Final answer:
On the moon, the sun would rise approximately once per month, and the earth would never set, hanging in the same position in the sky for observers on the near side. Stars would be visible for approximately half the lunar day/night cycle unless the sun's brightness obscures them.
Step-by-step explanation:
The question presents a hypothetical scenario involving the moon, the sun, and plant life, which relates to concepts in physics and biology. It delves into celestial mechanics and how they affect life processes. Let's explore the answers to each part of the question.
A. How often would the sun rise?
If you lived in the crater Copernicus on the Moon, the sun would rise approximately once every Earth month. This is because the Moon's rotational period is about 27.3 days, which is also the amount of time it takes to orbit the Earth—a phenomenon known as synchronous rotation.
B. How often would the earth set?
The Earth would never set for an observer on the Moon's near side, which always faces Earth due to the synchronous rotation of the Moon. Therefore, Earth would hang in roughly the same position in the sky as viewed from the crater Copernicus.
C. During what fraction of the time would you be able to see the stars?
Stars would be visible all the time from the lunar surface when it is not illuminated by the sun, which would be roughly half of an entire lunar day/night cycle. However, when the sun is up, its brightness would overwhelm the stars much like it does on Earth during the day. This is not so different from the situation on Earth, where stars are generally visible at night unless obscured by clouds or light pollution.