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1

Instead of using existing spacecraft, let's use a photon rocket powered by the gamma rays emitted by matter anti-matter annihilations in its reacor. Where does the anti-mater come from? We will produce it using solar energy. We'll use giant solar panels that generate a huge voltage in vacuum which leads to Swinger pair production. Moving away from the Earth ...

1

From ScienceMuseum: Apollo 10 holds the record as the fastest manned vehicle, reaching speeds of almost 40,000 km per hour (11.08 km/s or 24,791 mph to be exact) during its return to Earth on 26th May 1969. Using the formula (as above). After traveling for 40 years, you would be a little over 0.86 seconds younger. Added: I did some calculating and ...

2

Almost none. Let's be much more generous than your idea of human-carrying craft. Let's just use the fastest probe. The Helios II craft, after nearing the sun, reached a heliocentric speed somewhere near 70 km/s. Obviously, its speed was more due to the gravitational influence of the sun than its engines. $$t = \frac{t_o}{\sqrt{1 - \frac{v^2}{c^2}}}$$ ...

2

So let's just say that the spacecraft can accelerate until it's moving away from the Earth at the speed of the fastest currently-existing spacecraft First, note that the fastest speed, relative to Earth, that a spacecraft has obtained is an exceedingly small fraction of the $c$ and, thus, one should not expect significant time dilation. For ...

6

Your assertion that only relative speeds matter is absolutely correct. However, you might want to look at the velocity addition of special relativity for space ships or whatever else travelling at relativistic speeds. For speeds high above our everyday experience, two things which, relative to us, travel in opposite directions with a speed $v$ will not see ...

2

Photons generate what we call Radiation Pressure. From wikipedia, http://en.wikipedia.org/wiki/Radiation_pressure, we get the equation: $$P_{absorb} = \frac{E_f} {c} cos\space\alpha\\ \text{and} \space P_{reflect}=\frac{2E_f} {c} cos^2\space\alpha$$ Where:$P_{absorb}$ is the Radiation Pressure on an absorptive surface (in Pascals). $P_{reflect}$ is the ...

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