Question

if the distance between the sun and Earth were half of it's present value, then how many numbers of days will be there in a year​

Answer 1

$\LARGE\underline{\underline{\sf \red{Given}:}}$

• If the distance between the sun and earth were half .

$\LARGE\underline{\underline{\sf \red{To\:Find}:}}$

• How many days will be there in year = ?

$\LARGE\underline{\underline{\sf \red{Solution}:}}$

According to Kepler's Law :

$\large{\boxed{\sf \red{ T^2\:\:\alpha\:\:a^3}}}$

Square of time period of planet is directly proportional to cube of semi-major of its axis.

Now ,

$\implies{\sf \left(\dfrac{T_1)^2}{(a_1)^3}\right)=\left(\dfrac{(T_2)^2}{(a_2)^3}\right) }$

$\implies{\sf (T_2)^2=\left(\dfrac{a_2}{a_1}\right)^3×(T_1)^2}$

$\implies{\sf (T_2)^2=\left(\dfrac{1}{2}\right)^3×(T_1)^2}$

$\implies{\sf (T_2)^2=\left(\dfrac{1}{8}\right)×1\:year }$

$\implies{\sf T_2=\sqrt{\dfrac{1}{8}}×365\:days }$

$\implies{\sf T_2=129\:days}$

$\LARGE\underline{\underline{\sf \red{Answer}:}}$

•°• 129 days will be their in one year.