We present X-ray light curves of Cygnus X-3 as measured by the recently launched AstroSat satellite. The light curve folded over the binary period of 4.8 hours shows a remarkable stability over the past 45 years and we find that we can use this information to measure the zero point to better than 100 s. We revisit the historical binary phase measurements and examine the stability of the binary period over 45 years. We present a new binary ephemeris with the period and period derivative determined to an accuracy much better than previously reported. We do not find any evidence for a second derivative in the period variation. The precise binary period measurements, however, indicate a hint of short term episodic variations in periods. Interestingly, these short term period variations coincide with the period of enhanced jet activity exhibited by the source. We discuss the implications of these observations on the nature of the binary system.
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