Question

if the distance between the earth and sun is reduced to 1/4 then the number of days in one year approximately give explanation​

Answer 1

Answer:

MARK ME AS BRAINLISTER

Explanation:

Gravitational force of attraction provides the centripetal force to the earth to revolve around the sun.

Assuming circular orbit, we write

begin mathsize 12px style G fraction numerator M cross times m over denominator R squared end fraction space equals space m cross times omega squared cross times R space............ left parenthesis 1 right parenthesis

end style

where G is gravitational constant, M is mass of sun, m is mass of earth, R is radius of orbit and ω is angular speed.

If T is period of revolution, then

ω = 2π/T .........(2)

substituting for ω from eqn.(2) in eqn.(1), we getbegin mathsize 12px style T squared space equals space fraction numerator 4 pi squared over denominator G M end fraction R cubed space............. left parenthesis 3 right parenthesis end style

By considering all constants, we writebegin mathsize 12px style T space proportional to space R to the power of bevelled 3 over 2 end exponent end style...........................(4)

Let T ' be the time period of revolution if orbital radius is reduced to (1/4)th of its original value, then we have

begin mathsize 12px style fraction numerator T apostrophe over denominator T end fraction space equals space open parentheses fraction numerator R over denominator 4 cross times R end fraction close parentheses to the power of bevelled 3 over 2 end exponent space equals space open parentheses 1 fourth close parentheses to the power of bevelled 3 over 2 end exponent space equals space 1 over 8 end style

if we consider normal duration of year as 365 days, thenbegin mathsize 12px style T apostrophe space equals space 365 over 8 equals 45.625 space d a y s end style