Download 3.3 e describe the method of heliocentric parallax

3.3e
describe the method of heliocentric parallax to determine distances to
nearby stars
3.3f
recall the definition of one parsec (pc)
Heliocentric parallax (measurements made with the Sun at the centre) are carried out as
seen in the diagram. The view of a nearby star is taken on one day of the year from the
Earth. When 6 months has passed and the Earth is on the other side of its orbit around the
Sun, the view of the star has changed. The angular shift can be measured by the telescope
used (how much the angle of view has changed for the star during half a year).
January 1st
Distant star field
Earth orbit
Nearby
star
Sun
July 1st
Appearance of star on July 1st
Appearance of star on January 1st
The parallax angle ( π ) is measured in seconds of arc (arcsec).
1˚ = 60 minutes of arc
1 minute of arc = 60 seconds of arc
1˚ = 3,600 arcsec
Stars closer to Earth give rise to larger parallax angles.
Above 100 l.y. results give too small an angle to be measured and other methods to measure
the distances of stars have to be used.
Trigonometry allows details from a right-angled triangle to be worked out:-
300,000,000 km
January 1st
Nearby
star
SUN
Angular shift
of star
July 1st
150,000,000 km
Using the upper right-angled triangle, half the angular shift gives the
parallax angle π
π
Trigonometry gives us
Tangent
π
=
OPPOSITE =
ADJACENT
150,000,000
DISTANCE TO STAR
This converts to
DISTANCE TO STAR =
150,000,000 km
Tangent
(The distance in km can then be converted to parsecs)
π
Distances in km to nearby stars would give rise to very large numbers and the use of a
parsec becomes helpful as a unit.
One parsec (1pc) is the distance at which a star has a parallax angle Π of 1 arcsec
150,000,000 km
Shown on a similar diagram, 1 parsec can be seen:-
1 arcsec
π
1 parsec
An excellent simulation by Professor Terry Herter at Cornell University shows clearly the way
heliocentric parallax works:1).
2).
3).
4).
5).
Click on the link below (Java needs to be on your computer to operate the model.
This can be downloaded free of charge from the internet)
When the screen shows the parallax model, left click on the area once
Move the orange star to the left using the mouse
Left click on ‘Show Bounds’
Left click on ‘Animate’ - if the Earth does not rotate around the Sun, just
place the cursor over Earth, hold the mouse down and move Earth around
the orbit of the Sun. Note how the star moves compared with the
background stars between the red and blue boundary markers.
The orange star can be repositioned to show how stars further away from Earth hardly move
across the background stars.
Heliocentric Parallax
http://www.astro.cornell.edu/academics/courses/astro1101/java/parallax/parallax.htm#instructions
Simulation credit : Professor Terry Herter, Cornell University
Picture credits : (Sun) SOHO/ESA&NASA (Earth) NASA/JSC-Apollo 17