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From One North Pole to the Other (Posted on 2019-06-21) Difficulty: 5 of 5
There are two identical uniform spherical planets of radius R. The first has its center at the origin of the xyz coordinate system. The second has its center at (2R, 0, 0). The planets are touching.

A projectile is launched from the "North Pole" of the first planet at (0, 0, R) with its initial velocity pointed in the direction of the vector (1, 0, 1).

Let the escape speed relative to the planet's surface be ve. Note that here, the escape escape is for a single planet in isolation (following the typical convention).

With the given launch vector, let v0 be the minimum launch speed for the projectile to reach the "North Pole" of the second planet at (2R, 0, R).

How are the two speeds ve and v0 related?

No Solution Yet Submitted by Danish Ahmed Khan    
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re(3): Great Info | Comment 20 of 21 |
(In reply to re(2): Great Info by Hanna Jackson)

wow this was really an amazing info which made me to think about it after going through it. It was such a pleasure to learn about planets and their poles. I really love to study on solar system and have done several researches on Assignmentman blogs about them. The launch speed is minimum I guess if calculated base dont he given inputs.

  Posted by Haleigh Murphy on 2021-04-29 09:04:31

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