Question

calculate the mass of earth
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Answer 1

5.97219 × 1024kilograms

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Answer 2

According to Newton's Law of Gravity based on attractive force (gravitational force) that two masses exert on each other:

F=GmMr2

Where:

F is the gravitational force

G=6.67×10−11 m3 kg−1 s−2 is a constant of proportionality

M and m are the two masses exerting the forces

r is the distance between the two centers of mass.

From Newton's second law of motion:

F=ma

Where:

F is the force applied to an object

m is the mass of the object

a is its acceleration due to the force.

Equating both the equations:

F=GmMr2=ma

GMr2=a

(The m's canceled out.)

Now solve for M, the mass of the Earth.

M=ar2G

Where a=9.8 m s−2, r=6.4×106 m, and G=6.67×10−11 m3 kg−1 s−2.

M=9.8×(6.4×106)2/(6.67×10−11) kg

Hence,

M=6.0×1024 kg