(a) A certain vile alien gangster lives on the surface of an asteroid, where his

Question

(a) A certain vile alien gangster lives on the surface of an asteroid, where his weight is 0.20 N. He decides he needs to lose weight without reducing his consumption of princesses, so he’s going to move to a different asteroid where his weight will be 0.10 N. The real estate agent’s database has asteroids listed by mass, however, not by surface gravity. Assuming that all asteroids are spherical and have the same density, how should the mass of his new asteroid compare with that of his old one? (b) Jupiter’s mass is 318 times the Earth’s, and its gravity is about twice Earth’s. Is this consistent with the results of part a? If not, how do you explain the discrepancy?

Explanation / Answer

here ,

for the given density ,

the acceleration due to gravity is given as

g = G*M/R^2

g = G * p * (4/3) *pi * R^3/R^2

g = G*p*(4/3)pi *R

Now ,as the acceleration due to graity on the second planet is half ,

G*p*(4/3)pi *Rold = G*p*(4/3)pi *Rnew * 2

Rnew = Rold/2

Now, as Radius is half , the volume will beocme (1/2)^3 = 1/8 times

Now ,as the density is same , the mass will also becomes 1/8 times

he should move to an asteriod will 1/8 times the mass.

b)

here , we assumed that the density is constant ,
but the density of jupiter is less than the density of earth

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