## Circumpolar Calculations

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

Check AnswerTo 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.

Star | Dec. | V | C | ML | |||
---|---|---|---|---|---|---|---|

NY | SY | NY | SY | NY | SY | ||

Capella | 46N | ||||||

Betelgeux | 7N | ||||||

Vega | 39N | ||||||

Antares | 26S | ||||||

Alpha Crux | 63S |

**V**isible?

**C**ircumpolar?

**M**in **L**atitude?

###### Summary

**D >= 90° - L**

**D**= Declination

**>=**= Greater than or equal to

**L**= Latitude