Which theorem is utilized to combine radial velocity ($v_r$) and transverse velocity ($v_t$) for total speed?
Answer
Pythagorean theorem
The total speed of a star through three-dimensional space is synthesized by combining the two orthogonal components of motion: the radial velocity ($v_r$), which is along the line of sight, and the transverse velocity ($v_t$), which is perpendicular to that line. Because these two motions are at right angles to each other, the calculation for the total velocity ($v_{ ext{total}}$) necessarily employs the Pythagorean theorem, expressed as $v_{ ext{total}}^2 = v_r^2 + v_t^2$.
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