Question Number 52786 by peter frank last updated on 13/Jan/19
Commented by tanmay.chaudhury50@gmail.com last updated on 13/Jan/19
![mw^2 r=((GMm)/r^2 ) [ M=mass of sun, m=mass of planet] (((2π)/T))^2 =((GM)/r^3 ) [r=distance between planet and sun] ((2π)/T)=(√((GM)/r^3 )) [T=time T=2π(√(r^3 /(GM))) (T_(saturn) /T_(earth) )=(√(r_(saturn) ^3 /r_(earth) ^3 ))](https://www.tinkutara.com/question/Q52789.png)
$${mw}^{\mathrm{2}} {r}=\frac{{GMm}}{{r}^{\mathrm{2}} }\:\left[\:{M}={mass}\:{of}\:{sun},\:\:{m}={mass}\:{of}\:{planet}\right] \\ $$$$\left(\frac{\mathrm{2}\pi}{{T}}\right)^{\mathrm{2}} =\frac{{GM}}{{r}^{\mathrm{3}} }\:\left[{r}={distance}\:{between}\:{planet}\:{and}\:{sun}\right] \\ $$$$\frac{\mathrm{2}\pi}{{T}}=\sqrt{\frac{{GM}}{{r}^{\mathrm{3}} }}\:\left[{T}={time}\:\right. \\ $$$${T}=\mathrm{2}\pi\sqrt{\frac{{r}^{\mathrm{3}} }{{GM}}}\: \\ $$$$\frac{{T}_{{saturn}} }{{T}_{{earth}} }=\sqrt{\frac{{r}_{{saturn}} ^{\mathrm{3}} }{{r}_{{earth}} ^{\mathrm{3}} }} \\ $$
Answered by peter frank last updated on 13/Jan/19
