if the distance between sun and earth increases by 125% of its present value suddenly then the duration of one year will be
Answers
Explanation:
So let us suppose.
r1= initial radius
r2=final radius
r2=r1+125%r1=9/4r1
t1=initial duration of 1 year
t2=final duration of 1 year
by Kepler's law we know that t^2 is directly proportional to r^3
therefore
(t2/t1)^2=(r2/r1)^3
t2/t1=(r2/r1)^(3/2)
t2=t1*(9/4r1/r1)^(3/2)
t2=t1*(3/2)^3
t2=365*27/8
this will be the duration of 1 year if the distance of earth and sun increases by 125%.
Given:
The distance between the Sun and Earth is increased by 125% of present value
To find:
The duration of one year.
Solution:
Let us assume the initial distance between sun and earth be r.
Final distance be r'. Then:
r' = r + 125% of r
= r + 125/100 × r
= r + 1.25r
= 2.25r
From Kepler's law we know that:
Square of Duration of one year (T²) is directly proportional to r³.
Therefore:
T'²/ T² = r'³/ r³
T'² = (T²× r'³)/ r³
T'² = 365² × 2.25³
T' = 365 × 2.25^(3/2)
T' = 1231.875 days
Thus the duration if one year will be 1231.875 days.