For a spacecraft going from the Earth towardthe sun, at what distance from the E

Question

   For a spacecraft going from the Earth towardthe sun, at what distance from the Earth will the gravitationalforces due to the Sun and the Earth cancel?    Earth's mass: Me= 5.98 x 10^24 kg    Sun's mass: Ms= 1.99 x 10^30 kg    Earth-Sun distance: r= 1.50 x 10^11 m    For a spacecraft going from the Earth towardthe sun, at what distance from the Earth will the gravitationalforces due to the Sun and the Earth cancel?    Earth's mass: Me= 5.98 x 10^24 kg    Sun's mass: Ms= 1.99 x 10^30 kg    Earth-Sun distance: r= 1.50 x 10^11 m

Explanation / Answer

Let distance from earth be x Then distance from sun = 1.50 x 1011 - x Let mass of spacecraft be m Also we know , Gravitational force =GM1M2/r2 Gravitational forcebetween sun and spacecraft =G* 1.99 x 1030*m/(1.50 x1011 - x)2 Similarly Gravitational force between earth and spacecraft = G*5.98 x 1024*m/ x2For forces to cancel out, These two forces should be equal , G* 5.98 x 1024*m/ x2 =G* 1.99 x1030*m/(1.50 x 1011 -x)2x2 / (1.50 x 1011 -x)2 =1.99 x 1030/5.98 x 1024Taking square root x / (1.50 x 1011 - x) = 55.64 Solve for x .

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