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16 Astrometry
The European Space Agency’s (ESA), Gaia space mission is attempting to measure the position of a billion stars with a positional accuracy of 24 milliarcseconds.
If successful, this will be a major step forward in our goal of mapping the Milky
Way. Astrometry is also used to determine proper motion, the movement of a star
across the sphere of the sky—as opposed to radial motion, that is, toward or away
from the Earth. For example, suppose a star’s position is measured twice 10 years
apart. The first position is (α 1 , δ 1 ), and a decade later, it is at (α 2 , δ 2 ). The changes in
the angle are μ α = α 2 − α 1 and μ γ = γ 2 − γ 1 . To find the proper motion, we apply
μ
2
= μ
2
γ + μ
2
α · cos γ 1 .
Measuring changes in position is challenging over short time scales (i.e., years).
The change in position is small, and the resolution of a ground-based telescope is
limited by atmospheric seeing (which is why Gaia is space-borne). Finding the centre
of a star can be accomplished by finding the centroid of the Gaussian distribution
of the star, and repeating the process increases the reliability of the measurement.
Likewise, using many stars of known position to locate the position of the unknown
source also reduces uncertainties. Once the direction, position, and hence proper
motion vector of the star is known, we may need to account for the proper motion of
the Sun and Earth depending on the application.
We have already briefly mentioned plate solving in this book. Plate solving is a
form of astrometry that relates pixel location to sky location. Plate solving programs
such as Pinpoint determine the plate scale of your image from the pixel size and focal
length of the image. It then identifies the stars within the field, at which point it uses
one of several algorithms to match star patterns in its library to those in the image.
Once it has a match, it identifies the coordinate-to-pixel transform and writes it into
the header in the form of the world coordinate system WCS, which might include
scaling, rotation, and field curvature corrections.
16.2 The Proper Motion of Asteroids
The identification of solar system objects, for example comets and asteroids, is undertaken by their observed orbital properties, which are determined from repeated observations over consecutive nights, if possible. Three nights is the minimum the Minor
Planet Centre suggests.
In this practical, you will observe an asteroid at opposition over successive nights
to determine its proper motion and approximate distance, assuming a circular Keplerian orbit.
16.2.1 Aims
You will be taking images of a bright asteroid at opposition over several evenings to
determine its proper motion and its solar distance. You will also learn how to use the
DS9 vector and blink function.
16 Astrometry
The European Space Agency’s (ESA), Gaia space mission is attempting to measure the position of a billion stars with a positional accuracy of 24 milliarcseconds.
If successful, this will be a major step forward in our goal of mapping the Milky
Way. Astrometry is also used to determine proper motion, the movement of a star
across the sphere of the sky—as opposed to radial motion, that is, toward or away
from the Earth. For example, suppose a star’s position is measured twice 10 years
apart. The first position is (α 1 , δ 1 ), and a decade later, it is at (α 2 , δ 2 ). The changes in
the angle are μ α = α 2 − α 1 and μ γ = γ 2 − γ 1 . To find the proper motion, we apply
μ
2
= μ
2
γ + μ
2
α · cos γ 1 .
Measuring changes in position is challenging over short time scales (i.e., years).
The change in position is small, and the resolution of a ground-based telescope is
limited by atmospheric seeing (which is why Gaia is space-borne). Finding the centre
of a star can be accomplished by finding the centroid of the Gaussian distribution
of the star, and repeating the process increases the reliability of the measurement.
Likewise, using many stars of known position to locate the position of the unknown
source also reduces uncertainties. Once the direction, position, and hence proper
motion vector of the star is known, we may need to account for the proper motion of
the Sun and Earth depending on the application.
We have already briefly mentioned plate solving in this book. Plate solving is a
form of astrometry that relates pixel location to sky location. Plate solving programs
such as Pinpoint determine the plate scale of your image from the pixel size and focal
length of the image. It then identifies the stars within the field, at which point it uses
one of several algorithms to match star patterns in its library to those in the image.
Once it has a match, it identifies the coordinate-to-pixel transform and writes it into
the header in the form of the world coordinate system WCS, which might include
scaling, rotation, and field curvature corrections.
16.2 The Proper Motion of Asteroids
The identification of solar system objects, for example comets and asteroids, is undertaken by their observed orbital properties, which are determined from repeated observations over consecutive nights, if possible. Three nights is the minimum the Minor
Planet Centre suggests.
In this practical, you will observe an asteroid at opposition over successive nights
to determine its proper motion and approximate distance, assuming a circular Keplerian orbit.
16.2.1 Aims
You will be taking images of a bright asteroid at opposition over several evenings to
determine its proper motion and its solar distance. You will also learn how to use the
DS9 vector and blink function.