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

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Discussion Overview

The discussion centers around determining the day on which a specific star will rise at 10:40pm, based on the difference between solar and sidereal days. Participants explore the application of this concept through calculations involving time intervals and the effects of the longer solar day.

Discussion Character

  • Exploratory, Mathematical reasoning, Homework-related

Main Points Raised

  • One participant notes the difference between a solar day and a sidereal day, stating that the solar day is approximately 3.9 minutes longer.
  • Another participant calculates the total time from 9:00pm to 10:40pm as 100 minutes and questions how to proceed with this information.
  • A subsequent post confirms the calculation of 100 minutes and suggests dividing this by 3.9 minutes to find the number of days.
  • There is confusion regarding the units of the result, with one participant questioning what 25.6 represents.
  • Another participant proposes an alternative calculation using the total minutes in a day, suggesting that 1340 minutes could be used to find a different number of days.

Areas of Agreement / Disagreement

Participants express uncertainty about the calculations and the interpretation of results, indicating that the discussion remains unresolved regarding the correct approach to find the day when the star will rise at 10:40pm.

Contextual Notes

Participants have not reached consensus on the correct method or interpretation of the calculations, and there are unresolved questions about units and the application of time intervals.

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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How many minutes from 9:00pm to 10:00pm and then how many more from 10:00pm to 10:40pm?
 
9 -> 10 = 60 min
10 -> 10:40 = 40 min

100 min in total

Then what?

Is it :

100 min / 3.9 min = 25.6
 
n=100/3.9?
 
I cannot believe I am still confused...

25.6

but 25.6 what?

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

1340 / 3.9 = 343.6 days?
 

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