What Day Will You See the Same Star Rise at 10:40pm?

  • Thread starter dekoi
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In summary, the original value of time (9:00pm) minus the final value of time (10:40pm) divided by the difference between a sidereal and a solar day (3.9 min) yields the number of days (25.6) needed for the star to rise at 10:40pm. Alternatively, if we use the total number of minutes in a day (1440 min) minus the time difference (100 min), we get 1340 min, which when divided by 3.9 min, also yields the number of days (343.6) needed for the star to rise at 10:40pm.
  • #1
dekoi
Question:
Imagine you go out tonight at 9:00pm and see a star rising on the horizon. If you go out tomorrow at the same time, the star will be in a different location. What day would you be able to see the same star rise from the horizon at 10:40pm?

My half-answer:
The difference between a sidereal and a solar day is that the solar day is ~3.9 min longer.

However, I cannot seem to apply this concept to figure out which day the star would rise at 10:40pm.

I have formulated my own equation,

tn = to - 3.9n

Where tn is the final value of time (in this case, 10:40pm), and to is the original value of time (in this case, 9:00pm). n is the number of days (in this case, what we are trying to find).

By substituting values into my equation, I get:
n = (9:00pm - 10:40pm) / 3.9 min

However, I cannot figure out the answer from that. This is a very easy question but I am really stumped. Any help?
 
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  • #2
How many minutes from 9:00pm to 10:00pm and then how many more from 10:00pm to 10:40pm?
 
  • #3
9 -> 10 = 60 min
10 -> 10:40 = 40 min

100 min in total

Then what?

Is it :

100 min / 3.9 min = 25.6
 
  • #4
n=100/3.9?
 
  • #5
I cannot believe I am still confused...

25.6

but 25.6 what?

days? How does that work according to units?
 
  • #6
or how about instead of 100 min... 1440 min - 100 min = 1340 min

1340 / 3.9 = 343.6 days?
 

1. What is the difference between a sidereal and solar day?

A sidereal day is the time it takes for the Earth to rotate once completely on its axis with respect to the stars. This is approximately 23 hours, 56 minutes, and 4 seconds. A solar day, on the other hand, is the time it takes for the Sun to return to its highest point in the sky, which is approximately 24 hours. The difference between the two is due to the Earth's orbit around the Sun.

2. How is a sidereal day measured?

A sidereal day is measured by observing the time it takes for a specific star to return to its highest point in the sky. This is known as the star's sidereal day, and it is used as a reference point for measuring the Earth's sidereal day.

3. Why do we use solar days instead of sidereal days?

Solar days are used as a standard for measuring time because they are more closely aligned with our daily experience. We wake up and go to sleep based on the rising and setting of the Sun, not the stars. Therefore, solar days are more practical and convenient for our daily routines.

4. How do sidereal and solar days affect the length of a year?

Because the Earth takes slightly longer to rotate once with respect to the stars compared to the Sun, there are actually slightly more sidereal days in a year than solar days. This results in a difference of about 4 minutes per day, which adds up to an extra day every four years. This is why we have leap years to account for this difference and keep our calendar aligned with the seasons.

5. Is there any practical use for sidereal days?

Yes, sidereal days are important in fields such as astronomy and navigation. In astronomy, sidereal days are used to track the motion of stars and other celestial objects. In navigation, sidereal days are used to determine longitude by comparing the time of local noon to the time of noon at a reference point, such as Greenwich, England.

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