We discuss a method to determine orbital properties and masses of low-mass bodies orbiting eclipsing binaries .
The analysis combines long-term eclipse timing modulations ( light-travel time or LTT effect ) with short-term , high-accuracy astrometry .
As an illustration of the method , the results of a comprehensive study of Hipparcos astrometry and over a hundred years of eclipse timings of the Algol-type eclipsing binary R Canis Majoris are presented .
A simultaneous solution of the astrometry and the LTTs yields an orbital period of P _ { 12 } = 92.8 \pm 1.3 yr , an LTT semiamplitude of 2574 \pm 57 s , an angular semi-major axis of a _ { 12 } = 117 \pm 5 mas , and values of the orbital eccentricity and inclination of e _ { 12 } = 0.49 \pm 0.05 , and i _ { 12 } = 91.7 \pm 4.7 deg , respectively .
Adopting the total mass of R CMa of M _ { 12 } = 1.24 \pm 0.05 M _ { \odot } , the mass of the third body is M _ { 3 } = 0.34 \pm 0.02 M _ { \odot } and the semi-major axis of its orbit is a _ { 3 } = 18.7 \pm 1.7 AU .
From its mass , the third body is either a dM3-4 star or , more unlikely , a white dwarf .
With the upcoming microarcsecond-level astrometric missions , the technique that we discuss can be successfully applied to detect and characterize long-period planetary-size objects and brown dwarfs around eclipsing binaries .
Possibilities for extending the method to pulsating variables or stars with transiting planets are briefly addressed .