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Every orbit here is a true ellipse with its real eccentricity, drawn with the Sun (or the Earth) at a focus rather than at the centre. Positions come from published orbital elements, so the clock above shows where these bodies really are. Scroll down and the same machinery explains solar and lunar eclipses.
Distances are exactly to scale. The bodies are not: at this scale the Earth would be 0.02 pixels across, so each planet is drawn as a marker of fixed size with its true size printed beside it. The small cross on each orbit is the geometric centre of the ellipse. The Sun is not at it. That offset is the eccentricity you can actually see.
This panel is fully to scale, sizes included. The gap is thirty Earths wide. The Moon's orbit is an ellipse of eccentricity 0.055, so the Earth sits about 21,000 km off its centre, and the Moon swings between 356,500 km and 406,700 km away. That variation is the whole difference between a total and an annular solar eclipse. The line joins the two centres.
Sunlight comes from the left. Nothing here is exaggerated, which is the point: a shadow cone is preposterously long and thin, so at first glance both look like a line. Press Zoom to the shadow to drop into the last few tens of thousands of kilometres, where the Moon is visibly swallowed by the Earth's umbra. Both the Earth and the Moon trail a cone of full shadow (the umbra) and a wider cone of partial shadow (the penumbra). A lunar eclipse is the Moon entering the Earth's cone; a solar eclipse is the Moon's cone landing on the Earth. Nothing else is going on. The dashed line is the Sun–Earth axis; the solid line joins the centres of the Earth and Moon.
Drag the left panel to orbit the camera. The cone is drawn as a real cone in space with its true opening angle, and the dark patch on the globe is computed by testing points on the Earth's surface against it. The right panel is the sky from a point inside that patch: the Sun and the Moon at their true angular sizes for the selected instant. You cannot see the cone from the ground, you are inside it. What you see is the Moon's disc sitting on the Sun's.
There is a new Moon every 29.5 days, so why not an eclipse every fortnight? Because the Moon's orbit is tilted 5.1° to the Earth's. Each dot below is one new Moon (below the axis) or full Moon (above it), plotted by how far the Moon misses the shadow axis. Eclipses happen only in the shaded band, when the alignment falls near one of the two nodes where the orbits cross. Those windows come round every 173.3 days, which is why eclipses arrive in pairs and seasons rather than monthly.