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Science: asteroid vs. hero physics
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<blockquote data-quote="Ovinomancer" data-source="post: 7488017" data-attributes="member: 16814"><p>I disagree. The problem here is the same one you make about -- when you shifted the frame from the road/field to the car, you DON'T shift the vector of the wind -- it remains the same. Ergo, if you go with an Earth centric reference frame, the asteroid's motion is actually comprised of it's vector and the Earth's speed vector, creating the apparent straight line movement towards Earth. If you restart the Earth, you don't change the Asteroid's original vector, you just recover the Earth's vector back to Earth. The push that was perpendicular in the Earth frame is still in the same direction, which is now diagonal to the asteroid's path. This means you're both slowing the asteroid AND pushing it to the side. At 5 minutes out, the breakpoint speed where slowing becomes more efficient than pushing it to the side is:</p><p></p><p></p><p>Speed of Earth = 30 km/s; radius of Earth (with atmo at a bit of slop): 6500km</p><p>Time needed for Earth to move out of the way: 6500km/30km/s = 216.7 seconds. This is the time you need to generate by slowing the asteroid for Earth to get out of the way.</p><p></p><p>S1 * T1 = S2 * T2. Rearranging, we find S2 = S1 * T1/T2. T2 = T1 + 216.7s. T1 = 300 s (five minutes). So, simplifying, S2 = S1 *(300s/516.7s) -> S2 = 0.581*S1.</p><p></p><p>21.667 km/s - speed needed to push perpendicular to the asteroid's path to cause a miss (6500km/300 seconds <-- right this time!). Note the similarity in the time for Earth to move and this. Just a fun fact, no importance.</p><p></p><p>Setting S2 equal to 21.667 km/s, we get an S1 of 37.3 km/s.</p><p></p><p>So long as the asteroid's speed isn't exactly 37.3 km/s, your perpendicular push in the Earth reference frame will be less efficient than a different angle at generating a miss.</p><p></p><p>Here's a graphic showing the Earth centric frame of three scenarios: a 20km/s asteroid 5 minutes out in green, a 30km/s asteroid 5 minutes out in purple, and a 50km/s asteroid 5 minutes out in yellow-orange. The big things here is that the graphic is <em>to scale.</em> The Earth is the proper size, and the path of the asteroids is what they will appear to travel over the 5 minutes. </p><p></p><p>[ATTACH]100961[/ATTACH]</p></blockquote><p></p>
[QUOTE="Ovinomancer, post: 7488017, member: 16814"] I disagree. The problem here is the same one you make about -- when you shifted the frame from the road/field to the car, you DON'T shift the vector of the wind -- it remains the same. Ergo, if you go with an Earth centric reference frame, the asteroid's motion is actually comprised of it's vector and the Earth's speed vector, creating the apparent straight line movement towards Earth. If you restart the Earth, you don't change the Asteroid's original vector, you just recover the Earth's vector back to Earth. The push that was perpendicular in the Earth frame is still in the same direction, which is now diagonal to the asteroid's path. This means you're both slowing the asteroid AND pushing it to the side. At 5 minutes out, the breakpoint speed where slowing becomes more efficient than pushing it to the side is: Speed of Earth = 30 km/s; radius of Earth (with atmo at a bit of slop): 6500km Time needed for Earth to move out of the way: 6500km/30km/s = 216.7 seconds. This is the time you need to generate by slowing the asteroid for Earth to get out of the way. S1 * T1 = S2 * T2. Rearranging, we find S2 = S1 * T1/T2. T2 = T1 + 216.7s. T1 = 300 s (five minutes). So, simplifying, S2 = S1 *(300s/516.7s) -> S2 = 0.581*S1. 21.667 km/s - speed needed to push perpendicular to the asteroid's path to cause a miss (6500km/300 seconds <-- right this time!). Note the similarity in the time for Earth to move and this. Just a fun fact, no importance. Setting S2 equal to 21.667 km/s, we get an S1 of 37.3 km/s. So long as the asteroid's speed isn't exactly 37.3 km/s, your perpendicular push in the Earth reference frame will be less efficient than a different angle at generating a miss. Here's a graphic showing the Earth centric frame of three scenarios: a 20km/s asteroid 5 minutes out in green, a 30km/s asteroid 5 minutes out in purple, and a 50km/s asteroid 5 minutes out in yellow-orange. The big things here is that the graphic is [I]to scale.[/I] The Earth is the proper size, and the path of the asteroids is what they will appear to travel over the 5 minutes. [ATTACH=CONFIG]100961._xfImport[/ATTACH] [/QUOTE]
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