The noon shadow will point to the North Pole for the remainder of the year. A vertical stick on the Tropic of Capricorn, roughly 23.5 degrees south of the equator, will throw no shadow on December 21, the summer solstice for the southern hemisphere, and its midday shadow will point to the South Pole the rest of the year. This is why we have winter in the northern hemisphere and summer in the southern hemisphere: the Earth's axis of rotation is not parallel to its orbit around the Sun; instead, it points toward the center of the Solar System (the Sun and planets) at an angle of about 5 degrees.
During a day in December in the southern hemisphere, the sun rises on the east coast of Australia and sets on the west coast of South America. The western half of Africa is in darkness until after midnight when the sun rises on the eastern half of Africa and sets on the west coast of India. At some times of the year, Antarctica lies directly between the sun and the equator, so all parts of the continent experience days and nights with no change in season. However, at other times of the year, the Antarctic Peninsula gets more sunlight than other parts of the continent, causing the snow there to melt and lead to changes in the local environment. For example, since warm air can hold more water vapor than cold air, when the melting begins the atmosphere over the peninsula becomes more humid.
In conclusion, the southern hemisphere faces north at mid-year but by December it is facing south again.
The Northern Hemisphere is leaning the most away from the sun for the year at the December solstice. Near midday, the sun shines straight above as viewed from 23 1/2 degrees south of the equator, at the imaginary line around the globe known as the Tropic of Capricorn. This is the furthest south the sun ever goes. At the same time, near the north pole it is day and night for the entire world.
The sun will not return to its previous position until the next summer solstice in June 2021. During this time, the days get longer and the nights get shorter, with the first sunrise on March 20th and the last sunset on April 17th.
In addition to being dark outside during daytime, the winter solstice marks the beginning of meteorological winter in much of the Northern Hemisphere. In the mid-latitudes, seasonal temperatures begin to drop around this time, with coldest temperatures occurring between December 21st and 28th (the week surrounding the holiday season). Snow usually covers the ground in the northern half of the continent; ice forms in lakes and oceans above the freezing point. The winter solstice is the longest night of the year in areas closer to the poles.
At the moment of the winter solstice, the angle of inclination of the earth's axis relative to the plane of the orbit is 0 degrees.
The 21st of December is Earth Day. This is the date of the Northern Hemisphere's winter solstice. The North Pole is now dark for 24 hours, while the South Pole is lighted. The Sun is at its zenith for those living on the Tropic of Capricorn, and hence low in the sky for those living in the Northern Hemisphere. At the North Pole, there is no horizon to see when it is dark, only stars.
Earth orbits the Sun every 365.256 days. At the time of the winter solstice, the difference between the length of a year and the distance that Earth travels around the Sun is least. After the winter solstice, the length of year increases, and so does the distance that Earth travels around the Sun during one orbit. In fact, after three years have passed, the amount of travel has doubled back to where it was at the winter solstice.
At the North Pole, all daytime sights are obscured by darkness. Even at the South Pole, where there is sunlight throughout the year, everything is frozen in ice. So, no, an observer at the North Pole cannot see the Sun during the day in December.
However, at night, when it is not dark at the North Pole, they would see many stars within the constellation of Sagittarius.