Question

019 (part 1 of 2) 10.0 points On the way to the moon, the Apollo astro- nauts reach a point where the Moon's gravi- tational pull is stronger than that of Earth's. Find the distance of this point from the center of the Earth. The masses of the Earth and the Moon are 5.98 x 1024 kg and 7.36 x 1022 kg, respectively, and the distance from the Earth to the Moon is 3.84 x 108 m. Answer in units of m 020 (part 2 of 2) 10.0 points 0 What would the acceleration of the astro- naut be due to the Earth's gravity at this point if the moon was not there? The value of the universal gravitational constant is 6.672 x 10 Nm2/kg2 Answer in units of m/s.

Answer 1

Acceleration due to any planet on an object is given by: F = G m_plan times m_object/r^2 where r rightarrow distance of the object from the centre of the earth planet. Let the distance of the point where force due to moon is greater than the earth is r \r\n F_moon > F_earth m_earth m_object/r^2 > G m_moon m_object/(d - r)^2 d - r/r > squareroot m_moon/m_earth Given: Distance b/w earth & moon d = 3.84 times 10^8 m Mass of earth m_earth = 5.98 times 10^24 kg mass of the moon m_moon m_moon = 7.36 times 10^22 kg Putting these value in the above eqn. 3.84 times 10^8 m/r - r > squareroot 7.36 times 10^22/5.98 times 10^24 3.84 times 10^-8 - r/r > 0.11 3.84 times 10^8 m > 1.11 r r > 3.456 times 10^8 \r\n Part 2 If the moon was not there, Acceleration due gravity of the earth g = G M_earth/r^2