Comets lose their mass through water evaporation due to close encounter with sun, so my question is does the loss of mass create an observable change in a comet's orbit? What kind of change that may be shrinking orbit or expanding orbit?
This problem was studied in Yu & Zheng (1995), who evaluated the effects of the change in the Sun's mass over time and the change in a comet's mass over time, for the case of Shoemaker-Levy 9, which had recently crashed into Jupiter. Given their mass model for the comet (Equation 6), they found that the Sun's mass loss created an increase in semi-major axis of about 8.5 centimeters per year, whereas the comet's mass loss created an increase in semi-major axis of about 10,000 kilometers per year.
Several things to note:
- The comet orbited Jupiter prior to breaking up, so it did not come as close to the Sun as most short-period comets.
- Mass loss rates can change over time, depending on the distance from the Sun.
- Shoemaker-Levy 9 should not be considered a normal comet, in any sense, given its orbit and eventual destruction.
10,000 kilometers a year, though, is nothing to sniff at. Over the course of an orbit, that can be quite a lot - although keep in mind that longer orbits involve much larger semi-major axes - and I'd argue that it should be observable, given the correct calculations of how the orbit should evolve over time.