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Unformatted text preview: Distances and Motions Determining the AU
Today, the Earth-Sun distance (= 1 AU) is known to high precision from
radar measurements of the distances to the planets. (The relative scale
of the planet distances is known from Copernicus and Kepler.) Radar
observations of Venus began in 1958. Since we know the distance to
each planet in AUs, measurement of the time required by radar signals
to travel from the Earth to a planet and return establishes the size of the
AU in km.
c = 299,792.458 km/s
AU = 149,597,870.7 km (3.0 x 105 km/s)
(1.5 x 108 km) Triangulation and Parallax
To reach the nearest stars, we use
the orbit of the Earth as a baseline
and the technique of triangulation.
The greater the angular change
(i.e., parallax), the nearer the star. http://highered.mcgraw-hill.com/sites/007299181x/student_view0/interactives.html# Parsec
Baseline = 1 AU = 1 arcsec
d = 206,265 AU
= 1 parsec
= 1 pc Distance
d = 1 / p" (pc) = 1 / " (pc)
d = 206,265 / p" (AU)
where p" or "is in arcseconds
or p" = 0.11 arcseconds
d = 9.1 pc
= 9.1 x 206,265 = 1.9 x 106 AU Early Measurements of Distances
Stars are so distant that the parallaxes of even the nearest ones are too small
to be measured with the techniques available to Aristotle. William Herschel
tried to measured parallaxes, but instead got orbits of binary stars.
Parallaxes were eventually detected, but even the nearest star shows a total
annual displacement of only about 1.5 arcsec. The first observation of
parallax of a star is usually credited to the German astronomer Friedrich
Bessel (in 1838). Light Year
Light travels at a speed of about 186,000 miles per second (300,000 km/s).
So in one second, light has traveled 186,000 miles; in two seconds it has
gone 372,000 miles.
Let the clock run for one entire year, and the light will have traveled
5.9 x 1012 miles (9.5 x 1012 km) or 63,240 AU.
The distance that light travels in one year is defined as 1 Light Year.
The nearest star is about four light years away (distance), or you can say
that the light emitted by this star takes four years (time) to travel the
expanse of space between it and us. Units of Distance
Astronomical Unit (AU) Distance from the Earth to the Sun Parsec (pc) Parallax of 1 arcsecond Light Year (LY) Distance light travels in one year
d = 1 / p" (pc)
d = 206,265 / p" (AU)
pc = 3.26 LY The Nearest Stars
Sirius d = 1.3 pc
p" = 0.76 arcsec
d = 2.6 pc Good parallaxes can only be measured
for stars within 100 pc of the Sun.
There are about 5000 stars in this
region of space, but most are invisible
to the naked eye. PRS Question
1. If a star has a parallax of 0.04 arcsec, its distance is
a. 4 pc
d. 25 pc
b. 4 ly
e. 25 ly
c. 4 AU Radial Velocity
The radial velocity is the speed that a star has as it approaches or recedes
from the Sun. It is counted as positive if it is moving away from the Sun. = v / c = (obs – ) / v = c Since the motion of either the star or the observer (or both) produces a
Doppler shift in the spectral lines, a knowledge of the radial velocity alone
does not enable one to decide which one “is doing the moving”. What is
really measured is the speed with which the distance between the star and
Sun is increasing or decreasing. Proper Motion
The proper motion is the rate at which a star’s apparent position on the
sky changes. With respect to “background” stars, the motions of a few
nearby stars can be observed. is in arcseconds / year Barnard’s Star changes its position by 10.25 arcsec per year. Tangential Velocity Radial velocity is the motion of a star along the line of sight, while proper
motion is the angular motion produced by the star’s motion across the sky.
Whereas the radial velocity is known in km/s and is independent of distance,
the proper motion of a star does not give the star’s actual speed. The latter is
called the tangential velocity. To calculate it, one must know the proper
motion and distance (or parallax).
T = 4.74 d = 4.74 / p" (km/s) where is in arcsec/year, d is in parsecs, and p" is in arcsec. PRS Question
2. If a star has a proper motion of 10 arcsec per year and is at a distance
of 2 pc, what is its tangential velocity?
a. ~100 km/s
d. ~20 km/s
b. ~25 km/s
e. ~5 km/s
c. ~1 km/s Space Velocity The total space velocity is
V2 = VR2 + VT2 ...
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This note was uploaded on 03/04/2012 for the course PHYS 2022 taught by Professor Jarrio during the Spring '12 term at Central GA Tech.
- Spring '12