Connection between right ascension and time

[Wheelwalker]

I'm a physics major currently taking my first astro class. We're covering the basics at the moment but I am having trouble visualizing this question from our textbook. To preface this, I understand that declination is to the celestial sphere what latitude is to the Earth and RA is to the celestial sphere what longitude is to the earth. I also know that RA is measured from the vernal equinox. The problem references Hemingway's "The Old Man and the Sea" and describes a man in Cuba lay in his boat shortly after the sun set one September night and saw Rigel rising. I'm supposed to find what is incorrect about this. I'm fairly certain that Rigel wouldn't appear in the night sky until much later than the sun sets. Rigel's RA is 05h 14m. The longitude of Cuba (in a very general sense) is approximately 80 degrees west. But where do I go from here? Do I calculate how many hours away Cuba's longitude is from Rigel's RA? How do I factor in the time?

 

[Chronos]

You need to determine what 'clock' is used to define RA, and the clock used by the 'Old Man'. The rest is easy.

 

[Wheelwalker]

So the 'clock' used to define RA is that 0h is at the vernal equinox, and goes up east from there. The clock used by the Old Man allow him to read the time at approximately sunset in Cuba in late September?

 

[Philosophaie]

There is time in the Hour Angle:
$$LMST = GMST + time + Longitude/15$$$$HA = LMST - RA$$where LMST is Local Mean Sidereal Time in Hours. GMST is Greenwich Mean Sidereal time. The Sidereal Time above London, England. And time is in hours also.

 

[pmacias]

You are correct in your understanding of RA and its relationship to longitude on Earth. In order to answer this question, you need to understand the concept of sidereal time. Sidereal time is a measure of the Earth's rotation with respect to the stars, and it is directly related to RA. One sidereal day is equal to the time it takes for the Earth to complete one full rotation with respect to the stars, which is about 23 hours and 56 minutes.

In order to determine if the observation of Rigel rising shortly after sunset is correct, we need to calculate the sidereal time at the location of Cuba at the time of the observation. This can be done using the formula: Sidereal time = Right ascension of vernal equinox + (longitude of observer / 15).

Using this formula, we can calculate the sidereal time at Cuba's longitude of 80 degrees west to be approximately 5 hours and 20 minutes. This means that Rigel would have been visible in the night sky about 5 hours and 20 minutes after sunset, which is much later than the observation in the text.

Therefore, the incorrect aspect of this observation is the timing of Rigel rising. It would not have been visible shortly after sunset, but rather much later in the night. This highlights the important connection between right ascension and time, as it allows us to accurately predict the positions of stars in the night sky at different times.