Anilkumar

Hello IM Egdall, thank you for trying to help-out, So now, In the example of Space warp: If there was a Rocket, shuttling between those two points at a fixed uniform velocity, prior to our bringing Earth near them; will now take less time or may be more time, to reach between the points, after we place Earth near them? for the person observing from far away. If this is so; {I know that there are no WHYs in physics, but still} is there a reason for this? i.e. What TOOLS does Gravity have in its pockets, to change that distance? & What are the, OR Where are the, nuts & bolts placed in the 'BODY' of "THE 'EMPTY' SPACE", that the Gravity 'tightens' or 'loosens' to bring a STRUCTURAL change in the STRUCTURELESS STRUCTURE of the empty Space? Thank you

Hello Divinum1, great many thanks for connecting; 'gravitational field is composed of two forces' - I did not know this clearly. Is this what they say, that - One component is directed towards the center & the other is in a direction tangential to the cirular orbit?--------------------------------------------------------------------------------------------------- 'polar ends' - Does this mean; the polar ends of the earth or any body [the north/south pole]?------------------------------------------------------------------------------------------------------------------------------------------------------------ 'they become subtracted' - Vector subtraction?---------------------------------------------------------------------------------------------------------------------------- 'Which makes the curvature of the field something similar to magnetic field lines' - So due to the curvature of the the Gravitational field, things moving through that field, tend to follow the curved lines of Gravitational field, like a magnetic compass needle gets deflected along the magnetic lines in a magnetic field?

There is a force of attraction between any two objects with mass according to Newton's 'Law of universal Gravitation'; Given by :- ----------------F=GMm/r2 Edits: Grammar

Sorry Michel123456, I forgot to thank you personally, You gave me the first break by, pushing me sideways, while I was walking on the street in a straight line;

Fantastic; & that last piece of information, nice one, 'the docking process'; Swansont, Ewmon; you're great; Thank you both & everybody, for being with me.

At an height of 'h', I suppose the equation becomes; v2=GhM/(r+h), [Where Gh=Gravity at height 'h'] So from this we can infer that; The Tangential velocity that the Cannonball needs to remain in orbit is; independent of its own mass; inversely proportional to the radius of the orbit. Now does this also mean that; At any height, small or big, if sufficient Tangential velocity, calculated according to the above formula, is given to any object of any mass; it will remain in orbit arround the Earth. For a given height, all objects of all masses will need the same Tangential velocity to remain in orbit.

So when the object is in a net acceleration, there is a net force. And that net force is the Centripetal force (that was what, Swansont was repeatedly pointing out, shown below). Now that things have settled to some extent; how about testing them a little bit, if I am permitted. I have two Cannonballs A & B of mass 1kg & 2kg respectively. I want to put both of them in the Earth's orbit. If I take them up in a rocket along with the Cannon to a height 'h' above the Earth [Newton took them atop a tall mountain. But I am in a Rocket age now.]; I give them each an initial thrust Ta & Tb respectively with the help of my Cannon in a direction tangential to the orbit of radius 'h'. Their tangential velocities would be Va & Vb respectively. They start moving with accelerations Aa & Ab respectively in an orbit arround the Earth. What should/would be the minimum values of the following quantities? h, Ta, Tb, Va, Vb, Aa, & Ab.

This holds good only in ideal conditions where there is no atmospheric drag or in the absence of any resistance. So on the basis of these; I can say . . . Let me see if I have got it all correct. In case of an object moving in circular orbit arround Earth [or any body]: If I say the object is moving due to its velocity 'v' arround the Earth - I am wrong. If I say the Earth's Gravity is holding the object from escaping - I am wrong If I say the object is moving in any particular direction - I am wrong. If I say the object is moving at an uniform acceleration arround the Earth - I am right. ------------------------------------So " A circular motion is a SYSTEM in itself where all the forces, any velocities or any other entities [whatever their names - just don't mention them] acting on an object, have together given the object an ACCELERATION due to which it is going arround in an orbit". Or simply, we should say; "It is a "System" where the satellite is ACCELERATING [can't say moving] arround the Earth." [Due to all the forces, velocities etc inherent to the System] Am I correct?

Let us keep everything aside; let's first see how an object responds to forces; if an object is hit by a force 'Fa' in one direction; and hit by another force 'Fb' at the same instance in another direction; there will be a resultant force say, 'Fr' in a third direction other than the directions of either 'Fa' or 'Fb'; now will the object not move in the direction of the net resultant force; So if the net force in a circular/orbital motion is the Centripetal force, then will the object not move in the direction of the net centripetal force?

Thanks Ewmon for the painstaking explanation. I do not understand how to clear my doubts without expressing them. If my arguments are percieved as misrepresentation of physics, then I am being unfairly misunderstood. Having said that; OK, we shall consider there is no atmospheric drag & the the Initial force need not exist continuously to maintain the Tangential velocity & ceases to exist after giving an initial thrust & the Satellite will continue to be in a state of motion with that intial thrust. We shall stop talking about the Initial force. Now, Let us make things about physics , clear first. "Any motion occurs in the direction of the net force". [Am I representing Physics rightly here? Correct me if Iam wrong.] Then, if Centripetal force is the Net force; the motion should take place in the direction of the net force, which is towards the center of the Earth. The component of the force that is making the object move "to the side" at any instant; must be the Net force, because the only motion that is taking place is "to the side", at any instant. Thank you.

