- #1
mch
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Homework Statement
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A low flying Earth satellite travels at about 8000m/s. For the satellite, the relativistic factor $$\gamma = \frac{1}{\sqrt{1-\beta^2}}$$ where $$\beta = \frac{v}{c}$$ is close to 1 because v<<c. Estimate by how much gamma actually deviates from 1 by expanding gamma in a taylor series and evaluating all terms up to second order.
Homework Equations
The Attempt at a Solution
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To be sure, I plugged in 8000 for v in gamma originally. That is, I evaluated $$\gamma = \frac{1}{\sqrt{1-\beta^2}}$$ with $$\beta = \frac{8000}{3\times10^8}$$ When I put this gamma into my TI-89 and used 12-point-float, it came back with 1.00000000036. This makes sense, since the satellite is moving so slow compared to the speed of light. However, when I did the taylor expansion, I came up with $$\gamma \approx 1 + \frac{\beta^2}{2}$$ and when I put in the aforementioned beta value, i came up with the EXACT same value as before. So my question is a semantic one I suppose: what is the question wanting me to do? How can I get a more useful number when both "techniques" yield the same number?