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

Question

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

Tardigrade Admin · Accepted Answer

From Kepler's third law T2 propto r3 or T propto (r)3/2 ∴ (T2/T1) = ( ( r2/r1))3/2 or T2 =T1 ( (r2/r1) )3/2 = (365) ((1/2) )3/2 ⇒ T2 = 129 days

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

64.5

129

182.5

730

From Kepler's third law $T^{2} \propto r^{3} or T \propto (r)^{3/2}$
$∴ \frac{T _{2}}{T _{1}} = (\frac{r _{2}}{r _{1}})^{3/2} or T_{2} = T_{1} (\frac{r _{2}}{r _{1}})^{3/2} = (365) (\frac{1}{2})^{3/2}$
$\Rightarrow T_{2} = 129 d a ys$

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

64.5

129

182.5

730

From Kepler's third law T2∝r3orT∝(r)3/2 ∴T1​T2​​=(r1​r2​​)3/2orT2​=T1​(r1​r2​​)3/2=(365)(21​)3/2 ⇒T2​=129days

From Kepler's third law $T^{2} \propto r^{3} or T \propto (r)^{3/2}$
$∴ \frac{T _{2}}{T _{1}} = (\frac{r _{2}}{r _{1}})^{3/2} or T_{2} = T_{1} (\frac{r _{2}}{r _{1}})^{3/2} = (365) (\frac{1}{2})^{3/2}$
$\Rightarrow T_{2} = 129 d a ys$