# Velocity of earth

1. Mar 26, 2009

### monty37

has the earth been revolving around the sun with a constant velocity?if we
go about calculating the velocity ,wrt to we on earth it will change ,when calculated
from another planet.does the earth's rotation have a constant velocity,recent claims
have said that the earth's velocity is slowing down.

2. Mar 26, 2009

### Cantab Morgan

Be careful when you use the term "velocity," which has a different definition than "speed." You're really asking whether the speed is constant.

Kepler's laws of motion assure us that the speed of an orbiting planet is not constant. The rule is that a planet sweeps out equal areas (not equal arclengths) in equal times. There's a helpful picture here...

http://www.ancient-world-mysteries.com/kepler-equal-areas-law.html

I'm sorry I'm having trouble understanding the rest of your question. The velocity of an object with respect to itself is always zero, so I don't think that's quite what you mean.

3. Mar 26, 2009

### mgb_phys

The Earth's rotation rate (ie the length of a day) is slowing down.

4. Mar 26, 2009

### Cantab Morgan

That's really interesting! How can that be? Where is the momentum going?

5. Mar 26, 2009

### DaveC426913

Into the Moon's orbit.

6. Mar 26, 2009

### mgb_phys

Ultimately to the moon. Tidal friction between the Earth and the moon slows the Earth's rotation and increases the moon's orbital radius.

7. Mar 26, 2009

### Cantab Morgan

Whoa! That hurts my brain. So if I take mechanical energy out of the Earth-Moon system (presumably the tidal friction is creating heat), then the distance between them increases? That's really not what my intuition would have told me.

That must be why I'm finding this thread so interesting.

8. Mar 26, 2009

### DaveC426913

What? No.

Not out the Earth-Moon system, just out of the Earth. It is being transferred to the Moon.

The Moon pulls on the various knobs, protrusions and water-bodies on Earth, slowing it down. (Eventually, Earth will become tidally-locked with the Moon, just like the Moon is with Earth. ) The knobs, protrusions and water-bodies conversely pull on the Moon. They accelerate it, speed it up. A faster orbit means a higher orbit. Thus, the Moon is slowly spinning away from us.

9. Mar 26, 2009

### Cantab Morgan

DaveC426913, thanks for the kind explanation. Note that I wrote mechanical energy, not momentum. I'm trying to obey both the conservation of energy and the conservation of (angular) momentum. I had assumed that the tidal friction was converting mechanical energy to heat, so that the total mechanical energy of the Earth-Moon system is decreasing ever so slightly.

Really? Mercury orbits more slowly than Mars?

10. Mar 26, 2009

### DaveC426913

Mayhap, but it is not significant to your question.

No you misunderstand. For a given body, if you accelerate its orbital speed, you will increase its orbital distance.

11. Mar 26, 2009

### Cantab Morgan

Thanks for your patience. I am enjoying this exchange!

But if the Moon's centripetal acceleration is $$v^2/r$$ and the gravitational acceleration is $$GM/r^2$$, then when I set these equal, I find that the distance from the Earth to the Moon and the square of the Moon's orbital speed are inversely related. It would seem that increasing my speed will decrease my altitude.

Ah. I'm not quite willing to concede that point. I will continue to reflect upon it. I think that the transfer of momentum can only occur because of the loss of mechanical energy. Consider the famous experiment of sitting on a spinning swivel chair with barbells in my hands. When I pull in my arms, my rotation rate changes, but only because I have done work.

Also, I should explain where my original skepticism/difficulty comes from. If the Earth's changing rotation rate transfers momentum to its satellite, then it's hard for me to understand how objects without satellites can have their rotation rates change. And yet the star system offers many examples of moons with no satellites of their own whose "days" and "years" are in lockstep, so such changes must have occurred.

12. Mar 26, 2009

### DaveC426913

If you add energy to the orbit, what's going to happen? Is it going to move inward?

Well that would be wrong. I'm not sure what I can do to convince you of this.

How does the space shuttle achieve a higher orbit? It fires its rockets forward, increasing its orbital velocity, which raises it to a higher orbit.

Higher orbits require more energy. If they didn't, Moon shots would be easy.

Not sure what I've said that goes against this.

It works nicely with the parent star too. It's not specific to satellites - it's about tides. Suns cause tides too. Tides act to slow (or speed up) a body's rotation until it is in lock-step with the parent body. In Pluto/Charon's case, because they are so close in mass, it has worked both ways.

13. Mar 26, 2009

### Janus

Staff Emeritus
If you start with an object in orbit, and give it a forward thrust, it will be moving faster than its proper orbital speed for that altitude. It will start to climb upward, into a higher orbit, as it does so, it begins to lose kinetic energy in exchange for the potential energy it gains by climbing. It slows as it climbs, ending up in a higher but slower orbit.

