Final answer:
The maximum size of an astronomical object with a brightness variation period of 17 days can be determined by calculating the distance light travels in half of the period if the variation is due to rotation. However, the available answer options (astronomical units, light-years, solar radii, parsecs) are too large for such a period, suggesting a mistake in the question.
Step-by-step explanation:
If a new astronomical object is discovered that varies in brightness with a period of 17 days, the maximum size of this object can be estimated by considering the maximum distance light could travel in half of the brightness variation period, as this would represent the time for light to travel from one side of the object to the observer if the variation is caused by rotation. However, in this scenario it is not clear whether the cause of brightness variation is due to rotation or another factor such as orbital motion. Assuming circular rotation and that the period of brightness variation is due to the rotational period, the maximum distance light could travel in half of the period (8.5 days) can be converted to a maximum size for the object.
The speed of light is approximately 299,792 kilometers per second. Converting days to seconds, 8.5 days is equal to 8.5 × 24 × 60 × 60 seconds. Multiplying this by the speed of light gives the maximum radius that the object can have, which would then be doubled to get the maximum diameter. However, given the options provided in the question, none of the distances (astronomical units, light-years, solar radii, parsecs) seem to be a correct fit for an object of an assumed 8.5-day radius light-travel time, as these are all immensely large astronomical distances, far exceeding the size of an object with a brightness variation period of 17 days. Therefore, the question seems to present a disconnect between the provided options and the nature of the astronomical object's brightness variation period.