關於質量、體積、密度和重力的問題?

如果把地球擠壓到一半大小並保留所有質量，那麼地球的密度是多少?

Density = mass/volume, if the volume is reduced by half with the mass remains unchanged, the density of the earth will be doubled.

The density of the earth is estimated to be about 5500 kg/m^2, hence the new density will become 11,000 kg/m2
-----------------------------------------------------
另外，地球的表面重力會不會因為上述情況而加大?

Yes, the gravitational pull will increase.

From Newton's law of gravitation, the acceleration due to gravity g (which is a measure of the strength of a gravitational field) on earth surface is given by,

g = GM/R^2
where M is the mass of the earth, with radius R. G is the universal gravitational constant.

When volume of earth is reduced by half, the new radius of the earth R' is,
R' = R/cube-root(2)

thus, the new acceleration due to gravity at earth surface g' is,
g' = GM/R'^2 = [GM/R^2] x (2)^2/3 = [2]^(2/3) g = 1.587g

hence, the surface gravity will increase by about 59%
----------------------------------------------------
最後，重力和表面重力有可分別?

The earth gravity extends to large distances outside the earth surface (in principle, it extends to infinity), and its strength decreases with increase of distance from the earth, it is therefore necessary to specific where (the location) the gravity is referred to.

Thus surface gravity(表面重力) indicates the gravitational force on [earth surface.]