Answer
$\Delta \theta_{Sun} =9.30\times 10^{-3} rad$
$\Delta \theta_{Moon} =9.06\times 10^{-3} rad$
Work Step by Step
The angle in radians is the diameter of the object divided by the distance to the object.
$$\Delta \theta_{Sun} =\frac{2R_{Sun}}{r_{Earth-Sun}}=\frac{2(6.96\times 10^5km)}{149.6\times 10^6km}=9.30\times 10^{-3}rad$$
$$\Delta \theta_{Moon} =\frac{2R_{Moon}}{r_{Earth-Moon}}=\frac{2(1.74\times 10^3km)}{384\times 10^3km}=9.06\times 10^{-3}rad$$
Since these angles are practically the same (only a 2.6% difference), solar eclipses can occur. based on these values, the Sun would never be completely obscured. But since the orbits are not perfect circles but are ellipses, the above values are just averages. Total solar eclipses do occur.
