Consider a binary system consisting of two identical stars in circular orbits ab

Question

Consider a binary system consisting of two identical stars in circular orbits about their center of mass. The center of mass of the system is at rest relative to the earth. Sketch radial velocity curves for two cases: a) a case where the stars orbit in a plane perpendicular to our line-of-sight from earth (that is, a case where we are looking down face-on to the orbit plane) and
(b) a case where the stars orbit in a plane parallel to our line of sight (that is, edge on). Consider a binary system consisting of two identical stars in circular orbits about their center of mass. The center of mass of the system is at rest relative to the earth. Sketch radial velocity curves for two cases: a) a case where the stars orbit in a plane perpendicular to our line-of-sight from earth (that is, a case where we are looking down face-on to the orbit plane) and
(b) a case where the stars orbit in a plane parallel to our line of sight (that is, edge on). a) a case where the stars orbit in a plane perpendicular to our line-of-sight from earth (that is, a case where we are looking down face-on to the orbit plane) and
(b) a case where the stars orbit in a plane parallel to our line of sight (that is, edge on). (b) a case where the stars orbit in a plane parallel to our line of sight (that is, edge on). (b) a case where the stars orbit in a plane parallel to our line of sight (that is, edge on).

Explanation / Answer

If we plot a graph with the component of velocity in the line of sight as a function of time, it is called a radial velocity graph.

Given that the stars are identical and they move in circular orbits around the centre of mass. In this case;

a) When the stars orbit in a plane perpendicular to the line of sight, we see the radial velocity remains the same. Therefore, when v is plotted against t, it will be a horizontal straight line (corresponding to v).

b) When stars orbit in a plane parallel to the line of sight, we see the stars moving away and towards us at regular time intervals . That is, velocity as a function of time appears increasing , decreasing and reversing at regular intervals. (Spectral lines switch from red shift to neutral to blue shift, then repeating). The radial velocity curve will be a sinusoidal curve.

Hope it is clear..

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