There are two distinct questions in your post. I'll answer the first one.
There is a slight misconception in your question. A supermoon isn't just when the Moon is a periapsis, but when it is at periapsis during a full moon. Since the orbital period of the Moon is not the same as the time between two full moons, supermoons don't occur every month.
(On a ...
The Moon's orbit about the Earth is only approximately elliptical. The Moon's orbit precesses both axially and nodally, and the eccentricity of the Moon's orbit varies.
That the Moon's orbit precesses axially means that perigee sometimes occurs when the Moon is close to new, sometimes when it is close to half-full, and sometimes when it is close to full. ...
The moon's orbit is elliptical. This is what the moon's orbit looks like from above (A is the Earth, and C is moon, c is the orbit of the moon around the Earth)
As you see with an eccentricity of 0.056 it doesn't get very close to Earth, but if you look carefully enough, there is some variation. The moon in the diagram is at apoapsis, as far from the Earth ...
This can be seen geometrically:
Everywhere the lines touch a circle, they are tangent.
In some parts of the shadow, the sun is not visible at all. This is the umbra. It is visible in this construction as the inner cone of the shadow.
Outside this, the sun is only partially obscured. This is called the penumbra.
If the penumbra is small relative to the ...
The farther you go, the smaller the light source gets.
Imagine a tubelight and an LED diode, as in the picture below. The diffusion factor increases as you get closer. Animation artists will know what I'm talking about.
But to a common man: the bigger the light source, the softer will be the light's shadow. And we know Earth is nearer to the Sun than ...
Another factor is involved in addition to the above answers.
Io's umbral shadow is a bit over two million kilometers long, almost six times longer than the ~350 thousand kilometer distance between Jupiter's surface and Io. This means that most of Io's shadow on Jupiter's surface as seen from space is Io's umbral rather than its penumbral shadow. Io's umbral ...
Due to the basic proportionality theorem, the width of the boundary of the shadow is
where $\ell$ is the distance from the moon to the planet’s surface, $L$ is the distance from the planet to the sun, and $D$ is the diameter of the sun. Here
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