Final answer:
Tracking stars over two weeks allows us to infer that they create a stable pattern in the sky due to Earth's rotation, but the stars themselves do not significantly change position, color, or disappear in such a brief period.
Step-by-step explanation:
When tracking a group of stars over a period of two weeks, several inferences can be made regarding their behavior and characteristics. Firstly, stars create a pattern in the sky, known as constellations, which are relatively stable over short periods like two weeks. Secondly, the apparent motion of the stars in the night sky is primarily due to the rotation of Earth, not the stars moving faster than Earth. Over much longer time scales, the proper motion of stars (their actual motion through space) can be observed, but over two weeks, this motion is negligible.
Regarding the responses in the multiple-choice question: (a) Stars generally do not change color over a period of two weeks unless there are exceptional circumstances affecting their light, such as interstellar dust or gases. (b) They indeed create a pattern, but this is over much larger timescales. (c) Stars do not disappear in such short periods unless under rare astronomical events like a supernova. (d) In terms of the motion observed from Earth, stars move relatively slow and certainly not faster than Earth's rotation or revolution.
To determine the orbital speed of Earth, one could use the Doppler effect by analyzing the spectrum of a star at various times throughout the year. As Earth orbits the Sun, the star's spectrum will show slight shifts toward the blue when Earth is moving toward the star and toward the red when Earth is moving away, due to the Doppler effect. By measuring these shifts, one can infer Earth's velocity along the line of sight to the star.