Astronomical distancesAstronomical distancesThe 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

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

Astronomical distancesAstronomical distances

The light year (ly) – this is the distance travelled by the light in one year. The light year (ly) – this is the distance travelled by the light in one year.

1 ly = 9.46x1015

m

c = 3x108 m/st = 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

Astronomical distancesAstronomical distances

The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.

The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.

1 pc = 3.086x1016

m

or

1 pc = 3.26 ly

““ParsecParsec” is short for” is short forparparallax arcallax arcsecsecondond

1 parsec = 3.086 X 1016 metres

1 parsec = 3.086 X 1016 metres

Nearest Star 1.3 pc

(206,000 times further than the Earth is from the Sun)

ParallaxParallax

Angle star/ball appears to

shift

“Baseline”

Distance to star/ball

Where star/ball appears relative to background

Space

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 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.

ParallaxParallax

Baseline – R(Earth’s orbit)

Dis

tanc

e to

S

tar

- d

Parallax - p(Angle)

We know how big the Earth’s orbit is, we measure the shift (parallax), and then we get the distance…

ParallaxParallax

ParallaxParallax

For very small angles tan p ≈ p

(Distance) d

(Baseline) R (Parallax) tan p

d

R p

In conventional units it means that

m 10 x 3.986 m

36001

3602

10 x 1.5 pc 1 16

11

ParallaxParallax

arcsecond) ( p

1 (parsec) d

m 10 x 3.986 m

36001

3602

10 x 1.5 pc 1 16

11

d

R p

p

R d

The farther away an object gets, the smaller its

shift.

Eventually, the shift is too small to see.

Parallax has its limitsParallax has its limits

Quick ReferenceQuick 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.

Parallax ExperimentParallax 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.

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.

Usually, what we know is how bright the star looks to us here on Earth…

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…”

The Magnitude ScaleThe 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

The historical magnitude scale…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.

Magnitude Description

1st The 20 brightest stars

2nd stars less bright than the 20 brightest

3rd and so on...

4th getting dimmer each time

5th and more in each group, until

6th the dimmest stars (depending on your eyesight)

Later, astronomers quantified this system.

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)

Brighter = Smaller magnitudesFainter = Bigger magnitudes

Brighter = Smaller magnitudesFainter = Bigger magnitudes Magnitudes can even be negative

for really bright stuff! Magnitudes can even be negative

for really bright stuff!

Object Apparent Magnitude

The Sun -26.8

Full Moon -12.6

Venus (at brightest) -4.4

Sirius (brightest star) -1.5

Faintest naked eye stars 6 to 7

Faintest star visible from Earth telescopes

~25

However: knowing how bright a star looks doesn’t really tell us anything about the star itself!

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

We’d really like to know things that are intrinsic properties of the star

like:

Luminosity (energy output)and

Temperature

…we need to know its distance!

…we need to know its distance!

In order to get from how bright something looks…

to how much energy it’s putting out…

The whole point of knowing the distance using the parallax method is to figure out luminosity…

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: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!

Absolute Magnitude (M)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 magnitudeRemember magnitude scale is “backwards”

removes the effect of distanceand

puts stars on a common scale

Absolute Magnitude (M)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:

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:

5log5 dMm

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

So we have three ways of talking about brightness: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