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Where did you get that figure for the speed of the Earth's surface? The circumference of the Earth at the equator (it's greatest circumference) is 40,075km and it rotates once in 24 hours, so the speed is 40,075/24 or about 1,670 km/hour or 464 m/sec. If you calculate the time dilation at 464 m/sec it's insignificant, as you'd expect given that this speed is 0.0000015$c$. Response to comment: The velocity of rotation around the sun is about 29,800 m/sec (0.0001$c$), and at this speed the time dilation factor is about 0.999999995. This gives an error of about 23 years over the 4.54 billion lifespan of the Solar System. But in any case you need to define what you mean by the time. If a physicist uses radioactive decay to measure a date then because the physicist is moving at the same speed as the radionuclide the physicist and the radionuclide experience time flowing at the same rate. That means that by definition there can't be any dating errors. Response to response to comment: Suppose a block or Uranium-238 split in two at the beginning of the Solar System, 4.54 billion years ago, and one half ended up on Earth while another half ended up on Pluto. On the Earth a physicist dated the formation of the Solar System by measuring how much of the U-238 had decayed, while on Pluto an alien physicist did the same experiment. The two physicists would come up with different ages i.e. they would measure that different amounts of the U-238 had decayed. This is a real difference: time really does flow at a slightly different rate on Earth and on Pluto, though the difference is so small that you'd never actually be able to measure it. Some of the difference would be due to the different orbital velocities of Earth and Pluto, and some would be because Earth is deeper into the Sun's potential well and gravity affects time as well. I'd have to sit down with a pen and paper to work out which effect was stronger. Although the time dilation is insignificant for the Solar System gravitational time dilation can be significant for neutron stars and especially for black holes. In fact if you sat some distance from a black hole and watched someone falling into it you'd see time for the falling astronaut slow to a stop as they approached the black hole event horizon. One last comment: You might be interested in this article. I've already mentioned that the gravitational field of the Earth affects time, and this has been used to measure the Earth's geoid by measuring the differences in the rate atomic clocks run. |
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