The earth of mass m , radius r is revolving around sun in an orbit of radius D with an angular velocity ω and rotating around itself with an angular velocity ω' . What is the total kinetic energy of the earth ?

Hi,

It sometimes is convenient to split the total kinetic energy of a body into the sum of the body's center-of-mass translational kinetic energy and the energy of rotation around the center of mass (rotational energy):

where:

E_k is the total kinetic energy

E_t is the translational kinetic energy

E_r is the rotational energy or angular kinetic energy in the rest frame

=.5mω²D²  + .5I(ω')²

where, I = moment of inertia