Fireing projectile from north pole to equator

In summary, the problem of finding the velocity and angle required for a projectile to land from the North pole to the equator is a difficult one, involving solving a non-linear differential equation. While it may be simple in a flat plane with constant acceleration, the curvature of the Earth and other factors must be taken into account. Neglecting air friction and deviations in the Earth's surface, an infinitesimally close circular orbit may be used, but this is not a realistic solution.
  • #1
greaser
2
0
I am trying to find what velocity and angle of launch is required for a projectile to be fired from the North pole and land somewhere on the equator. I was thinking 45 degrees with muzzle velocity 9401m/s but that sounds ridiculous. Also how much time would it be in the air for?
 
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  • #2
Looks to me like a very difficult problem, probably involving solving a nasty non-linear differential equation.

IF it were a matter of finding the angle and initial velocity of a flat plane, with constant gravitational acceleration, a distance equal to the distance from the north pole to the equator, then it would be relatively simple. However, if you REALLY mean "north pole to the equator" you will have take into account the curvature of the Earth and the fact that you are firing the projectile around 1/4 of that curvature. Your trajectory will be high enough that you will have to take into account the fact that the gravitational force falls off as 1/r2.
 
  • #3
I think this problem becomes simple if we may neglect air friction and any deviations of the Earth's surface from being a sphere.
Because in this case, an orbit will do which is 'infinitesimally close' to a circular orbit. Which means: fire horizontally with circular orbit velocity.

I'm afraid we must *not* neglect those...
 

1. How does the rotation of the Earth impact the trajectory of a projectile fired from the North Pole to the Equator?

The rotation of the Earth causes a Coriolis effect, which means that an object moving in a straight line will appear to curve due to the Earth's rotation. This would impact the trajectory of a projectile fired from the North Pole to the Equator, causing it to veer off course and potentially miss its target.

2. What factors would affect the distance a projectile could travel from the North Pole to the Equator?

Several factors could affect the distance a projectile could travel, including the initial velocity of the projectile, air resistance, and the rotation of the Earth. The height and angle of the launch could also impact the distance.

3. Is it possible to accurately aim and hit a target at the Equator from the North Pole?

Due to the Coriolis effect and other factors, it would be challenging to accurately aim and hit a target at the Equator from the North Pole. It would require precise calculations and adjustments to account for the Earth's rotation and other variables.

4. Can a projectile fired from the North Pole reach the Equator in a straight line?

No, due to the Coriolis effect and the curvature of the Earth, a projectile fired from the North Pole cannot reach the Equator in a straight line. It would appear to curve and potentially miss its target.

5. How could we improve the accuracy of firing a projectile from the North Pole to the Equator?

To improve the accuracy, we could use advanced calculations and technology to account for the Earth's rotation and other variables. We could also adjust the launch angle and velocity to compensate for the Coriolis effect and aim for a specific target at the Equator.

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