# General Relativity, Newtonian Mechanics and Gravity

Gravity is considered to be the curvature of spacetime by Einstein and a force by Newton. So are both notions equally correct or Einstein's perspective completely replaced Newton's thinking?

Einstein's relativity is more correct than Newton's equations for gravity. There are details to keep in mind, though.

For weak sources of gravity, like Earth, General Relativity and Newton's equations give indistinguishable answers. NASA scientists used Newton's equations to send astronauts to the moon and probes beyond our solar system because the math is easier and the answers the equations give are different by an immeasurable amounts.

However, as gravity gets stronger, like when you get close to a star, General Relativity and Newtonian equations start to give different answers. At the beginning of the 20th century, Newton's equations were failing to predict the motion of the planet Mercury. Einstein's relativity equations make correct predictions.

This often happens in science. Newton's equations are not wrong. It's better to say that we have found limits to where they give correct results. General Relativity has a larger area where it gives answers that agree with our measurements. At the moment, we have not found limits where General Relativity stops giving correct answers.

• So is it true that we can consider gravity both as a force and a curvature in spacetime? What really confuses me is the validity of the saying that gravity is not a force. – Benjamin Jul 27 '17 at 22:19
• @Benjamin It depends on what people mean by "force." In one sense, gravity is a force because it causes acceleration. In another sense, the acceleration is somewhat fictional because an object in a gravitational field is traveling in a straight line through curved space-time. This is similar to the way walking in a straight line on Earth will eventually cause you to walk in a circle due to the Earth being spherical. This is what people mean by "gravity is not a force." It's also fine to think of gravity as a force transmitted by curving space-time. – Mark H Jul 27 '17 at 22:37
• @Benjamin We say that gravity isn't a force because gravity affects everything equally (compare this with electromagnetism, which only affects charges/currents). So if you are in free-fall, you will not actually feel a force on you, because gravity affects all your particles equally. On the other hand, when you are sitting on your chair, you feel a force on your buttocks, even though you are "unaccelerating". So would it not be more natural to consider a freely falling object unaccelerated? Obviously, there are more mathematical answers to this, but as heuristics go, this is it. – Bence Racskó Jul 28 '17 at 12:24
• @Uldreth It depends on context whether calling gravity a force is useful. Gravity causes measurable acceleration, so the word "force" is very appropriate. On the other hand, the deeper you get into fundamental physics, the more the idea of force becomes less useful. Relativity is not unique in this since Quantum Mechanics also has little use for "force" as a quantity. When particles don't have definite positions or momenta, acceleration (and thus force) becomes a fuzzy concept. – Mark H Jul 28 '17 at 19:12

Newton's Theory of Gravity, just stated it as a force that exists, and explained how the force works but it never interpreted the origin of Gravity. He himself stated in his paper of Philosophia Naturalis Principa Mathematica that he does not know the origin of the gravitational force and leaved the task to the reader.

Einstein's General Theory of Relativity explained the origins of the Gravitational Force along with its precise working. The General Theory of Relativity is considered to be more accurate and correct and it has replaced Newton's theory of gravity because of the following reasons :-

1.) Newtons's Theory of Gravity basically explained the nature of the gravitational force but nevertheless stated its origin.

2.) Newton's Theory of Gravity was not able to explain the precession of the perihelion of Mercury, that is the periodic shift in the perihelion (lowest point of an orbit) of Mercury.

3.) According to Newton's perspective, the force of gravity acting between two bodies is directly proportional to the product of their masses and inversely proportional to the distance between them squared. So according to his theory, since light particles - photons are massless, they would not be affected by a gravitational field. But General Relativity proved that the path of a light ray is influenced by a Gravitational Field, this phenomenon is known as - Gravitational Lensing.

4.) All the Newton's theories are based on absolute space and time, whereas both the Special and General Theory of Relativity are based on relative space and time.

Due to these reasons, General Relativity is used for making precise and accurate calculations. However, Newton's Theory of Gravity is still used in some cases for weak sources of gravity like Earth because of its simplicity.