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
D. is incorrect. Proper motion is the long term trend in stellar position change, with the parallax taken out. It may take many years to measure it, and the measurements should be taken at the same time of year, to eliminate the parallax effect
from the measurements. Meanwhile, parallax is measured over intervals of exactly six months.
Step 1: Read and understand the question.
The question asks for the incorrect statement about stellar motion.
Step 2: Analyze each statement.
A. In general, the closer a star is, the more its proper motion. - This statement is correct. Proper motion refers to the apparent motion of a star due to its actual motion through space. Closer stars tend to have larger apparent motions.
B. The radial velocity is measured by the Doppler shift. - This statement is correct. Radial velocity refers to the motion of a star along the line of sight, which is measured through the Doppler shift of its spectral lines.
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 the line of sight, which is measured using the proper motion and the distance to the star.
D. Like parallax, proper motion is measured over intervals of exactly six months. - This statement is incorrect. Proper motion is measured over long periods, usually years, and is not necessarily dependent on intervals of exactly six months.
E. The Pythagorean Theorem relates space, transverse, and radial velocities. - This statement is correct. The Pythagorean Theorem can be used to relate the three-dimensional space velocity of a star to its transverse velocity and radial velocity.
Step 3: Determine the incorrect statement.
The incorrect statement is D.
Step 4: Provide the answer.
The incorrect statement about stellar motion is D. Proper motion is not measured over intervals of exactly six months.
To determine which statement about stellar motion is incorrect, let's go through each option:
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, and it is influenced by the star's proximity to us.
B. The radial velocity is measured by the Doppler shift. This statement is correct. The Doppler shift of the star's spectrum can reveal its motion toward or away from us, also known as the radial velocity.
C. The transverse velocity is measured by the proper motion and distance. This statement is correct. Proper motion combined with the distance to the star allows us to calculate its transverse velocity, which is the motion perpendicular to our line of sight.
D. Like parallax, proper motion is measured over intervals of exactly six months. This statement is incorrect. Proper motion is the long-term trend in stellar position change, with the parallax effect removed. It may take many years to measure proper motion accurately, and observations should be performed at the same time of year to eliminate the parallax effect.
E. The Pythagorean Theorem relates space, transverse, and radial velocities. This statement is incorrect. The Pythagorean Theorem is a geometric theorem and does not directly relate to the velocities of stars.
Therefore, the incorrect statement is option D: Like parallax, proper motion is measured over intervals of exactly six months.