# Gravational force

I would like to address the question with my limited physics knowledge(not to mention limited English grammar)

Anyway, I heard that you CAN increase the mass of an object by accelerating it.

Is that true?

DaveC426913
Gold Member
Thinktank said:
If both Earth and Jupiter become black holes, will the (jupiter) black hole suck the earth (black hole)? Or both forces will pull each other and expand the space between them?
If Jupiter and Earth both turned into black holes - but did not increase their mass, then there would be no difference in how they interacted with each other.

Gravity is contingent on only two factors: the mass of the object and the distance to it. Black holes do not change this. The thing that makes black holes unique is that, with that same mass, they are much, much smaller. And that means you can get much, much closer. The closest you can get to the centre of the Earth is 6000km; the closest you can get to the centre of a black hole of that size is a few hundred metres. At that range, the gravitational force is way, WAY stronger (it increases 4x for every half distance).

rbj
pallidin said:
I would like to address the question with my limited physics knowledge(not to mention limited English grammar)

Anyway, I heard that you CAN increase the mass of an object by accelerating it.

Is that true?
i suppose so. i think what you are asking about are the effects of special relativity. time, length (along the direction of motion), and mass all change as an object is accelerated to a velocity that is very fast (in the same order of magnitude as the speed of light). specifically, for mass,

$$m = \frac{m_0}{\sqrt{1 - v^2/c^2}}$$

where m is the mass that a "stationary" observe measures of an object that is moving past him or her at a velocity of $v$ and $m_0$ is the "rest mass" or the mass an observer who is moving along with the object observes.

r b-j

rbj said:
i suppose so. i think what you are asking about are the effects of special relativity. time, length (along the direction of motion), and mass all change as an object is accelerated to a velocity that is very fast (in the same order of magnitude as the speed of light). specifically, for mass,

$$m = \frac{m_0}{\sqrt{1 - v^2/c^2}}$$

where m is the mass that a "stationary" observe measures of an object that is moving past him or her at a velocity of $v$ and $m_0$ is the "rest mass" or the mass an observer who is moving along with the object observes.

r b-j

Ok, so is the mass increase dependent on a specific range of accelerative velocity? Or, is the mass increase an inherent nature of acceleration, regardless of how small the acceleration?

pervect
Staff Emeritus
"Relativistic mass" does increase with velocity, but invariant mass does not increase with velocity. See the sci.physics.faq

http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

Furthermore, the gravitational field of a moving object is MOST DEFINITELY NOT the gravitational field of a stationary object with a mass equal to the relativisitc mass of the moving object. The gravitational field of a moving mass is non-isotropic, for one thing. For another point, objects defintely do not become black holes if they move too fast.

An issue that makes it hard to talk rigorously about "the gravitational field of a moving mass" is that the idea of gravity as a force starts to fail when objects move at relativistic velocities. This demands a treatment of gravity as curved space-time rather than as a force, which requires a significant amount of math to explain properly.

pallidin said:
Ok, so is the mass increase dependent on a specific range of accelerative velocity? Or, is the mass increase an inherent nature of acceleration, regardless of how small the acceleration?
For velocities much smaller than c, mass can be treated independently from velocity, since the denominator is approximately
1, but strictly speaking, any object has mass determined by the formula above,
no matter what velocity it has.

Special relativity tends to deal in inertial (non-accelerating) reference frames,
so I'm not sure if that formula holds for a mass of non-constant velocity.
Any SR experts wanna help me out? I'm a bit curious myself.