If a planet is found with a radius 5% greater than Jupiter, which is the best first estimate of that planet's mass?
A)about 1 times Jupiter's mass
B)about 10 times Jupiter's mass
C)about 3 times Jupiter's mass
D)about 0.3 times Jupiter's mass

Question

If a planet is found with a radius 5% greater than Jupiter, which is the best first estimate of that planet's mass?
A)about 1 times Jupiter's mass 
B)about 10 times Jupiter's mass 
C)about 3 times Jupiter's mass 
D)about 0.3 times Jupiter's mass

Quizplus · Accepted Answer

There is a relationship between a planet's radius and mass that is described by the formula:

Density = Mass/Volume

Assuming that the planet is made of similar materials as Jupiter, the density will be roughly the same.

If the radius is 5% greater than Jupiter, then the volume will be about 1.05^3 times greater (because volume scales with the cube of the radius).

Therefore, the mass will be roughly 1.05^3 times greater than Jupiter's mass, which is about 3 times Jupiter's mass.

If a Planet Is Found with a Radius 5% Greater