Question 212: Units , Dimensions and Error Analysis

Question

The relative uncertainly in the period of a satellite orbiting around the earth is 10
-2
. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

Accepted Answer

From kepler's law,
T = 2$\pi $ $\sqrt {{{{r^3}} \over {GM}}} $
$ \Rightarrow $$\,\,\,$T
2
= ${{4{\pi ^2}} \over {GM}}{r^3}$
$ \Rightarrow $$\,\,\,$ M = ${{4{\pi ^2}} \over G} 	imes {{{r^3}} \over {{T^2}}}$
$	herefore\,\,\,$ ${{\Delta M} \over M}$ = 2 ${{\Delta T} \over T}$ + 3 ${{\Delta r} \over r}$
as ${{\Delta r} \over r} \simeq 0$
$	herefore\,\,\,$ $\left| {{{\Delta M} \over M}} ight|$ = 2 ${{\Delta T} \over T}$ = 2 $ 	imes $ 10
$-$2

Answer

10
$-$2

Answer

2 $ 	imes $ 10
$-$2

Answer

3 $ 	imes $ 10
$-$2

Answer

6 $ 	imes $ 10
$-$2

Units , Dimensions and Error Analysis

The relative uncertainly in the period of a satellite orbiting around the earth is 10 -2 . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

Choose the correct answer: