How Does Special Relativity Affect Space Travel and Communication?

AI Thread Summary
The discussion revolves around a homework problem involving a spaceship traveling to Alpha Centauri at 0.5c and sending a radio message back to Earth. Participants are asked to create a spacetime diagram and determine the timing of the radio signal's arrival at the spaceship. There is confusion regarding the application of special relativity, particularly in relation to the speed of light and how it affects the timing of the message. The original poster expresses uncertainty about whether to consider relativistic effects in their calculations. Clarification on the use of Lorentz transformations and the implications of constant light speed across reference frames is sought.
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Homework Statement


Suppose that we send a spaceship on a trip to Alpha Centauri, 4 light years away. The spaceship travels at a constant speed of .5c, it stops at Alpha C. for 1 year and then it returns to the Earth at constant speed .5c.
a. Draw a spacetime Diagram with axes x,ct and plot the worldine of the spaceship.
b. suppose that 1 year after the departure of the spaceship we send a radio message from Earth to the spaceship. Plot the worldline of the radio signal.
c. At what time does it reach the spaceship?

Homework Equations



The Attempt at a Solution


a.
ct
|\
| .\
| .. \
| ... |
| .. /
| ./
|/________________x
where the angle between the ct and x-axis is given by

theta = arctan(.5)

b.)I drew a cone with an angle of 45 between the ct and x axis.
c.) this is what I'm confused about. I'm not sure if I have to take relativity into account since c is the same in all reference frames. So, my answer is 1 year after the message is sent.

Can anyone please tell me if any of this is right? Any help will be greatly appreciated.
 
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does anyone have any ideas? I'm still really confused about this one. The only things that we've gone over so far are the basic Gallilean transformations and Lorentz transformations. But, i just don't see how either of them would help here. Once again, if anyone could offer any guidance or feedback I would really appreciate it.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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