Measuring Distance to a Star

Height of Flag PoleStellar Parallax

Spectroscopic Parallax

MEASURING THE HEIGHT OF THE FLAG POLE

Do Now How do you tell if something is closer or

father away?

DISTANCE TO FLAG POLE

S-f H-r S-r H-f11.4 m 1.0 m 1.5 m

11.4 m 1.0m 1.12 m

Tangent Angle from Rico’s eyes to top of flag pole=

45 degree

HOW DO WE CALCULATE THE DISTANCE TO THE STARS?

Parallax An object appears to shift position when the

observer moves.

Stellar Parallax The nearby stars will

appear to move relative to the background stars

Use trig to find the distance

Tanθ = D/orbital radius

http://abyss.uoregon.edu/~js/glossary/parallax.html

Animation http://highered.mcgraw-hill.com/olcweb/cgi/

pluginpop.cgi?it=swf::800::600::/sites/dl/free/007299181x/78778/Parallax_Nav.swf::Stellar%20Parallax%20Interactive

Now you try it: Calculate the distance to the star if a) the angle is 47 degrees and the baseline

radius is 15 AU. b) the angle is 78 degrees and the radius is

16 AU.

What is the relation ship between the angle and the star distance? 

LABCork Activity

Calculating Error Compare your measurements or calculations to

the actual (accepted) value % Error = measure – accepted x 100 accepted

In this case, = measured – calculated X 100 measured

http://astro.unl.edu/naap/distance/parallax.html

Stars are very far away – yet some stars are closer than others. Do these closer stars exhibit parallax? The answer turns out to be yes, but the parallax is very small – far smaller than can be seen with the naked eye. The first successful measurements of a stellar parallax were made by Friedrich Bessel in 1838, for the star 61 Cygni.

Hipparcos and Gaia Satellites

Before Hipparcos, literally only a hundred or so parallactic angles were known to any accuracy

Hipparcos (1989 to 1993)- measured a parallactic angle of about 0.001 arcsecond.. giving the distances to several thousand stars to < 5% error.

Gaia (Global Astrometric Interferometer for Astrophysics) - increase the angular resolution of Hipparcos by a factor of over a 1000.

To find distance calculate the Distance Modulus Distance Modulus is (m-M) Where

m = apparent magnitude M = absolute magnitude

Distance Modulus (m-M)Where m = apparent

magnitude And M = absolute

magnitude

where D is the distance in parsecs

Spectroscopic Parallax Assumption- stars with the same spectral

class and pressure class have the absolute magnitude

SPECTROSCOPIC PARALLAX

WHAT IS A PARSEC?

http://astro.unl.edu/naap/distance/parallax.html

http://astro.unl.edu/naap/distance/parallax.html

Parsec The basic unit for measuring astronomical

distances.

One second of arc of parallax

1 second of arc (1") = 1 / 3600 degrees

Equivalent to 3.26 light years

From the figure above, the distance between the Sun and the star is :

d = r / tan P

If P is 1 second of arc: d = 150,000,000 / tan 1" = 30 million million km

How to calculate the distance to a star

For the star above, the parallax angle - P is half the distance moved by the star between photos.

Therefore P = 0.5 / 2 = 0.25 seconds of arc.

Distance in parsecs = 1 / P

Where p is in seconds of arc

                                                                               For the star in the figure above:

d = r / tan P We know that for very small angles, tan P = P.

So d = 1 / P = 1 / 0.25 = 4

Therefore the star is four parsecs away.

m – M = 5 log (D/10)

Where D is distance in parsecs