# How many times faster than light is this?

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• RosutoTakeshi

#### RosutoTakeshi

Ok so I'm having trouble understanding how to calculate this

If an object is moving so fast that it would take...

"Hours for light to catch up to it"

.. how fast would it have to be moving?

Let's say it would take 2 hours for light to catch up to it. What kind of speed are we looking at here?

Light speed is 186,282 mi/s
At that speed, in 2 hours light would cross 1,341,200,000 miles

So how fast would an object be moving, if light would take 2 hours to catch up to it? Is it possible to get a close estimate or is the time it took for that object to cross over 1.34 billion miles necessary to solve this?

You cannot answer this. The object could be at rest relative to the light source, or moving in any direction at any speed below the speed of light.

You cannot answer this. The object could be at rest relative to the light source, or moving in any direction at any speed below the speed of light.
I'm afraid I don't understand. If this object gets from point A to point B (crossing over 1.34 billion miles) at such a speed that it would take light 2 hours to catch up to it, that's not solvable?

No. Imagine it is at rest and exactly 1,341,200,000 miles away, then it takes light 2 hours to get there. If it is moving at e.g. 10% of light speed, and it was 1,207,080,000 miles away when the light was emitted, then it will take again 2 hours for the light to get to the object.

No. Imagine it is at rest and exactly 1,341,200,000 miles away, then it takes light 2 hours to get there. If it is moving at e.g. 10% of light speed, and it was 1,207,080,000 miles away when the light was emitted, then it will take again 2 hours for the light to get to the object.

OK I understand a bit, but am still confused. Let me reword it

Say said object was in a race against lightspeed, to cross 1,341,200,000 miles

When the object takes off and arrives at the finish line (over 1.34 billion miles) lightspeed would reach the finish line in 2 hours

How fast was the object going to leave lightspeed that far behind?

This is a very theoretical question, because nothing is faster than light. As a consequence you cannot simply add speeds.

I don't get your setup. If they start the race at the same time, and light takes two hours for the distance, then how can the object be two hours ahead? This would mean that the object is simultaneously at the start and at the finish line.

• RosutoTakeshi
This is a very theoretical question, because nothing is faster than light. As a consequence you cannot simply add speeds.

I don't get your setup. If they start the race at the same time, and light takes two hours for the distance, then how can the object be two hours ahead? This would mean that the object is simultaneously at the start and at the finish line.
Ok, (now) I understand what you're saying and how my question doesn't exactly make sense

Nothing with mass can go as fast as - let alone faster than - light.

But just for fun:

If your spaceship used a magical (read: science fantasy) "Wormhole Drive" that allowed it to go from point A to point B instantly, then point A and point B could be as much as two light-hours (1,341,000,000 miles) apart.

With the ship at A, the skipper presses the 'Go There' button at the same time the referee fires a laser.
Boop! Your MWD (Magical Wormhole Drive) arrives at B*. The laser light takes two hours to arrive.

* ideally with the rest of the ship, and the skipper, still attached.

So how fast would an object be moving, if light would take 2 hours to catch up to it? Is it possible to get a close estimate or is the time it took for that object to cross over 1.34 billion miles necessary to solve this?
How far behind was the light when the clock starts ticking?

If the light is 2 light-hours behind then the answer is trivial: Zero velocity. It takes 2 hours for light to move 2 light-hours.

If the light is 1 light-hour behind then the answer is still trivial: half light speed. In 2 hours, the light will have moved 2 light-hours and the object would have moved 1 light-hour.

If the light is 6 light-hours behind then the answer is still trivial: Can't get there in time.

If you knew the time it took for the object to cross 1.34 billion miles then you would not have to worry about the light and the two hours. You already know the object's speed.

Note: Relativity is largely irrelevant here. We're only using one inertial frame of reference. There is no time dilation, length contraction, relativity of simultaneity or relativistic velocity addition to worry about. Regular first grade physics still works.

• nasu
How far behind was the light when the clock starts ticking?

If the light is 2 light-hours behind then the answer is trivial: Zero velocity. It takes 2 hours for light to move 2 light-hours.

If the light is 1 light-hour behind then the answer is still trivial: half light speed. In 2 hours, the light will have moved 2 light-hours and the object would have moved 1 light-hour.

If the light is 6 light-hours behind then the answer is still trivial: Can't get there in time.

If you knew the time it took for the object to cross 1.34 billion miles then you would not have to worry about the light and the two hours. You already know the object's speed.

Note: Relativity is largely irrelevant here. We're only using one inertial frame of reference. There is no time dilation, length contraction, relativity of simultaneity or relativistic velocity addition to worry about. Regular first grade physics still works.