4a. Consider a binary system whose observed eccentricity is e. Assume that the true orbit is circular. Assume that the two masses are MA and Mg such that MA/MB = 3 and the time period of the orbit is T. Determine the radial velocities (velocity along the line of sight) of the two stars as a function of time. Assume that the center of mass is Vī 1- fixed. You may use: € = b2 4b. Briefly explain why binary star systems have a tendency to become circular with spins synchronized with orbital motion during evolution.
4a. Consider a binary system whose observed eccentricity is e. Assume that the true orbit is circular. Assume that the two masses are MA and Mg such that MA/MB = 3 and the time period of the orbit is T. Determine the radial velocities (velocity along the line of sight) of the two stars as a function of time. Assume that the center of mass is Vī 1- fixed. You may use: € = b2 4b. Briefly explain why binary star systems have a tendency to become circular with spins synchronized with orbital motion during evolution.
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Transcribed Image Text:4a. Consider a binary system whose observed eccentricity is e. Assume that the true orbit
is circular. Assume that the two masses are MA and MB such that MA/MB = 3 and
the time period of the orbit is T. Determine the radial velocities (velocity along the
line of sight) of the two stars as a function of time. ASsume that the center of mass is
b2
fixed. You may use: € =
-
4b. Briefly explain why binary star systems have a tendency to become circular with spins
synchronized with orbital motion during evolution.
Expert Solution
Step 1
By the definition of centre of mass, the masses of a binary system of stars, MA and MB are related -
,
where a1 and a2 are the semimajor axis of the respective stars of mass MA and MB.
This gives
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