The Earth is applying a constant forward thrust to the Moon, in response, the moon climbs and sheds speed. But, since the Earth is constantly applying a forward thrust, the Moon is always moving just a bit faster than it should for its distance, So it just keeps climbing.

And yes, the Earth does lose a fair amount of energy to heat. So the Earth-Moon system does lose net energy. But there is also a transfer of energy from Earth to Moon. IOW, the amount of energy the Moon gains is less than the total energy the Earth loses.

14. Mar 27, 2009

### Cantab Morgan

Janus, thanks for explaining so crisply what I was unable to articulate. What I really was going for was that if I were to change the altitude of my circular orbit -- however I accomplish that -- my orbital speed at the higher orbit will be smaller.

Of course Dave is correct. Adding energy does not make a satellite move inward. But ultimately it does make it move more slowly. The devil is in the details of course, because I would need at least two rocket burns. One to gain the altitude and the other to restore circularity to my orbit. I think where I was getting so confused is that the first of these burns does increase my speed, which is where Dave was so gently trying to steer my thinking.

Earth applying thrust to the Moon is exactly what is so difficult for me to visualize, given that gravity is a central force. But I guess it must somehow be true, or else, how could the moon's orbit be climbing?

15. Mar 27, 2009

### DaveC426913

Pretend Earth is a merry-go-round.

Every mountain that protrudes from the Earth is a kid on the merry-go-round with his hand sticking outward.

Pretend the Moon is you, standing next the the merry-go-round.

Every time a kid with an outstuck hand comes around (a mountain), he grabs your shirt for a second. Slowly, you are propelled forward, tangential to the motion of the merry-go-round (i.e. Moon achieves greater velocity in its orbit).

16. Mar 28, 2009

### monty37

the earth has had protrusions from the time it had existed(oceans etc) so,why should it
suddenly slow now,and when reffering to earth,we call its angular'velocity'
and not speed ,right,since it has a fixed orbit or direction,elliptical if iam right.so
if i calculate earths velocity sitting on earth itself,it will change from
the velocity of earth calculated wrt space or another planet.how can u call
it tidal 'friction'?and are the revolutions constant,will the moon's tidal friction affect earth's revolution??

17. Mar 28, 2009

### mgb_phys

Tidal friction is what slows Earth down, it's a little bit mis-named you can have tidal locking due to any irregularities - it's not necessarily due to water tides (mercury is tidally locked in a resonance to the sun)

The rotation rate of the Earth has been slowing down since the moon was formed. For dinosaurs the year was 4-500days, it was the same length of time (in seconds) but the faster rotating earth meant they got more days.

18. Mar 28, 2009

### Count Iblis

This is a nice exercise:

Suppose that in the future we use all of the Moon's materials here on Earth so that nothing is left of the Moon and all the matter from the Moon ends up here on Earth. What will then be the length of a day?

19. Mar 28, 2009

### Janus

Staff Emeritus
The moon raises tidal bulges on the Earth. Friction between the rotating Earth and the tidal bulges tends to drag these bulges out of alignment with the Moon. The bulge nearest the Moon then leads the Moon a little bit. The gravitational attraction between this bulge acts to pull forward on the Moon in its orbit (The bulge on the other side of the Earth will tend to pull backwards on the Moon, but since it is further away by the diameter of the Earth, it has a smaller effect).

The drag between tidal bulges and rotating Earth also slow the rotation of the Earth. Thus the Earth transfers rotational energy to the Moon.

If the Moon orbited the Earth in less time than the Earth rotates (Like the situation between Phobos & Mars), The opposite would occur, the tidal bulges would lag behind the Moon, exerting a force against its orbital direction, and the Moon would spiral in towards the Earth while the Earth gained rotational speed(the drag between tidal bulges and Earth would pull it forward with respect to its rotation).

If the Moon orbited retrograde( in the opposite direction of Earth's rotation), then the bulges would pull backward on the Moon, drawing it into a lower and lower orbit, and the drag between tidal bulges and Earth would slow its rotation.

20. Mar 28, 2009

### Cantab Morgan

Hi, monty37. There's quite a lot going on in your post, but let me try to parse it out.

I don't think anyone is suggesting that the Earth has suddenly started to get slower, but that it has been doing so all along.

I'm afraid I'm too obtuse to understand what you have written there. Can you be a little clearer, please?

Friction is a non-conservative force that produces heat. Gravity is a force whose strength falls off with distance. (Actually with the square of the distance.) The Earth is so large that the side of the Earth closest to the Moon experiences a greater gravitational pull than the side farthest from it. This causes the tides. The continual deformation of the shape of the Earth by the tides produces heat, so the phrase tidal "friction" seems appropriate.

That is a very intelligent question. We've been talking about the slowing of the Earth's rotation, but it's interesting to speculate about whether there's also an effect on its revolution.