The Solar System

Since the mass of Earth is much smaller than that of the Sun (M_⊕ = 0.000 003 M_☉), we can assume that the C.O.M of the system lies somewhere within the surface of the Sun, and almost coinciding with its center.

Thus value of {R_☉} can be assumed negligible and value of {R_⊕} + {R_☉} \approx {R_⊕}. In other words we can assume that the Sun is fixed at the C.O.M and only Earth is orbiting around the Sune for all its worth.

Substituting for values of mass, velocity and distance of Earth from the Sun, we get:

F_c={3.57 \times 10^{19} N}

The Gravitation pull on Earth:

F_g=\tfrac{G \times M_⊕ \times M_☉}{R_⊕^2}.

Substituting values for the Gravitational constant G , mass and radii of both Earth and Sun:

{F_g} \approx 3.57 \times 10^{19} N

Thus:

{F_c} = {F_g}