PPT Slide
Mass and Density of Earth
Newton's Second Law of Motion: F = m . g
Newton's Law of Universal Gravitation: F= G . (m1 . m2) . r-2
F is gravitational force, m is mass and g is gravity acceleration (9.8 m.sec-2 at surface). G is Universal Gravitational Constant (6.67E-11 Nm2.kg-2). The values m1 and m2 are two masses that attract each other, whereas r is Earth's radius (6.4E6 m).
For m1, consider a body at the surface of Earth (say, you)
compared to the mass of Earth (m2).
Combining these two equations gives: g = G . m2 . r-2
Resolved for m2, gives Earth mass of 6E24 kg.
Volume of sphere (Earth) is 4/3.p.r3, i.e. ~1.1E21 m3.
Earth's average density, r=m/V, is ~5500 kg.m-3.
However, density of material deep within Earth is affected
by gravitational forces. The consequence is an uncompressed density
(at surface conditions) of ~4300 kg.m-3.