Question 184: 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 :

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