Final answer:
The minimum muzzle speed to reach 2 times Earth's radius is related to escape velocity, calculated by the formula ve = sqrt(2*G*ME/r). In Verne's "From the Earth to the Moon", a giant cannon would need to propel a projectile at or exceeding this escape speed, ignoring air resistance and rotation for simplicity.
Step-by-step explanation:
To find the minimum muzzle speed needed to shoot a shell straight up to an altitude equal to 2 times Earth's radius (RE), we can use the concept of escape velocity. The escape velocity from Earth is the speed needed to break free from Earth's gravitational pull without further propulsion. This velocity can be calculated using the formula ve = sqrt(2*G*ME/r), where G is the gravitational constant, ME is the mass of Earth, and r is the distance from the center of Earth. Since we want the shell to reach an altitude of 2RE, r would be 3RE (as the altitude is 2RE above the surface, and RE is the radius of Earth).
When Jules Verne proposed sending men to the moon in "From the Earth to the Moon", he imagined a cannon in Florida achieving this feat. However, the shell fired from this hypothetical cannon would need to reach or exceed escape velocity to overcome the Earth's gravitational force significantly. For a simplified calculation ignoring air resistance and Earth's rotation, we could use the aforementioned formula. However, in reality, the speed required would be higher due to these additional factors affecting the trajectory of the projectile.