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Science: asteroid vs. hero physics
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<blockquote data-quote="freyar" data-source="post: 7487963" data-attributes="member: 40227"><p>You missed what I said about being in the rest frame of the earth <strong>over a short time</strong>. For someone sitting on the earth, in the last little bit before the asteroid hits, it's going to look like the asteroid is coming straight at the earth. Over longer periods of time, yes, you're right that you have to take the earth's acceleration around the sun into account. But not over the course of a few hours. Looking at the numbers, the difference between the earth's actual orbit and a constant velocity path is less than the earth's radius for about a 12-hour period, so that's about how long we can neglect the acceleration (sorry, I was just guessing when I said a day or two).</p><p></p><p></p><p>That's in the rest frame of the baseball field. In the rest frame of the car --- assuming no acceleration, which would change your scenario as well --- the baseball has to come straight at the car, or it will miss. You and the baseball field are, however, moving compared to the car. This is a simple example of change of reference frame from introductory physics.</p><p></p><p></p><p></p><p></p><p>Depends on what frame you're measuring the wind's speed from. In the earth's frame (the natural one for our hero), slowing down the asteroid won't stop it from hitting the earth. It will just make it hit later.</p><p></p><p></p><p></p><p>That's only if you're talking about longer time periods than this problem. The OP was talking about a 5-minute time frame, which seems to have been extended maybe to a few hours. If you want to talk about a day, you have to worry about this a little. More than a day or two, yes, I agree you have to worry about the full orbital mechanics. Kepler is certainly important over the course of a year, but one thing we learn in physics is how to know when different effects are actually important.</p></blockquote><p></p>
[QUOTE="freyar, post: 7487963, member: 40227"] You missed what I said about being in the rest frame of the earth [B]over a short time[/B]. For someone sitting on the earth, in the last little bit before the asteroid hits, it's going to look like the asteroid is coming straight at the earth. Over longer periods of time, yes, you're right that you have to take the earth's acceleration around the sun into account. But not over the course of a few hours. Looking at the numbers, the difference between the earth's actual orbit and a constant velocity path is less than the earth's radius for about a 12-hour period, so that's about how long we can neglect the acceleration (sorry, I was just guessing when I said a day or two). That's in the rest frame of the baseball field. In the rest frame of the car --- assuming no acceleration, which would change your scenario as well --- the baseball has to come straight at the car, or it will miss. You and the baseball field are, however, moving compared to the car. This is a simple example of change of reference frame from introductory physics. Depends on what frame you're measuring the wind's speed from. In the earth's frame (the natural one for our hero), slowing down the asteroid won't stop it from hitting the earth. It will just make it hit later. That's only if you're talking about longer time periods than this problem. The OP was talking about a 5-minute time frame, which seems to have been extended maybe to a few hours. If you want to talk about a day, you have to worry about this a little. More than a day or two, yes, I agree you have to worry about the full orbital mechanics. Kepler is certainly important over the course of a year, but one thing we learn in physics is how to know when different effects are actually important. [/QUOTE]
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