Which statement about stellar motion is incorrect?
A.In general, the closer a star is, the more its proper motion.
B.The radical velocity is measured by the Doppler shift.
C.The transverse velocity is measured by the proper motion and distance.
D.Like parallax, proper motion is measured over intervals of exactly six months.
E.The Pythagorean Theorem relates space, transverse, and radial velocities.
To determine which statement about stellar motion is incorrect, we need to examine each statement and identify any inaccuracies.
A. In general, the closer a star is, the more its proper motion.
This statement is generally correct. Proper motion refers to the apparent motion of a star across the sky over time. Stars that are closer to us appear to have greater proper motion than those that are farther away.
B. The radial velocity is measured by the Doppler shift.
This statement is accurate. The radial velocity of a star, which is its motion toward or away from us, is measured by observing the Doppler shift in its spectral lines. A blue shift indicates the star is moving towards us, while a red shift indicates it is moving away.
C. The transverse velocity is measured by the proper motion and distance.
This statement is correct. Transverse velocity refers to the motion of a star perpendicular to our line of sight. It is measured by combining the star's proper motion (angular speed across the sky) and its distance.
D. Like parallax, proper motion is measured over intervals of exactly six months.
This statement is incorrect. Proper motion is not measured over intervals of exactly six months. Parallax, which is the apparent shift of position of a nearby star when observed from different points in Earth's orbit, is indeed measured over intervals of approximately six months. Proper motion, however, is measured by tracking the star's position over a longer period of time, typically years or decades.
E. The Pythagorean Theorem relates space, transverse, and radial velocities.
This statement is incorrect. The Pythagorean theorem, which describes the relationship between the sides of a right triangle, does not directly relate to the space, transverse, and radial velocities of stars. The equations and principles used for calculating these velocities are based on trigonometry and observational data, rather than the Pythagorean theorem.
Therefore, the incorrect statement is statement D: Like parallax, proper motion is measured over intervals of exactly six months.