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3

You're absolutely correct - objects do not need to ever reach earth's escape velocity of 11.2 km/s, and many spacecraft that leave orbit, don't. That being said, note that escape velocity depends on where you are: the velocity that a cannonball 1000 km above the earth's surface would need to escape is substantially lower than that needed by a cannonball on ...

-1

Might boron carbide perhaps work? Its pretty strong, neutron absorbing, 3,000 K melting temperature, Mohs hardness is around 9.5. Density is around 2.5 g/cm^2. It is also relatively easy to produce.

1

$\theta$ is the angle made between the positive x-axis and the spacecraft's velocity vector (all at closest approach). Don't you need $\theta$ to be the angle of the spacecraft's velocity relative to Mars? Try subtracting the Mars velocity vector from the spacecraft's velocity vector, calculating $\theta$ for the resultant vector and using that angle ...

4

Assumptions we start with an observer and a star at rest with respect to each other and 1000 lightyears apart. Both observer can agree on these facts. The observer then sets out toward the star in a reasonable fast starship, arriving after 10,000 years as measured in their original frame, recording the light from the star as he goes. The traveller ...

2

Firstly, if we travel at 90% the speed of light, the relativistic effects will be too magnified to ignore. If you are travelling at a speed of $0.9c$ towards the star, according to your frame of reference, the star is coming towards you at $0.9c$ too. You'll observe that the speed of rotation of the star slows down by a factor of ...

5

We certainly would, or at least we would if we had telescopes powerful enough. However, better still, we could choose to watch its history unfold at an arbitrarily high fast-forward rate! Suppose our universe were classical/Newtonian/Galilean (or whatever you want to call it) but with a finite speed of light propagation (and let's just say that we're still ...

0

Considering that hitting a 1mg grain of dust at 0.1c speed would release the energy equivalent to an explosion of a 200 kg bomb, I really would not hold my breath. The only way I can imagine interstellar travel is as a swarm of nanobots. They would be sent on their way, and would have to be somehow decelerated at the destination. They would not carry fuel, ...

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