it, as you increase horizontal speed, the craft goes forward horizontally a little bit more, while falling down at the same rate, so the trajectory begins to flatten, and you climb. Then, as you slow down, your horizontal speed decreases and you're still falling at the same rate, so the trajectory curves more towards the thing you're orbiting. Does that make sense? BTW, thanks for all your patience guys, I appreciate it

[Camacha]

What always confuses me is that the orbital velocity becomes smaller as you add energy.

Edited January 26, 2016 by Camacha

[Fez]

Well actually I understand that, because as you climb, the pull of gravity becomes weaker, so you fall towards the thing you're orbiting less, so you need less horizontal speed to counteract the fall

[mikegarrison]

4 minutes ago, Fez said:

Well actually I understand that, because as you climb, the pull of gravity becomes weaker, so you fall towards the thing you're orbiting less, so you need less horizontal speed to counteract the fall

Sorry, this is actually mostly wrong. The pull of gravity does get *very slightly* weaker, but not so much that it makes any difference. It's all because you are converting speed energy (1/2*V^2) into height energy (g*H). "g" is actually staying almost the same. It's "H" that is changing.

[mikegarrison]

9 minutes ago, Camacha said:

What always confuses me is that the orbital velocity becomes smaller as you add energy.

Not really. Speed goes up where you add the energy, just like you would expect. But when you trade it for height at the other side of the orbit, it goes down because height is being traded for the square of speed.