8.12 A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2×1030 kg, mass of the earth = 6×1024 kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 1011 m).

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8.12 A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2×10³⁰ kg, mass of the earth = 6×10²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹ m).

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Pallavi Pathak | Contributor-Level 10

5 months ago

8.12

Mass of the Sun, $M_{s}$ = $2 \times 10^{30}$ kg, Mass of the Earth, $M_{e}$ = $6 \times 10^{24}$ kg

Orbital radius, r = $1.5 \times 10^{11}$ m

Let the mass of the rocket be, m

Let x be the distance from the centre of the Earth where the gravitational force acting on satellite P becomes zero.

From Newton’s law of gravitation, we can equate gravitational forces acting on the satellite P under the influence of the Sun and the Earth as:

$\frac{G_{m} M_{s}}{({r - x)}^{2}}$ = $G_{m} \frac{M_{e}}{x^{2}}$ or( ${\frac{r - x}{x})}^{2}$

= $\frac{M_{s}}{M_{e}}$ ( ${\frac{r - x}{x})}^{2}$ = $\frac{{2 \times 10}^{30}}{{6 \times 10}^{24}}$ ,

$\frac{r - x}{x}$ = 577.35 , r = 578.35x ,

x = $\frac{1.5 \times 10^{11}}{578.35}$ = 2.59 $\times 10^{8}$ m

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8.12 A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero? Mass of the sun = 2×10³⁰ kg, mass of the earth = 6×10²⁴ kg. Neglect the effect of other planets etc. (orbital radius = 1.5 × 10¹¹ m).

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