Calculation of the Mass of the Earth: Mass of the Earth M = aR^2/G; R = Radius o

Question

Calculation of the Mass of the Earth: Mass of the Earth M = aR^2/G; R = Radius of the Earth = 6.378 Times 10^6 m G = Gravitational Constant =6.67 Times 10^-11 m^3/kg s^2 Experimental value of the Mass of the Earth using Light Object = Experimental Value Mass of the Earth using Heavy Object = Actual Value of the Mass of the Earth = 6. 0 Times 10^24 kg. Percentage Error using the Mass of the Earth using the Light Object: Actual - Experimental/Actual Times 100 Percentage Error using the Mass of the Earth using the Heavy Object: Actual - Experimental/Actual x100 Explanation of your result and assumptions:

Explanation / Answer

Using newton's law of gravity, we have

F = G M m / r2

According to newton's second law of motion, we have

F = m a

From an above two equations, we get

G M m / r2 = m a

G M / r2 = a

where, G = universal gravitational constant = 6.67 x 10-11 Nm2/kg2

M = mass of the Earth = ?

r = radius of the Earth = 6.4 x 106 m

a = acceleration due to gravity = 9.8 m/s2

then, we have

M = a r2 / G

M = (9.8 m/s2) (6.4 x 106 m)2 / (6.67 x 10-11 Nm2/kg2)

M = (401.4 x 1012 m3/s2) / (6.67 x 10-11 Nm2/kg2)

M = 60.1 x 1023 kg

M = 6 x 1024 kg

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