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An ideal planet of mass M is perfectly smooth and spherical with radius R and with...

An ideal planet of mass M is perfectly smooth and spherical with radius R and with no atmosphere. Express all answers in terms of G, M and R. a. Determine the launch speed that would allow a projectile to leave the surface of the planet without returning (i.e., the “escape speed”). b. If an object is to be launch vertically from the planet’s surface so that it reaches a maximum height of 3R above the surface of the planet, determine its launch speed.

Science   Advanced-Physics   
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Answer #1

a] The kinetic energy of the object must equal the gravitational potential energy to leave the surface of the planet without coming back.

=>

this is the required launch speed.

b] Here, instead of taking R2 as infinity, take R3 = 3R

=>

=> .

this is the desired launch speed.

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