If the distance between the earth and the sun is half its present value, the number of days in a year would have been

Question

If the distance between the earth and the sun is half its present value, the number of days in a year would have been (A) 730 (B) 182.5 (C) 129 (D) 64.5

Tardigrade Admin · Accepted Answer

According to Kepler's law of period (T1/T2)=((R1/R2))3 / 2=((R1/R1 / 2))3 / 2(∵ R2=(R1/2)) =(2)3 / 2=2 √2 ∴ T2 =(T1/2 √2)=(365/2 √2) days =129 days

Q. If the distance between the earth and the sun is half its present value, the number of days in a year would have been

$730$

$182.5$

$129$

$64.5$

According to Kepler's law of period
$\frac{T _{1}}{T _{2}} = (\frac{R _{1}}{R _{2}})^{3/2} = (\frac{R _{1}}{R _{1} /2})^{3/2} (∵ R_{2} = \frac{R _{1}}{2})$
$= (2)^{3/2} = 22$
$∴ T_{2} = \frac{T _{1}}{2 2} = \frac{365}{2 2}$ days
$= 129$ days

Q. If the distance between the earth and the sun is half its present value, the number of days in a year would have been

730

182.5

129

64.5

According to Kepler's law of period T2​T1​​=(R2​R1​​)3/2=(R1​/2R1​​)3/2(∵R2​=2R1​​) =(2)3/2=22​ ∴T2​=22​T1​​=22​365​ days =129 days

$730$

$182.5$

$129$

$64.5$

According to Kepler's law of period
$\frac{T _{1}}{T _{2}} = (\frac{R _{1}}{R _{2}})^{3/2} = (\frac{R _{1}}{R _{1} /2})^{3/2} (∵ R_{2} = \frac{R _{1}}{2})$
$= (2)^{3/2} = 22$
$∴ T_{2} = \frac{T _{1}}{2 2} = \frac{365}{2 2}$ days
$= 129$ days