# How do I calculate acceleration with a mass of Zero

Hi all,

If I have an object with zero mass in a vacume and apply say 1n of force to the object how
can I calculate its acceleration, and current speed at any time?

Thanks all.

Staff Emeritus
2021 Award
You can't. You'll have a division by zero.

all massless particles travel at the speed of light.

As Vanadium50 pointed out, a = F/m gets you in trouble. You can understand this more clearly by considering what happens if you apply this same force to a succession of increasingly smaller masses. Look at the curve of a = F/m (a hyperbola), and you see that the lighter the mass, the higher the acceleration, which goes to infinity as the mass goes to zero.

That's the nonrelativistic answer, i.e. what Newton would have told you. Cragar's response comes from Einstein's Theory of Relativity, where there are no infinite speeds (or accelerations). The speed of light is the absolute speed limit, so massless particles must all move at that speed (they can't ever be at rest, or they would appear to be moving at a speed less than c to some observers).

As Vanadium50 pointed out, a = F/m gets you in trouble. You can understand this more clearly by considering what happens if you apply this same force to a succession of increasingly smaller masses. Look at the curve of a = F/m (a hyperbola), and you see that the lighter the mass, the higher the acceleration, which goes to infinity as the mass goes to zero.

That's the nonrelativistic answer, i.e. what Newton would have told you. Cragar's response comes from Einstein's Theory of Relativity, where there are no infinite speeds (or accelerations). The speed of light is the absolute speed limit, so massless particles must all move at that speed (they can't ever be at rest, or they would appear to be moving at a speed less than c to some observers).

thanks. I was getting a div zero, and needed a fix for it. I also don't subscribe to the absolute speed limit thing. I need a formula that ignores the speed of light and gives me the acceleration and speed of a mass-less object.

Basically I need a way of working out the following scenrio.

An object with a mass of say 10kg is sat in geo stationary orbit.
The object has a way to reduce it's mass to zero.
It applies some thrust say 1n for 1 second
It then returns to normal mass
How far has it traveled?

I also don't subscribe to the absolute speed limit thing. [....]
Fail.

(How were you going to push so hard against something that doesn't resist being pushed against, anyway?)

Pengwuino
Gold Member
Basically I need a way of working out the following scenrio.

An object with a mass of say 10kg is sat in geo stationary orbit.
The object has a way to reduce it's mass to zero.
It applies some thrust say 1n for 1 second
It then returns to normal mass
How far has it traveled?

The laws of physics will fail if you intentionally make them fail. What more do you want? If you want to pretend the laws of physics need not apply, your object has traveled to the planet infinity. Or it fell to the ground. Who knows? You make up the rules.

russ_watters
Mentor
I also don't subscribe to the absolute speed limit thing. I need a formula that ignores the speed of light and gives me the acceleration and speed of a mass-less object.
If you choose to ignore the laws of physics, then you can do anything you want (just ask superman!)....except speculate about it on this forum. On this forum, we deal only in reality. Thread locked.