The characteristic size of a (non-spinning) black hole is given by the \"Schwarz

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The characteristic size of a (non-spinning) black hole is given by the "Schwarzschild radius", rs = 2GM/c^2, where G is Newton's gravitational constant and M is the mass of the black hole. The Schwarzschild radius can also be calculated for bodies which are not black holes simply based on their masses. General relativity effects like "gravitational redshift" and the bending of light emitted from the surface of the object are significant if the Schwarzschild radius is comparable to (say, within a factor of 10) of the actual size of the object. What is the Schwarzschild radius of the Sun? Based on this, would you say there are significant general relativity effects on sunlight, or not? a typical neutron star has a mass about 1.4 times the mass of the Sun, but with a radius of only about 10 km. What is the Schwarzschild radius of a neutron star? Would you expect significant relativistic effects on radiation emitted from its surface? The Earth has a Schwarzschild radius of 8.9 mm much smaller than its radius, obviously! but the relativistic effects are large enough to require corrections for GPS to work properly... [See the "Global Positioning System" article in Wikipedia for more info.] One the one hand, a GPS satellite in its orbit is moving with a speed of about 3.9 km/s, so its atomic clock will appear to run a little slower than a clock on the ground due to time dilation. In other words, gamma will be slightly greater than 1. Calculate the value of (gamma - 1) for the satellite's speed. Use the binomial approximation to ensure you get a reliable numerical result.

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The characteristic size of a (non-spinning) black hole is given by the "Schwarz

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