Gravity: Will Low Velocity Bodies Revolve or Fall to Ground?

[batballbat]

a body with uniform motion at surface of Earth would revolve around the earth. is it true that if the velocity of the body is sufficiently low than it would not revolve and fall to ground? can we determine the velocity is it is so?
So is it true that the moon, on the grounds that moon was not a part of earth, was traveling in uniform motion before it came to Earth's field and started to revolve? And if had it not been in uniform motion, would collide with the earth?

 

[PrakashPhy]

a body with uniform motion at surface of Earth would revolve around the earth. is it true that if the velocity of the body is sufficiently low than it would not revolve and fall to ground?

How can you say a bod with uniform motion at the surface of Earth would revolve around the earth? There is friction.. If you assume there is no friction then also it wouldn't be possible for Earth is not a perfect sphere. It has mountains and hills.

and what is difference between surface of Earth and ground in your question?? If it is already on the surface how can it fall to ground??

 

[sophiecentaur]

Are you talking about Orbits here? You mention "fall to the ground".
For an object to stay in a circular orbit, its speed must be exactly right so that the gravitational force is equal to the centripetal force needed for circular motion at the particular radius of that orbit.

 

[batballbat]

to praksah phy sorry my question makes even someone interested in physics pose questions to a mathematical model. so please someone who is not deterred by thought experiments help me with this.

 

[sophiecentaur]

You need to describe your "thought experiment" in more detail if you want a proper response. So far you have not made it clear what you want.

 

[DaveC426913]

a body with uniform motion at surface of Earth would revolve around the earth.

If its velocity was orbital velocity, sure.

is it true that if the velocity of the body is sufficiently low than it would not revolve and fall to ground?

Certainly.

can we determine the velocity is it is so?

Certainly. Anything less than orbital velocity for that altitude.

So is it true that the moon, on the grounds that moon was not a part of earth, was traveling in uniform motion before it came to Earth's field and started to revolve? And if had it not been in uniform motion, would collide with the earth?

Do you mean it was on a hyperbolic trajectory and got captured?

I think the question you are trying to ask is this:
Is it possible that the Moon was once a free floating body, on its own trajectory though the solar system and not gravitationally bound to Earth, but was captured when the Moon made a close fly-by of Earth?

The answer is: Mechanically speaking, it is certainly possible.

But there are other factors in considering that as a likely account of actual events. There are many facets of the Moon that must be considered in determining its origin - such as its composition when compared to Earth. They seem to be made out of similar materials - enough to suggest they were once the same body. However, there are competing theories.

 

[batballbat]

thanks dave
i just meant that the moon must have had been in motion because otherwise it would not revolve, rather fall to the centre. am i correct?

 

[DaveC426913]

thanks dave
i just meant that the moon must have had been in motion because otherwise it would not revolve, rather fall to the centre. am i correct?

Yes.

Sort of. Mostly.

Your question assumes that the Moon's motion is independent of the Earth Moon system. This is not necessarily so. There is at least one theory that suggests the Earth underwent a massive collision which knocked off a giant portion of it which eventually formed the Moon. So the formation of the Moon and its revolution about the Earth occurred as the same event. In this scenario it is nonsensical to talk about the Moon's motion independently of its origin.

However, even in this scenario, there was a body that has a respectable tangential velocity wrt Earth that it imparted to the Earth. So even in this case, angular velocity is required for orbit.

So: yes, insufficient angular velocity of a body at a distance from Earth would eventually fall to Earth (which much of the rubble from that aforementioned collision likely did).

 

[sophiecentaur]

thanks dave
i just meant that the moon must have had been in motion because otherwise it would not revolve, rather fall to the centre. am i correct?

Revolving (=spinning on its own axis) is not the issue. It is orbiting (translational motion around the Earth) that you are discussing. The two words have distinct meanings. But your ideas are correct. As I wrote in my earlier post, an object is in orbit when the force of gravitational attraction provides just the right centripetal force. If the object is not orbiting (has no tangential velocity) then there will always be an unbalanced force towards the Earth and it will fall.

The present idea (I believe) is that two planets collided and the Earth - Moon pair were the result. Our particular Moon is very big, relative to the Earth's mass - compared with many of the moons around other planets.

 

[DaveC426913]

Revolving (=spinning on its own axis) is not the issue. It is orbiting (translational motion around the Earth) that you are discussing. The two words have distinct meanings.

I do believe the Earth revolves around the Sun and the Moon revolves around the Earth.

http://oxforddictionaries.com/definition/revolve
to revolve about/around - to move in a circular orbit around (as in) the Earth revolves around the sun

 

[sophiecentaur]

One thing worth pointing out is that two bodies traveling through space cannot, independently, suddenly get into orbit round each other. In the same way that a spaceship needs to slow down in order to land on a planet, there needs to be some other influence at work (like a collision) for two objects to change from a hyperbolic (glancing) interaction to an orbital situation. It is necessary for kinetic energy to be lost at a critical time in the trajectories or they will just depart in the same way that they arrived.

 

[sophiecentaur]

I do believe the Earth revolves around the Sun and the Moon revolves around the Earth.

http://oxforddictionaries.com/definition/revolve
to revolve about/around - to move in a circular orbit around (as in) the Earth revolves around the sun

That's one way of looking at it but the Moon does, actually, orbit around the Sun, too.
There are orbits (horseshoe orbits) for satellites around planets that share nearly the same orbital distance as their planet but they spend some time at the opposite side of their Star from the planet. They then 'come back' to their planet (catch up) and hare off past it to the other extreme point of their weird orbit. They then 'come back and the process repeats. I don't know what the local observers would say about that? I wonder what Galileo or Keppler would have made of it.

 

[DaveC426913]

One thing worth pointing out is that two bodies traveling through space cannot, independently, suddenly get into orbit round each other. In the same way that a spaceship needs to slow down in order to land on a planet, there needs to be some other influence at work (like a collision) for two objects to change from a hyperbolic (glancing) interaction to an orbital situation. It is necessary for kinetic energy to be lost at a critical time in the trajectories or they will just depart in the same way that they arrived.

Yes, I was thinking about going into this when I mentioned the hyperbolic trajectory, but I thought it premature. I figured the OP needs to sort out his scenario at a basic level first.

 

[DaveC426913]

That's one way of looking at it but the Moon does, actually, orbit around the Sun, too.

The point being that the OP was not incorrect in his use of terminology.

 

[sophiecentaur]

I see where you're coming from but I would suggest there is an essential difference between 'revolve around' and 'revolve', which was the term he used. The dictionary extract uses 'around'. There are so many ways of getting hold of the wrong end of sticks that I often feel duty bound to resolve these things. We could often be half way through a thread where there is actual confusion in this respect.

btw what are sig lines??

 

[DaveC426913]

btw what are sig lines??

Yours is
There are no 'really's in Science - they are all models. (Really)

Mine is

 

[sophiecentaur]

Yours is
There are no 'really's in Science - they are all models. (Really)

Mine is

Right!