Astronomical distances

1. Astronomical distances The SI unit for length, the meter, is a very small unit to measure astronomical distances. There units usually used is astronomy: • The Astronomical Unit (AU) – this is the average distance between the Earth and the Sun. This unit is more used within the Solar System. 1 AU = 1.5x1011 m

2. Astronomical distances • The light year (ly) – this is the distance travelled by the light in one year. c = 3x108 m/s t = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 107 s Speed =Distance / Time Distance = Speed x Time = 3x108 x 3.16 x 107 = 9.46 x 1015 m 1 ly = 9.46x1015 m

3. Astronomical distances • The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond. “Parsec” is short for parallax arcsecond 1 pc = 3.086x1016 m or 1 pc = 3.26 ly

4. 1 parsec = 3.086 X 1016 metres • Nearest Star 1.3 pc (206,000 times further than the Earth is from the Sun)

5. Parallax Space Where star/ball appears relative to background Angle star/ball appears to shift Distance to star/ball “Baseline”

6. Parallax Parallax is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer.

7. Parallax We know how big the Earth’s orbit is, we measure the shift (parallax), and then we get the distance… Parallax - p (Angle) Distance to Star - d Baseline – R (Earth’s orbit)

8. Parallax For very small angles tan p ≈ p In conventional units it means that

9. Parallax

10. Parallax has its limits The farther away an object gets, the smaller its shift. Eventually, the shift is too small to see.

11. Quick Reference • 0.5 degree • The width of a full Moon, as viewed from the Earth's surface, is about 0.5 degree. The width of the Sun, as viewed from the Earth's surface, is also about 0.5 degree. • 1.5 degrees • Hold your hand at arm's length, and extend your pinky finger. The width of your pinky finger is about 1.5 degrees. • 5 degrees • Hold your hand at arm's length, and extend your middle, ring, and pinky fingers, with the three fingers touching. The width of your three fingers is about 5 degrees. • 10 degrees • Hold your hand at arm's length, and make a fist with your thumb tucked over (or under) your other fingers. The width of your fist is about 10 degrees. • 20 degrees • Hold your hand at arm's length, and extend your thumb and pinky finger. The distance between the tip of your thumb and the tip of your pinky finger is about 20 degrees.

12. Parallax Experiment • Using the quick reference angles that I gave you determine how far something is away near your house based on the parallax method. Include a schematic to show the placement of all objects. Your schematic should include relevant distances and calculations.

13. Usually, what we know is how bright the star looks to us here on Earth… We call this its Apparent Magnitude “What you see is what you get…”

14. The Magnitude Scale • Magnitudes are a way of assigning a number to a star so we know how bright it is • Similar to how the Richter scale assigns a number to the strength of an earthquake Betelgeuse and Rigel, stars in Orion with apparent magnitudes 0.3 and 0.9 This is the “8.9” earthquake off of Sumatra

15. The historical magnitude scale… • Greeks ordered the stars in the sky from brightest to faintest… …so brighter stars have smaller magnitudes.

16. Later, astronomers quantified this system. • Because stars have such a wide range in brightness, magnitudes are on a “log scale” • Every one magnitude corresponds to a factor of 2.5 change in brightness • Every 5 magnitudes is a factor of 100 change in brightness (because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)

17. Brighter = Smaller magnitudesFainter = Bigger magnitudes • Magnitudes can even be negative for really bright stuff!

18. However: knowing how bright a star looks doesn’t really tell us anything about the star itself! We’d really like to know things that are intrinsic properties of the star like:Luminosity (energy output) andTemperature

19. In order to get from how bright something looks… …we need to know its distance! to how much energy it’s putting out…

20. The whole point of knowing the distance using the parallax method is to figure out luminosity… Once we have both brightness and distance, we can do that! It is often helpful to put luminosity on the magnitude scale… Absolute Magnitude: The magnitude an object would have if we put it 10 parsecs away from Earth

21. Absolute Magnitude (M) removes the effect of distanceandputs stars on a common scale • The Sun is -26.5 in apparent magnitude, but would be 4.4 if we moved it far away • Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitude Remember magnitude scale is “backwards”

22. Absolute Magnitude (M) Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation: • Example: Find the absolute magnitude of the Sun. • The apparent magnitude is -26.7 • The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pc • Therefore, M= -26.7 – log (4.9x10-6) + 5 = • = +4.8

23. So we have three ways of talking about brightness: • Apparent Magnitude - How bright a star looks from Earth • Luminosity - How much energy a star puts out per second • Absolute Magnitude - How bright a star would look if it was 10 parsecs away