## Circumpolar Calculations

6.15 - Be able to use a starâ€™s declination to determine whether the star will be circumpolar from an observerâ€™s latitude

In the exam you may be asked to determine:

• Which stars are circumpolar and which are not.
• What latitude you would have to be at in order to see a certain star
• The smallest or largest Declination a star would be at from a given latitude

The formula for working out if a star is circumpolar or not is:
D >= 90° - L

D= Declination
>== Greater than or equal to
L= Latitude

#### Questions

##### Question 1

Deneb = Dec 45°
Arcturus = Dec 19°
Alpha Centuri = Dec -61°
If you were in London would Deneb be circumpolar?

D greater than or equal to 90 - L
90 - L (51) = 39
45 is greater than 39 so Deneb is circumpolar
Arcturus (19N) is less than 39 so is not circumpolar but seasonal
Alpha Centuri has a declination -61 is less than 39 and so would not be viewable from London.

##### Question 2

How far south would you have to be to see Alpha Centuri?
Tip - treat negative numbers as positive and then convert them afterwards.

So to see it add 90 to -61 which makes 29 so you would have to travel to latitude 29N to see this star.

##### Question 3

How far south would you have to be to see Alpha Centuri as a circumpolar star?

To see it as a circumpolar star = 90 - 61 = 29 so you would have to be at least 29° south to see it as a southern circumpolar star.

##### Question 4

State whether or not each of these stars would be:
Visible from New York (41°N) or Sydney (34°S) and circumpolar from either city or seasonal.
Also state the minimum latitude (north and south) they would have to be seen from to be circumpolar.
Key: New York = NY, Sydney = SY.

Question Table of Locations
Star Dec. V C ML
NY SY NY SY NY SY
Capella 46N
Betelgeux 7N
Vega 39N
Antares 26S
Alpha Crux 63S

Visible?
Circumpolar?
Min Latitude?

###### Summary

D >= 90° - L

D= Declination
>== Greater than or equal to
L= Latitude