### Why does Io cast a hard shadow on Jupiter, but the Moon casts a soft shadow on Earth?

• Io (source):

The Moon (source):

• It's due to the larger relative apparent size of the Sun. When the source of light is a point source the shadow is harder, and when it is extended it is softer.

Jupiter is approximately 5 times more distant from the Sun than the Earth, so the Sun is approximately 5 times smaller in the sky.

*Source: University of North Carolina CS

But the (relative) distance between body 2 and body 3 must also play a role (for the same distance to the sun). If they are sufficiently far apart it would all be penumbral.

Yes, as well as the scale of the photographs of the shadows.

@PeterMortensen Correct. Every dotted line on the image is defined by the position of the vertices of the orange triangle _and_ the vertices of the blue square, both their positions matter. But the distance between the moon (blue square) and planet (white square) absolutely pales in comparison to the distance between the sun (orange triangle) and the moon (blue square). More correctly, the proportional difference between Sun-Luna and Sun-Io is much larger than the difference between Luna-Earth and Io-Jupiter..