Separate a radial-velocity amplitude from an instantaneous sample

1. Define the orbital evidence

A spectroscopic binary produces changing line-of-sight velocities as its components orbit. A fitted velocity amplitude K is not the same as one instantaneous velocity sample. In an original circular orbit with systemic motion removed, the two radial signals are opposite sinusoids. Near a zero crossing, neither star has stopped moving; its instantaneous velocity is directed mostly across the line of sight.

2. Connect geometry, force and conservation

The supplied fit gives K₁=10 and K₂=20 compatible velocity units and period P=2 compatible time units. We deliberately set G=1 in the corresponding abstract unit system; no numerical shortcut combining kilometers per second with years is implied. For inclination i measured from face-on, the relative radius is P(K₁+K₂)/(2π sin i), and total mass is P(K₁+K₂)³/(2πG sin³ i).

The mass ratio is M₂/M₁=K₁/K₂=0.5, independent of inclination under these double-lined circular assumptions. Spectroscopy alone therefore constrains the projected total mass M sin³ i, while a smaller inclination raises the compatible true total. An eclipse or resolved geometry can add inclination information, but its own selection and model assumptions must be checked.

The phase control changes instantaneous samples while preserving the fitted amplitudes and inferred mass. It must not recompute a zero mass when both radial velocities cross zero. Eccentricity introduces further factors and waveform structure; a single-lined system leaves different degeneracies. This lesson is an original inverse-model comparison, not an actual stellar catalog measurement.

3. Work the original case

At i=90°, total mass is 27000/π≈8594.37 compatible units, divided 2:1 between primary and secondary. At i=30°, sin³ i=1/8, so the same fitted radial amplitudes imply eight times that total. At phase 90° the radial samples are +10 and −20; at phase 0° both are zero without changing the mass.

4. Predict and investigate

Would observing a binary at a radial-velocity zero crossing imply its orbit has no motion or mass?

Hold fitted amplitudes fixed while changing inclination; retain projected and true mass separately. Then change phase without changing the fitted orbit and explain which new evidence could constrain inclination.

Source and boundaries

Primary mechanism reference. Checked 30 October 2026. Original prose, numerical cases and diagrams; source context is not a claim that these fictional records were observed. No actual mission operation or instrument aiming is requested.