why does amount of solar radiation change with changes in calendar dates?

Answer 1

It does? I don't think so. The total solar radiation received by the Earth is constant (to +/- 0.1%).

Perhaps you mean, why does the amount of solar radiation
... received at one place ...
change with changes in calendar dates?

When the northern hemisphere gets less sunshine (winter), the southern hemisphere gets more (it's summer there).
This is because the northern hemisphere is tilted away from the Sun. In summer, it's tilted toward the Sun.

Answer 2

Of course the amount of solar radiation that the entire earth receives is fairly constant. However, as the seasons change, the northern hemisphere receives more radiation than the southern due to the tilt of the earth's axis. This is reversed six months later. A square yard of the earth's surface receives less radiation when the angle of the sun at high noon is lowest in the sky (winter) and maximum radiation when the angle is high (summer).

Answer 3

The earth's axis is tilted 23.5 degrees away from a line that is perpendicular to the plane of the earth's orbit. Because the earth rotates on its axis it has angular momentum, which makes the axis of rotation point in the same direction as the earth revolves around the sun. That means that at one point in the earth's orbit around the sun, the sun is higher over head and above the horizon for longer. During this time, there is more radiation. Not only is there more total radiation because the sun is up longer, but the light has less atmosphere to pass through and that effect yeilds more radiation too.