A question that asks you to figure out the mass of the moon

[Hmpca]

Homework Statement

the radius of the moon is 1 over 3.65 of the radius of the earth, while the acceleration due to gravity of the moon is 1 over 6 of that on the earth`s surface. calculate the mass of the moon.

 

[PeterO]

Homework Statement

the radius of the moon is 1 over 3.65 of the radius of the earth, while the acceleration due to gravity of the moon is 1 over 6 of that on the earth`s surface. calculate the mass of the moon.

The acceleration due to gravity - we call it g on Earth - is given by GM/R². Where G is the universal constant of gravitation; M is the mass of the central body; and R is the distance form the centre of mass - the radius of the body if we consider g on the surface. You know sufficient of those values to calculate the mass of the Moon as a fraction of the mass of the Earth, which is a value that can be looked up easily.

 

[Hmpca]

i thought you could figure out the mass of the moon without knowing the mass of the earth. tomorrow i have an exam and my teacher said don`t expect me to give you any sheet with equations and constants. so i guess i got to memorize the mass of the earth.
thank you

 

[homevolend]

a = GM/R²

g = (1/6)(9.81) = X m/s²

r = (1/3.65)(6.378x10⁶) = Y m

m/r² = a/G

m/(Y)² = X/ (6.67x10^-11)

m = ANS kg

 

[netgypsy]

the person asking for help is supposed to set up the problem, give relevant equations etc. before getting help from outside. Where are your equations??

In answer to your question - you do have to know the formulas probably but not the mass of the earth.