What's
the technical definition of
a Sunset or Sunrise?

How is it determined at what time the sun sets or rises?
The definitions are easy:

A
sunrise is defined as occurring when
the top of the sun appears on a sea-level horizon.

A
sunset occurs when the top of the sun
goes just below the sea-level horizon.

But
how do scientists determine the times? No, they do not send
meteorologists out on a ladder and have them crane their necks.

No observation is involved at all—just math.

By
crunching the numbers based on the orbit of the Earth around
the Sun, the sunrise and sunset times can be calculated long in
advance. Richard Williams, a meteorologist at the National Weather

Service, explains that published times are only approximations of

what we observe with our naked eyes:

The
time of sunrise and sunset varies with day of the year,
latitude, and longitude. The published sunrise and sunset times are calculated without regard to surrounding terrain. That is, all computations are made for a sea-level horizon, even in mountainous areas. Thus the actual time of sunrise at a particular location may vary considerably from the "official" times.

Why
Is there natural light before sunrise and after sunset?
When we observe sunset, the Sun has already gone below the
horizon. The Earth's atmosphere "bends" the Sun's rays
and delays
the sunset by about three minutes. Likewise with sunrise, the sun

makes its first appearance before it would on a planet with
no atmosphere. We actually get five to ten minutes of
extra sunlight due to this effect.

From
... Do Penguins Have Knees?" By
David Feldman