Introduction

What is gravity?

We all wonder why we fall to ground and don’t go up or fly away. What makes planets revolve around the sun and moon revolve around earth. Well, it is still a mystery but two persons are given credit for their brilliant explanations: Newton to his Universal law of gravitation and Einstein to his General theory of relativity. Let us now see how they defined gravity.

Newton’s Universal law of gravitation

               According to Newton’s Universal law of gravitation any two particles or masses naturally attract each other. This attraction or force of attraction is directly proportional to product of their masses and inversely proportional to square of their distances between them.

F= GM1M2/R

Where G - Universal gravitational constant

But, in Newton’s law of gravitation, gravity is an instantaneous force.ie; if sun were to disappear all of a sudden we would feel that instantaneously. Also Newton’s law couldn’t explain the perihelion of mercury, a discrepancy of mercury’s orbit.

                                                                                                       

Einstein’s theory of General relativity

               Einstein came up with a brilliant idea that gravity is not a force but a consequence of curvature of space-time. According to General theory of relativity a mass curves space-time around it and a free-falling objects are moving along locally straight path in curved space-time. Einstein considered time a dimension and related gravity to space & time. This is best explained by a trampoline, though it really is not right example.

When you put a heavy mass on a trampoline we observe the mass pulls down the fiber creating a curvature. If we throw a light mass pointing just away from the mass we observe that it moves in elliptical path just as mercury perihelion effect. This is how a free-falling object rotates. Mass bends space-time around it and so the path of planets is curved and freely falling.

Understanding Space-time curvature

Above explained example of trampoline is best example to understand the path of object moving in space-time but really is not how the space-time is curved. A mass would curve space-time equally in all direction. In trampoline example, gravity pulls lighter mass down and so it decelerates while moving away from larger mass. But in reality space-time is curved same above and below. The net force seems to be equal either up or down. So any mass would follow the curved path initially but would fly away once it reaches other side because there is no force pulling it back. So, the example of trampoline is not quite complete to explain curvature of space-time.

“Curvature of space-time is not a heavier mass curving a space-time around it but a lighter mass following path of curve instead of straight line under influence of gravitation.”

According to general relativity mass curves space-time but not just space. It means an object moving in space will go in a straight path for any amount of time but once it approaches any other object it starts to deviate from straight line path and moves in a curved path. The curvature of path depends on strength of gravity between mass A and B but the path of object A is curved not because of curvature of just space.

In the above figure, let us assume that Mass B is at rest and mass A is initially moving with velocity V. Let us assume that curvature of space-time is not felt till it reaches a point Y . So the path from X to the point of arrow(Y) it would follow a straight path. Now let us assume that suddenly both bodies feeling the strength of gravity. At this point mass A bends it path slightly as if a some force is pulling it perpendicular to its path.

Note: there is no space curved but still mass A follows a path of curve instead of straight line. Hence it is called curvature of space-time because mass A takes a path of curve even though space is not curved.

But why does the mass A takes the path of curve instead of straight line if space is not curved? Does it mean a force acting perpendicular to its path that it starts to curve upward or downward?

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Relation between Einstein’s theory and Newton’s theory

Now we understand the difference between Space curvature and space-time curvature

If we carefully observe these two theories we can understand two points

•       According to Newton's law, under influence of gravity the path of the body is linear and in Einstein's theory the path of the body is linear in curved space-time

•       Acceleration due to gravity causes linear motion in Newton's theory and angular velocity or radial acceleration is velocity of the body in Einstein's theory

If we compare and understand these two theories we can infer one point. In Einstein’s theory the force of attraction between two bodies is reduced to a dimension in space-time i.e., the force of attraction is replaced with addition of new dimension to space. To explain what I meant from this let me give you an example.

Consider a force F acting on a mass that makes it move linearly with some acceleration. If I stop applying force after sometime it will decelerate and stop eventually.

Now let us replace the force on the body as a natural moment of the body or assume force is some invisible kind. If we don’t see the force on the body we get a notion that the body is under motion naturally without any force acting on it. The position of the body is changing in space coordinates even though there is no force. So, we account this with a new dimension of time and conclude the body is moving naturally in four dimensions of space-time.

But what causes a force to curve the path of the body. According to Newton’s law the path of the body should be linear, the force should pull the mass directly towards each other. If the force is linear why would every planet revolve around the stars without colliding? This challenge can be eliminated if we understand that the gravitational force cause angular velocity or radial acceleration on a body but not linear acceleration. This can explain why all bodies revolve instead of colliding. Because the path of the body curves planets never collide with their stars or bumps into each other. This explains the relation between these two theories.

“Gravity causes radial acceleration and not linear acceleration. Strength of gravity can be determined using Newton's theory. Path of the body can be determined by Einstein's theory reducing force into a dimension in space-time”.