The maximum range of a missile_the earth is not flat

AI Thread Summary
The discussion centers on the maximum range of a missile when accounting for the Earth's curvature. It highlights that while a 45-degree launch angle maximizes range on a flat Earth, this changes when considering the Earth's curvature and air resistance. For long-range projectiles, such as ICBMs, the trajectory becomes elliptical due to varying gravity with altitude. If a missile is launched horizontally at high velocity, it can achieve an elliptical orbit, potentially covering a range of approximately 40,000 km. The conversation concludes with a realization about the implications of these factors on missile trajectory.
myleo727
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We know if the Earth is considered flat the maximum range is obtained when the missile is launched at an angle of 45 degrees. But what if we take into account the curvature of the earth? what is the maximum arc-length of the range? :confused:
Thank you!
 
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When the range of a projectile is such that it "misses" the Earth due to the Earth's curvature the projectile will go into orbit.
 
The problem is, it does go into an orbit. I think it's an ellipse...
 
sorry. a part of the ellipse. It'll fall back to the earth.
 
myleo727 said:
We know if the Earth is considered flat the maximum range is obtained when the missile is launched at an angle of 45 degrees. But what if we take into account the curvature of the earth? what is the maximum arc-length of the range? :confused:
Thank you!
First of all, the 45 degrees value is valid if there is no air resistance. If we take this into account we should use higher angles and this is what is done in artillery.
Secondly, even in the absence of air, the parabolic trajectory is an approximation valid for short range projectiles. In this case we can consider the Earth flat.
For long range artillery, like ICBM, the gravity changes with the altitude of the projectile, so you must consider an elliptic trajectory.
 
What happens if you shoot the rocket at more than... say... 7 miles per second?
 
Yeah...I'm now considering the long distance missile, and ignore air-resistance...
 
myleo727 said:
Yeah...I'm now considering the long distance missile, and ignore air-resistance...
Then you should consider the change of gravity with altitude (distance to the center of the Earth). The resulting equation of movement is an elliptic trajectory. If you shoot your missile horizontally and with enough velocity, you will have an elliptical orbit whose perigee is at the launch site (supposing no obstacles in the way), so you have a 40000 km range.
 
hmm. I think I just solved it. Thank you!:smile:
 

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