ME = mass of Earth = 5.97 x 1024 kg MM = mass of the Moon = 7.35 x 1022 kg Ms =

Question

ME = mass of Earth = 5.97 x 1024 kg

MM = mass of the Moon = 7.35 x 1022 kg

Ms = mass of spacecraft = 1000 kg

vo = initial velocity of spacecraft = 15 km/s

d = distance from Earth’s center to Moon’s center = 3.84 x 108 m

Don’t plug the values in until the end! Before plugging in values you should be able to reduce the formula to the following. ( ) M E M E M M M M M M d h ± =

Hints: Treat the masses MM and ME as point masses located at the Moon's center and Earth's center, respectively. This is essentially an algebra problem in which you'll end up with a quadratic expression for h (i.e., includes both h2 and h terms). You will want to use the quadratic equation to solve for h.

Explanation / Answer

we know that the gravitational force between two bodies of masses m1,m2 separated by a distance x , by Universa law of gravitaion

   F = Gm1*m2/x^2

here the space craft is launched from the earth headed directly the moon

so that the force on spacecraft by both moon and earth will be equal at a positions form the sureface of earth is x

GMm*m/(x-r)^2 = GMm/r^2

Mm /(X-r)^2 = M/r^2

7.35*10^22 /(3.84*10^8 -r)^2 = 5.97*10^24 /r^2

solving for r

   r = 3.45647798*10^8 m from the earth the acceleration due to gravity by eartha dn moon are equal after

that the spacecraft begins to experience stronger gravitational force from the moon than from earth.

that is from the moon surface the distance is 3.84*10^8- 3.45647798*10^8 m = 38352202 m

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