Centre of mass of the earth-moon system lies

The centre of mass of two particles system lies

the path of the center of mass of earth- moon system around the sun is -circular path -helical path -parabolic path -elliptical path

Period of revolution of the moon is 27.32 days and its mean distance from earth is 384,400km . Use the equation M_(1)+M_(2)=(4pi^(2))/G.(a^(3))/(T^(2)) to calculate the sum of the masses of the earth and moon. Further, using the known fact that the earth moon system lies ate 4.75xx10^(6)m from earth's centre, calculate the mass of each.

The earth is slowing down and as a result the moon is coming nearer to it. The angular momentum of the earth-moon system is not conserved.

Calculate centre of mass of the system

Assertion :- The mechanical energy of earth-moon system remains same when a another heavenly body passes nearby the earth - moon system. Reason :- Force exerted by heavenly body on the earth - moon system is non - conservative.

Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1,2,3) and centre of mass of another system of particles 3 kg and 3 kg lies at the point (-1, 3, -2) . Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system ?

The radius and acceleration due to gravity of the moon are 1/4 and 1/5 that of the earth, the ratio of the mass of the earth to mass of the moon is