Umbra, penumbra and antumbra I'm trying to understand following schema of the wikipedia page here.



Image subtitle is "Umbra, penumbra, and antumbra, for a lunar eclipse".

Distances and sizes are not to scale. 

If distance Earth-Sun is about 150 Gm (gigameters) and Sun diameter is 1.4 Gm, $\arctan 1.4/150 = 0.57º$ (degrees). Thus, the Sun is seen from Earth with an angle of approx. 0.57º (0.01 radians). The Blue and red lines in schema should be near to parallel.

That means the point where umbra and antumbra touch is (being 12 Mm the approx diameter of Earth) at a distance of about $\frac{150}{1.4\times0.012}=1.3 \mathrm{Gm}$ from Earth. 

As distance Earth-Moon is only 0.400 Gm, it seems impossible that Moon was never in the antumbra zone of the Earth.

I'm doing a basic error somewhere, but I do not know where.
The calculations seem reasonable. The conclusion is wrong.

The Earths antumbra starts 1.3 Gm from Earth. At less than 1.3 Gm there is umbra, penumbra and non-shadow. The moon is 0.4 Gm from Earth. 

$$0.4 &lt; 1.3$$

Hence it is impossible for the moon to be in the Earth's antumbra.

However, the Moon's antumbra forms at almost exactly one lunar distance. We notice that the moon and the sun are almost exactly the same size in the sky. When the moon is further from the Earth, an annular eclipse can form, as a small part of the Earth will then be in the moon's antumbra.

I've made a scale model of the sun-earth-moon shadows, at https://ggbm.at/CbbvmBFq