# Is law of universal gravitation really correct?

1. Sep 15, 2009

### DarkestNight

hello, i'm not saying that newton's law of universal gravitation is really wrong but there are phenomenons which i don't think the law is really correct and i want someone to help me. There might be explanations but i don't really know any explanations right now so an explanation would be appreciated.

1. When two masses are at one point (centers align), from the equation you should get undefined amount of force but doesn't the force becomes zero when that happens as the two objects should merge into one? This scenario should have occurred many times in daily life, eg. a bullet is fired at a person. The center of the bullet might be able to exactly align with the center of the person as it pierce through the person.

2. When two centers are extremely close to each other, (d->0 but not equal to zero), acceleration should approach infinite from the equation but doesn't that mean the two masses should travel at extreme velocities toward each other? Firstly doesn't it mean that the masses will be able to exceed the speed of light as the acceleration is approaching infinite which violates Einstein's theory. Secondly if the speed of one mass does not exceed speed of light then from law of conservation of mass and momentum, the mass should approach infinite as velocity is converted to mass from equation E=mc^2. But this would lead to more problems such as the mass would attract other objects with force approaching to infinite from law of universal gravitation.

So can anyone give me an explanation to the points i mentioned above? Thanks

2. Sep 15, 2009

### vanesch

Staff Emeritus
Newton's gravity is quite correct for "normal" applications to not-too-extreme situations, but we know since Einstein that relativity imposes modifications of gravity. It is Einstein's general relativity which replaces Newton's gravity (and reduces to Newton's gravity in daily applications).

Gravity is not "concentrated" in the center of an object. It is only for a spherical object, *outside the object*, or when you are far from the object (as a good approximation) that it is allowed to replace the gravitational effect of an extended body by the gravity of its mass in its center.

For instance, in the center of the earth, the gravitational force is zero.

Yes. But in Newton's theory, there is no "speed limit". This is the kind of extreme cases where Newton's gravity, although mathematically consistent in a way, doesn't coincide with what is observed to happen in our universe, and where General Relativity is a better description of gravity as it happens in our universe.

Again, Newton's law of gravity doesn't include any relativistic effects. When these become important, Newton's law of gravity is not a good description of nature anymore. But for more daily phenomena, these corrections are so tiny that Newton's law of gravity is still a good (very good) approximation.

3. Sep 15, 2009

### D H

Staff Emeritus
Welcome to PhysicsForums, DarkestNight!

The answer to your question, "Is the law of universal gravitation really correct?", is no -- but not quite for the reasons you gave.

1. Even in Newtonian mechanics, Newton's law of gravity applies only to point masses. Real objects are not point masses. To compute the gravitational force between a point mass and a real object, you have to compute the forces between each bit of matter in the real object and the point mass and add all those little bits up -- a volume integral. For example, consider the gravitational force inside the Earth. Newton's law of gravity, properly applied, says the gravitational force at the center of the Earth is zero, not infinite. For two real objects, a double volume integral is needed. Because real objects are not point masses, your concern never materializes.

2. This is closer to the mark, but still not quite correct. If the point masses are moving, the time during which the acceleration is infinite is infinitesimally small. Just because the acceleration becomes infinite does not necessarily mean that velocity necessarily becomes infinite.

However, the velocity does not have to become infinite to create big problems with respect to special relativity. All it has to do is exceed the speed of light. One can easily come up with orbits that would follow Newton's law of gravity but would have superluminal velocities somewhere along the orbit. Newton's law of gravity is not quite right. In addition to special relativity, Einstein also developed general relativity, which is a more accurate model of how gravity works that Newton's law.

So why don't they teach general relativity rather than Newton's law of gravity? Simple: If you are a high school student, neither you nor your teacher have anywhere near enough math background to be able to understand it. That's not an insult. There are a lot of people who majored in physics in college who don't have the math background to understand it.

Newton's law of gravity is a very good approximation to how gravity does work. It does a very good job of explaining the solar system. It took a couple hundred years after Newton's time Einstein before scientists started seeing problems.

4. Sep 15, 2009

### DarkestNight

Thanks for your explanations, i got the idea now