Earth

Sun

Star

2. Careful measurement of a celestial object’s position in the sky (astrometry) may be used to determine its distance

Define the terms parallax, parsec, light year

the apparent shift in position of a close object against a distant background due to a change in position of the observer

(or parallax-second), the distance that corresponds to an annual parallax of 1 second of an arc 1 AU

1 arcsecond

1 parsec

the distance travelled by light (or other EMR) in one year

Explain how trigonometric parallax can be used to determine the distance to stars

d = 1/pd = 1/pd = 1/pd = 1/p

Earth

Sun

Star1 AUp

dThe annual parallax (p) is half the angle through which a nearby star appears to shift over a period of 6 months.

It can be seen that sin p = 1/d

The parallax angles are small, so sin p = p, so p = 1/d and d = 1/p

and since 1 parsec = d when p = 1 arcsecond

can be used to determine the distance to stars

and p = measured parallax (in arcseconds)

where d =distance to star (in parsecs)

Solve problems and analyse information to calculate the distance to a star given its trigonometric parallax using

d = 1/pd = 1/pd = 1/pd = 1/p

Procyon has an annual parallax of 0.286 arcseconds.How far away is Procyon in parsecs and light years?

d = 1/p

= 1/ 0.286 = 3.50 parsecs = 3.50 x 3.26 light years = 11.4 ly

Limitations of trigonometric parallax

•extremely difficult to measure parallaxes less than 0.01 arc seconds because of atmospheric seeing. This therefore restricts observations of stars beyond 100 pc because the measured angle is too small to accurately determine.

Discuss the limitations of trigonometric parallax measurements

Gather and process information to determine the relative limits to trigonometric parallax distance determinations using recent ground-based and space-based telescopes

Hipparcos (launched by European Space agency in 1989)

•orbital satellite is unaffected by atmospheric seeing

•measured the parallaxes of 1000’s of stars with extremely high accuracy ( 0.001 arcsecs)

•enabled astronomers to determine higher stellar distances (out to several hundred parsecs) much more accurately

•ESA will launch GAIA in 2010 to measure to 0.00001 arcsecs