# Relative Mass & Inertia: Could Near-c Collision Destroy a Star?

• B
• Chris Miller
In summary, a bullet striking the Earth at a velocity close enough to c that its relativistic mass approaches that of the Earth would cause equivalent damage to an object of similar invariant mass colliding at a non-relativistic velocity.
Chris Miller
If a bullet were to strike the Earth at a velocity close enough to c that its relativistic mass approached that of the Earth, would the damage be equivalent to that of an object of similar invariant mass colliding at a non-relativistic velocity? (The reason I ask is that in Liu Cixin's sci-fi, The Dark Forest, a star is destroyed by hitting it with a small projectile traveling at near c.)

I wouldn't use relativistic mass in this (it's largely a deprecated concept these days outside of pop sci, due to it engendering a lot of confusion), but yes, in theory. The kinetic energy ofa mass moving at speed ##v## is ##(\gamma-1)mc^2##, where ##\gamma =1/\sqrt {1-v^2/c^2}##. That number can be as large as you like, tending to infinity as you approach the speed of light.

Whether or not you can actually destroy a star with a kinetic strike, I don't know. Earth, yes.

Thanks for the clarification, Ibix. Amazing, almost unbelievable, to me that something the size of a BB... a grain of sand... even a neutron? could theoretically destroy the Earth (and why not a star then?) if its velocity were close enough to c. Hope those big particle accelerators have some safety features.

Chris Miller said:
Hope those big particle accelerators have some safety features.
They aren't needed, at least as far as accidentally letting a world-destroying particle loose. The only way of accelerating a particle to world-destroying energies is to supply that much energy to the particle in the first place - the particle never has more energy than what you put into it to accelerate it.

Now, it would be an interesting exercise to calculate the amount of energy required to accelerate a particle to a speed such that its relativistic mass is equal to the mass of the earth... try it.

Chris Miller said:
Hope those big particle accelerators have some safety features.

The only kind of mass I ever talk about is the ordinary mass, so I'll restate your proposal in those terms. A bullet of mass ##0.001## kg collides with Earth, mass ##6 \times 10^{24}## kg. In a frame of reference where Earth is at rest, the bullet is moving so fast that it has an energy of ##6 \times 10^{24}## kg. (Note that I'm measuring energy in kilograms. To convert to joules you would multiply by ##c^2 \approx 9 \times 10^{16}## J/kg.)

Therefore we have ##\gamma \approx \frac{6 \times10^{24}}{0.001} = 6 \times 10^{27}##.

(Note that when a particle's speed is so close to the speed of light that the difference is negligible, we speak of ##\gamma## rather than the speed because the former is more meaningful. This is analogous to speaking of the speed rather than of ##\gamma## when the speed is so small that the difference between ##\gamma## and ##1## is negligible.)

The LHC is the biggest particle accelerator. Its protons move at nearly the speed of light. The ratio of Earth's mass to the proton mass is ##\frac{6 \times10^{24}}{2 \times10^{-27}} \approx 3 \times10^{51}## but those protons are given only enough energy to make ##\gamma \approx 7500##. I think we're safe because we'd need a ##\gamma## of ##3 \times10^{52}## to make that proton as dangerous as your bullet. We have nothing remotely capable of producing that much energy.

SLAC moves electrons at nearly the speed of light and achieves a ##\gamma## of about ##98\ 000##. The ratio of Earth's mass to the electron mass is ##\frac{6 \times10^{24}}{9 \times10^{-31}} \approx 7 \times10^{54}##. Again, we're safe.

SiennaTheGr8

## 1. What is relative mass and inertia?

Relative mass and inertia refer to the measurement of an object's mass and its resistance to changes in motion. In other words, it is a measurement of an object's tendency to maintain its current state of motion.

## 2. How does relative mass and inertia affect the destruction of a star in a near-c collision?

In a near-c collision, the relative mass and inertia of the objects involved play a significant role in determining the outcome. If the relative mass and inertia of the objects are similar, it is possible for the collision to result in the destruction of a star. However, if the relative mass and inertia are vastly different, the star may not be affected as much.

## 3. Can a near-c collision completely destroy a star?

Yes, it is possible for a near-c collision to completely destroy a star. This is because the immense force and energy generated during such a collision can cause the star to break apart and disintegrate.

## 4. Are there any factors other than relative mass and inertia that can affect the outcome of a near-c collision?

Yes, there are other factors that can influence the outcome of a near-c collision, such as the speed and angle of collision, the density and composition of the objects involved, and the strength of their gravitational fields.

## 5. How do scientists study the effects of near-c collisions on stars?

Scientists use computer simulations and mathematical models to study the effects of near-c collisions on stars. They also analyze data from astronomical observations of actual near-c collisions that have occurred in the universe.

• Classical Physics
Replies
20
Views
1K
• Special and General Relativity
Replies
10
Views
2K
Replies
2
Views
1K
• Special and General Relativity
Replies
18
Views
11K
• Special and General Relativity
Replies
5
Views
4K
• Sci-Fi Writing and World Building
Replies
21
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K
Replies
18
Views
2K
• Special and General Relativity
Replies
1
Views
2K
• Beyond the Standard Models
Replies
11
Views
3K