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

Question

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

Filo · Accepted Answer

Mass of the Sun, Ms​=2×1030 kgMass of the Earth, Me​=6×1024 kgOrbital radius, r=1.5×1011 mMass of the rocket =mLet 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 satellite P under the influence of the Sun and the Earth as:(r−x)2GmMs​​=x2GmMe​​[x(r−x)​]2 = Ms​/Me​(r−x)/x = (60×10242×1030​)1/2 = 577.351.5×1011−x=577.35x578.35x=1.5×1011x=1.5×1011/578.35 = 2.59×108m.

Question Text	A rocket is fired from the earth towards the sun. At what distance from the earths centre is the gravitational force on the rocket zero? Mass of the sun = $2 \times 1 0^{30} k g$ , mass of the earth = $6 \times 1 0^{24} k g$ . Neglect the effect of other planets etc. (orbital radius = $1.5 \times 1 0^{11} m$ ).
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