Answer :
Using Newton's Law of gravity, the length of the year is 364.24 days.
According to Newton's law, there exist a force of gravitation between the sun and the earth, The gravitational force is responsible for the revolution of earth around the sun,
So, we can write,
MW²/R = GMm/R²
Where,
M is the mass of earth,
m is the mass of the sun,
R is the distance between the sun and the earth,
G is the universal Gravitational constant.
Solving the relation,
W² = Gm/R
W = √(Gm/R)
The time period of revolution is given by,
T = 2π/W
So, we can write,
T = 2π√(R/Gm)
Bow, putting all the values,
T = 2π(147 x 10⁶/2 x 10³⁰ x 6 x 10⁻¹¹)
T = 364.24 Days.
So, the length of the year is 364.24 years.
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