At your telescope, you measure the parallax of the star Regulus to be one-half of the parallax of the star Denebola. What do you immediately know about their relative distance from us?
a) That Regulus is further away than Denebola.
b) That Regulus is closer than Denebola.
c) That Regulus and Denebola are approximately the same distance from Earth.
I think it's a, that Regulus is further away than Denebola.
b) That Regulus is closer than Denebola.
To determine the relative distance between two stars based on their parallax measurements, you need to understand that parallax is the apparent shift of an object's position due to the motion of the observer. It is measured by observing the object from two different positions and comparing the angle of apparent displacement.
In this scenario, if the parallax of Regulus is one-half of the parallax of Denebola, it means that Regulus appears to move half as much compared to Denebola when observed from two different positions.
Since parallax is inversely proportional to distance, meaning closer objects have a larger parallax than farther objects, we can conclude that Regulus is closer to us than Denebola.
Therefore, the correct answer is b) Regulus is closer than Denebola.