Special Relativity.

[Anonymous No.2381700]

Alright, so the Modern Physics problem is kicking my ass. I don't see how it gives me enough variables:

The Apollo astronauts returned from the moon under the Earth's gravitational force and reached speeds of almost 25,000 mi/h with respect to Earth. Assuming(incorrectly) they had this speed for the entire trip from the moon to Earth, what was the time difference for the trip between their clocks and clock on Earth?

I almost want to say they want an equation that finds dT (T = t1 - t2), but that seems too damn complicated for the 2nd chapter and the first set of problems.

Anybody see where I'm being stupid?

[Anonymous No.2381728]

bumping for... uh... help with special relativity and lorentz transformations?

[Anonymous No.2381743]

just at a glance i'd say you want special relativity, so just get v in metres per second and plug it in.

distance between earth and moon you can find on internet really easily, it's a standard given that people know it.

then do speed=distance over time, find time taken to get from moon to earth travelling at 25000mi/hr, then multiply that by gamma (see special relativity)

gamma = 1/(root(1-(v^2/c^2))

[Anonymous No.2381782]

It's 11,176 m/s. Got that. The major problem I was having was that they don't give you either the proper time or the time on the Apollo.

As for the distance, you might be right, that could be the one where I'm being stupid. But they don't say which Apollo it was, and just because they went to the moon and back doesn't mean they traveled the straight line distance. I know at least one of the Apollo actually slingshot around the moon.

But, I could solve it for the straight line there and back scenario. I'll just privately rage that they don't tell you the proper distance or time in the problem...

[Anonymous No.2381817]

>Assuming(incorrectly) they had this speed for the entire trip from the moon to Earth

If they were traveling directly towards Earth at a constant speed for the whole trip, that implies there was no acceleration. As such, both the Earth and the Apollo spacecraft can correctly be labeled as inertial frames of reference. Thus by the twin paradox reasoning, their clocks must have been running at the exact same speed... right until the moment the Apollo spacecraft slammed into the Earth at 25000 m/h, killing the astronauts in the process.

...wait what

[Anonymous No.2381840]

>>2381817

I'll play with the troll because I can. They aren't in inertial frames of reference, because inertial frames are classical.

25,000 mi/hr is small compared to c but not completely negligible.

They'd still die when they slammed into the Earth at 25,000 mi/h.

[Anonymous No.2381887]

>>2381840
If you really believe that it's possible for the Earth to think the astronaut clock is running slow AND the astronauts to think the Earth clock is running slow, even as they get closer and closer and eventually meet (so as to be able to compare clocks), then you're allowed to brush off my post

But that's too hard to believe