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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 = 1.5x10 11 m 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 = 1.5x10 11 m

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Astronomical distances The light year (ly) – this is the distance travelled by the light in one year. 1 ly = 9.46x10 15 m c = 3x10 8 m/s t = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 10 7 s Speed =Distance / Time Distance = Speed x Time = 3x10 8 x 3.16 x 10 7 = 9.46 x 10 15 m

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Astronomical distances The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond. 1 pc = 3.086x10 16 m or 1 pc = 3.26 ly “Parsec” is short for parallax arcsecond

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1 parsec = 3.086 X 10 16 metres Nearest Star 1.3 pc (206,000 times further than the Earth is from the Sun)

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

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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. Parallax

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

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

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Parallax

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

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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. 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.

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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.

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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…”

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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 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 This is the “8.9” earthquake off of Sumatra Betelgeuse and Rigel, stars in Orion with apparent magnitudes 0.3 and 0.9

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The historical magnitude scale… Greeks ordered the stars in the sky from brightest to faintest… …so brighter stars have smaller magnitudes. Greeks ordered the stars in the sky from brightest to faintest… …so brighter stars have smaller magnitudes. MagnitudeDescription 1stThe 20 brightest stars 2ndstars less bright than the 20 brightest 3rdand so on... 4thgetting dimmer each time 5thand more in each group, until 6ththe dimmest stars (depending on your eyesight)

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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) 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)

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Brighter = Smaller magnitudes Fainter = Bigger magnitudes Magnitudes can even be negative for really bright stuff! ObjectApparent Magnitude The Sun-26.8 Full Moon-12.6 Venus (at brightest)-4.4 Sirius (brightest star)-1.5 Faintest naked eye stars6 to 7 Faintest star visible from Earth telescopes ~25

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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) and Temperature

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

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The whole point of knowing the distance using the parallax method is to figure out luminosity… 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 Once we have both brightness and distance, we can do that!

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Absolute Magnitude (M) 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 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” removes the effect of distance and puts stars on a common scale

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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

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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 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

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