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If the distance between the earth and the sun shrinks to half the present distance then find the new duration of year.

If the distance between the earth and the sun shrinks to half the present distance then find the new duration of year.
 

Grade:10

2 Answers

Vikas TU
14149 Points
4 years ago
Let distance b/w the earth and the sun be x meters.
And from kepler’s law square of Time period is directly proportional to the cube of Radius of the earth.
Therefore initially,
T^2 = k*x^3........................(1)
after 
t^2 = k*(x/2)^3..............(2)
Divide them get the value of t.
Adarsh
733 Points
4 years ago
Let T is the time period and r is the distance between the earth and the sun.
Then,
by Kepler’s law
    T2∝r3
=> T∝r3/2 
=> 365days ∝ r3/2 ..............(1)
When r becomes r/2
So new time period, T’ ∝ (r/2)3/2..............(2)
Eqn (2) ÷ (1) => T’ / 365 =1/ 23/2
Thus new time period T’ = 365/ 23/2 days
 
Hope you understand my solution.
 
Please approve only if my answer is correct.

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