# Orbital speed - faster is closer?

1. Jan 16, 2014

### Edi

I am very confused about the fact that, for example, Pluto moves around the Sun much slower then Earth and is also much further from the Sun, so its period is way longer that that of Earth's..
if I want to increase orbital height, I add speed to the object I want to raise, no? How come objects further away move slower and dont fall down to a lower orbital height?

2. Jan 16, 2014

### Edi

If I take Mercury's speed and apply it to the Earth (regardless of mass), Earth would rise in a higher orbit, longer period and.. slow down?

And if I then slow down the Earth again, it will drop back to the lower level, speed up and shorten the orbital period?

3. Jan 16, 2014

### Staff: Mentor

An orbit is a combination of potential and kinetic energy. If you increase the speed, the total energy rises, but as the spacecraft moves up in altitude as a result, it trades that speed (kinetic energy) for potential energy.

4. Jan 16, 2014

### tiny-tim

Hi Edi!
The planets are in very nearly circular orbits.

If you increase the speed of a satellite, it goes into a considerably elliptical orbit that takes it further out.

When it reaches the new desired distance (further out), it has slowed down, and you need to fire retro rockets to slow it down further so that it goes into circular orbit there.

The total result is that the speed is slower.
Because everything in orbit is falling towards the sun, but is also going "horizontally" just fast enough that it balances out the falling (this was good ol' newton's point about the falling apple … if you throw it fast enough, it balances out the falling).

Something further out falls less fast, so it needs a slow "horizontal" speed to balance.

5. Jan 16, 2014

### Bandersnatch

Try to not think in terms of circular orbits.

Increasing velocity of a body in a circular orbit does not simply change into a different circular orbit, but gives it a 'kick' that changes the orbit to an elliptical one. It starts to move farther away from the central body, slowing down as it moves farther away. Finally, it reaches the apoapsis(the point furthest away). Here, it has too low a velocity to stay at this distance, so it gets closer again, increasing its velocity as it moves towards the periapsis(closest point) again.

If you wanted to make the orbit circular again, you'd have to give the body an extra kick(like firing thrusters of a rocket) at the apoapsis, so that it has enough orbital velocity at that point to move in a circle.

It's all according to the conservation of energy - you give the body extra KE, and as it moves away it exchanges it for PE, and then back again.

I always recommend playing the free game "Orbiter", which lets you fly spaceships around the solar system and learn all the quirks of orbital mechanics by heart. To be found here:
http://orbit.medphys.ucl.ac.uk/

There's also the arguably more fun, albeit less free "Kerbal Space Program".

By the way, if you were to increase Earth's orbital speed to that of Mercury's(~48km/s), it would exceed the escape velocity w/r to the Sun at 1AU(~42km/s), and it'd drift away on a hyperbolic trajectory.

@tiny-tim:
I think you got that bit about firing retro rockets backwards. You need to add energy to the orbit to circularise it at the apoapsis, not slow it down further. That would only serve to lower the periapsis, instead of rising it.

6. Jan 16, 2014

### pikpobedy

7. Jan 16, 2014

### D H

Staff Emeritus
No! You need to fire *with*, not *against* the velocity vector. When it reaches the new desired distance, it is going slower than circular velocity at that distance.

8. Jan 17, 2014

### tiny-tim

Hi D H!
ooh, yes, if you wait for aphelion … i wasn't thinking of that, i was thinking of returning to circular orbit soon, don't you then have to brake?

(i haven't worked it out, but intuitively that seems correct )

9. Jan 17, 2014

### sophiecentaur

I think it is standard to give two boosts - one (tangential) in the lower orbit to make it elliptical and then one at aphelion to make it circular again. That makes best use of fuel and gives a circular orbit.

10. Jan 17, 2014

### pikpobedy

From a "circular" orbit: A retro-boost will create a perehelion on the opposite side.
A retro boost at the perehelion will lower the aphelion on the opposite side thus making the orbit "circular".
"Circular" is in quotes because orbits are ellipses. A circle is a special ellipse.

It is also important to have powerful short boosts. These are the most efficient.

Do not forget the inverse square law of gravity. This is another factor.

11. Jan 17, 2014

### sophiecentaur

Sandra Bullock would do it fine with a fire extinguisher!

12. Jan 17, 2014

### sophiecentaur

It is worth while noting that the Angular velocity goes down as the radius of the orbit increases (it takes longer to go round BUT it actual speed it's travelling goes up. That can be confusing (it certainly confused me to start with). It's a good lesson about stating the facts n the right way.

13. Jan 17, 2014

### willem2

If you do not wait for aphelion, you will still be moving away from the sun, and you'll have to change direction to get in a circular orbit. This is wasteful, because thrusting sideways won't add to the kinetic energy of the ship. If you get much more speed than is necessary to get to the higher orbit, you'll have to brake as well.

14. Jan 17, 2014

### jbriggs444

Not only does angular velocity go down. Linear velocity also goes down. A object in a circular orbit with a larger radius really moves more slowly in both senses.

Within a single elliptical orbit the same principle holds true. Kepler's "equal areas in equal times" principle (i.e. conservation of angular momentum) means that orbital velocity must decrease as distance from the primary increases.

The above holds for the case of an inverse square central force. If the force increased linearly with distance, as would be the case when spinning a weight around your head using an ideal spring then the orbital period for a circular orbit would be independent of distance and orbital velocity would increase in direct proportion to orbital radius.

15. Jan 17, 2014

### sophiecentaur

Yes of course. What was I thinking of?