This is what I was arguing with Swansont in #25. But now I understand why Swansont was saying that. How can Centripetal force be the net force? The part of the Initial force that is giving the Initial Tangential velocity, counter balances the Centripetal foce & the residual part of that Initial force is the net force that is giving the Satellite the forward motion. Don't we need some force to keep the satellite in motion? The centripetal force only plays the part of continuously correcting & counter-balancing that component of the Initial force that is giving the Satellite the Tangential path. The centripetal force is completely spent at every instant in correcting the Tangential path into a Circular path. So the net force has to be that component of the the Initial force that is giving the Satellite the Velocity with which it is moving forward. If Centripetal/Gravitational force is the net force here, then the Satellite, instead of moving forward in the circular path, should trace a path along the direction of the Centripetal force towards the center of the Earth i.e. it should fall down.

Ah. It is that simple. Someone has rightly said - "Keep it simple, stupid". My prejudice that science can't be simple made me search for complicated things. But why only orbital motion? It could be any circular motion. When a stone is tied to a thread and given a circular motion, only the Gravity is replaced by the Centripetal force caused by the tension of the thread. The same thing happens there also. Right?

So you mean to say; that the satellite is trying to move in a tangential direction; and the Gravitational/Centripetal force is continously pulling it towards the Earth; but the pull is not sufficient enough to make it fall on Earth. It simply is able to change the direction of the satellite, to make it move in an orbit. No other force is neither involved nor necessary. And this is, what is called; Circular motion. Right?

In the Newton's Cannonball experiment the ball is thrown horizontall to the surface of the Earth i.e. perpendicular to the Gravity. In this case, if you decompose 'v' which is horizontall to the surface of the Earth and so perpendicular to 'a', into its three components, the two of those components, other than the horizontal one, would be zero. None of them can counter-balance 'a'. Unless the Cannonball/Satellite is given an Initial force in a direction such that the three components of that Initial force are such that, one vector component of that initial force is equal & opposite to 'a' & counter-balances 'a'; and second vector component of that initial force gives it a forward motion; and its third vector component is zero, I don't see how an object would stay rotating in an orbit.

I don't understand how two forces acting mutually perpendicular to each other, oppose each other. I have known that only forces which are acting in opposite directions or those which are at 1800 to each other and moving in opposite directions, oppose each other.

I agree. When a Satellite is orbiting the earth there is motion going on. So it certainly needs a net force. I have no doubts about it. But when we consider the forces acting on the satellite, we see that there are only two forces acting on it. 'a' and the force responsible for 'v'. But taking into consideration only these two forces, we see that they are not sufficient to keep the satellite into orbit. There has to be another force that is keeping it in the orbit.

'a' which is the Gravitational/Centripetal force, pulls the satellite towards the earth & also gives it the near circular orbit. 'v' the Initial velocity, is spent solely in moving the satellite forward. To keep the satellite into orbit we need another force which is equal & opposite in direction to 'a', so that it counter-balances 'a' & stops it from falling on Earth. Where is it? We can not say a vector component of 'v' will counter-balance 'a', because 'v' is perpendicular to 'a'. So its vector component in the opposite direction to 'a', which could counter-balance 'a' would be zero. OR Is it that, the satellite is given an initial force in such a direction that one vector component of that initial force counter-balances 'a' and second vector component of that initial force gives it a forward motion and its third vector component is zero. And again, For this to happen, there should be nill atmospheric resistance in the path of the satellite. Otherwise the initial force given to it gets reduced gradually & ultimately the satellite should fall on Earth.

But how equating gravitational/centripetal force alone would keep the satellite in orbit. The satellite is in orbit because the forces acting on it are in equilibrium & have kept it in orbit. Which is the other force that is countering the gravitational/centripetal force to keep it in the orbit in the second model. You said If Tangential velocity is not countering the gravitational/centripetal force then which other force is countering the gravitational/centripetal force. [Edits: Words in italics have been added.]

What & what have to be equal.

Yes, I have no acquaintance with German language. But I don't think that would be a hindrance. Every word Einstein has uttered or written has been translated into English, I suppose. I have read that translation earlier. The mathematical tools no doubt existed. But Einstein did not have those tools with him when he imagined the ‘Theory of Relativity’. He always stressed that ‘IMAGINATION IS MORE IMPORTANT’. He did not arrive at the ‘Theory of Relativity’ because he knew Differential geometry. He could imagine what was not known till then, because he was Einstein. Why can’t we explain & understand that which is known already in simple terms. When he could discern an unknown thing without the help of mathematics, why can’t we discern what is known already without the help of mathematics. Einstein said & I quote “If you can't explain it simply, you don't understand it well enough”. Anyway, I have begun to learn Differential geometry.

OK. Then you said How can Tangential velocity determine centripetal force? The centripetal force is here is nothing but Gravity. How can Tangential velocity determine Gravity?

I am not getting this falling part. Why would it fall at all? Tangential velocity is horizontal in direction? Let us see if I can put it right. "The centripetal force is pulling down the satellite at 9.8m/s^2 which is just sufficient enough, only to pull the satellite down by a distance equal to the length by which the surface of the earth goes down due to its curvature. So it does not come in contact & the distance between the satellite & surface remain unchanged" Is this what happening, there?

I suppose Albert Einstien did not know differential geometry when he descerned the Theory of relativity, an unknown theory then. But why would we need mathematics to just understand what is already known. But I don't want to drift into an off-the-subject argument.

So what is keeping the satellite in orbit in the second model?

I understand V= Tangential velocity. Which accelaration does 'a' denote?