I've been trying to graph an idea I had, but frankly I don't understand SR well enough to ensure my assumptions are correct, and that I'm using the correct formulas. I would appreciate any input/corrections you folks could give. Here's the idea, which I'll follow with my assumptions:(adsbygoogle = window.adsbygoogle || []).push({});

Idea: Place a powerful laser in space at a location you'd like to travel to quickly. Let's say near Epsilon Eridani because Wikipedia says it has a planet and is approx. 10 light years away. Now build a space vessel with a dish to collect this laser light from the front of the vessel, and convert it into usable energy for the propulsion system. The closer the vessel approaches c, the higher it observes' the laser's frequency to be. Since the energy of light is a function of its frequency, the vessel should receive more energy the faster it goes, helping it maintain constant acceleration despite its mass also increasing.

Assumptions:

1. While the energy of the laser light doesn't actually increase, the vessel should encounter more wave fronts/sec., which I'm equating to an observed increase in energy. If we combine Planck's relation with the relativistic doppler shift, we get:

[tex]E=h\left(\sqrt{\frac{1+\beta}{1-\beta}}\right)f_{s}[/tex]

(Note: I've reversed the signs above because we're heading toward the source, so I'm looking for the "blue shift" rather than the "red shift". This allowed me to use positive fractions of c rather than negative.)

2. This is correct formula for determining an object's mass at relativistic speeds?

[tex] m_{\mathrm{rel}} = { m \over \sqrt{1-{v^2\over c^2}}}[/tex]

Results:

When I graphed these, the laser's observed energy was 300% of original at 0.8c, but the mass was only 166% of rest mass... something seems wrong to me. Are my assumptions just flat wrong?

Thanks again, folks. I'm new here, so please be kind :)

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# Planck relation, relativistic doppler effect, and relativistic mass

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