Why is the genitive of ziemia ziemi, and not ziemii (like biologia->biologii)
Why not What is the weight of the Earth? In this case it does mean the same.
Well... I guess we probably don't have to go into the Physics discussion, ok. Added.
EDIT 6 months later: Change of plans, let's keep to science.
Weight is the measurement of the pull of gravity on an object. So unfortunately I cannot even begin to answer your question.
Strictly speaking, this answer needs to be "what is the mass of THE earth" or "what is the mass of PLANET earth" if it refers to our planet. Otherwise it is ambiguous as earth also means soil.
"What is the mass of the earth?" is less likely to be referring to the planet than, "What is the mass of Earth?" - Earth is the name of the planet, so should have a capital letter.
Technically it's a different word, also it doesn't really work in Physics, I believe.