# Macroscopic objects traveling at relativistic speed

How much energy would be required to accelerate something the size of the space station to the same speed as protons colliding at the LHC?

https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies

Plug in the appropriate values for v and m.

Many objects already travel at ‘relativistic’ speed. In particular GPS and GLONASS satellites whose signals have to have relativistic compensation applied before they can be used in your GPS unit.

They also have to have ‘General Relativity’ corrections but these are essentially fudge-factors to make the numbers work out and they happen to coincide roughly with GR predictions.

As I understand it, GR works exactly as predicted on those satellites.

I have no idea how to do that.

I used my old calculator to do it for you, and I got the result: about 3*10^26 J.

How much is that?

It’s a lot.

How much of a lot?

It’s, by chance, almost exactly the same amount of energy the sun generates in a second.

That is hard to relate to.

Admittedly; let me try another one: it’s about 10 000 times the estimated energy of all known fossil fuel reserves on Earth.

Again, that is hard to relate to.

Let’s try one more: it’s close to a million times the annual energy production on Earth. If we started today, and used all our energy for that purpose, it would take us a million years to accelerate that spacecraft to such a ludicrous speed, provided we could keep energy production at its’ present.

How much is a million years?

It’s been like a million years since our ancestors lit the first fires.

Or if we employ a constant acceleration of 1 g, we will get to c in about a year.

Energy as per Ignotus = a lot.
Acceleration as per K84 = energy to do this, an even bigger ‘a lot’ :eek:

Exactly how fast are those bad boys zipping around? I’ll calculate the Lorentz factor myself.

With E = 7 TeV:

v = 99.9999991% times the speed of light
The Lorentz factor has a value of about 7460

That’s quite a lot, but how much energy would it take to get the ship go to plaid?

It’s worth pointing out that the protons in the LHC are moving more slowly than did the electrons and positrons in the earlier LEP collider, though the latter particles did have lower energy. LEP particle speeds reached 99.9999999988% c.