derive an expression to find the density as well as mass of earth
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The mass of the Earth may be determined using Newton's law of gravitation. It is given as the force (F), which is equal to the Gravitational constant multiplied by the mass of the planet and the mass of the object, divided by the square of the radius of the planet. We set this equal to the fundamental equation, force (F) equals mass (m) multiplied by acceleration (a). We know that the acceleration due to gravity is equal to 9.8 m/s2, the Gravitational constant (G) is 6.673 × 10−11 Nm2/kg2, the radius of the Earth is 6.37 × 106 m, and mass cancels out. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 × 1024 kg.
F = Gm1m2/r2 = ma
Gm/r2 = g
m = gr2/G
m = (9.8 m/s2)(6.37 × 106 m)2/(6.673 × 10−11 Nm2/kg2)
m = 5.96 × 1024 kg
The Earth gains mass each day, as a result of incoming debris from space. This occurs in the forms of "falling stars", or meteors, on a dark night. The actual amount of added material depends on each study, though it is estimated that 10 to the 8th power kilograms of in-falling matter accumulates every day. The seemingly large amount, however, is insignificant to the Earth's total mass. The Earth adds an estimated one quadrillionth of one percent to its weight each day.
F = Gm1m2/r2 = ma
Gm/r2 = g
m = gr2/G
m = (9.8 m/s2)(6.37 × 106 m)2/(6.673 × 10−11 Nm2/kg2)
m = 5.96 × 1024 kg
The Earth gains mass each day, as a result of incoming debris from space. This occurs in the forms of "falling stars", or meteors, on a dark night. The actual amount of added material depends on each study, though it is estimated that 10 to the 8th power kilograms of in-falling matter accumulates every day. The seemingly large amount, however, is insignificant to the Earth's total mass. The Earth adds an estimated one quadrillionth of one percent to its weight each day.
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