As I was explaining to my 10 year old what comets are, it hit me that things don’t quite add up. I have taken the dirty snowball theory for granted and accepted carte blanche (as we all have) that a portion of the dirty snowball melts away as a comet approaches the sun, thereby forming the tail. Very simple, neat, and easy for anyone to understand, right? Then, I thought about the basic physics of this. If a portion of a comet melts away while in reasonably close proximity to the sun, then the comet is losing mass. If it is losing mass, the period of the comet must change. So, how can Halley’s comet keep a regular period for so generations upon generations of returns? Its orbit should have decaying, perhaps making Halley a sun-grazing comet. Does something happen in the Oort cloud that refreshes a comet? For all the books on astronomy I have read, the SHRINKING dirty snowball aspect of a comet’s life has never been considered. What’s the factual SD on this?
Also, the mass loss is estimated to be approximately .1% (.001 of the mass) for each pass, and that it’s lost perhaps half of it’s original mass over the course of 2300 passages. It’s not shrinking nearly as much as you might think.
Googling around, I see Kepler’s 3rd law uses the mass of the body around which an object is revolving. It’s been quite awhile since I’ve done such calcs. Memory is fuzzy…
Eventually it will pass too close to the sun or a planet and be absorbed or kicked into a different orbit.
Nope. That’s the long and short of it, as you’ve found in Kepler’s Third Law, which is completely independent of the mass of the orbiting body under the usual assumptions (e.g., the central mass is much heavier).
The mass loss has a different effect on the comet’s orbit, in that sublimating gases acts as little mini-thrusters, adding a bit of jitter to the orbit. Also, interactions with other bodies in the solar system can perturb the orbit, with major deviations (including possible ejection from the solar system) happening on a time scale measured in 1,000s or 10,000s of years.
Just to add, a change in mass of the satellite would change where the barycenter is but the effect on the period in this case in infintesimal.
I’d add that short-period comets really don’t last all that long to begin with. Halley’s comet’s current orbit is on the order of tens to hundreds of thousands of years old. Not even close to the age of the solar system as a whole. It’s got a few thousand orbits in it, which is hardly “stable”.
They’ve literally flown probes up and landed on actual comets- they ARE dirty snowballs. There’s no theoretical component to it.
And… basically if I’m understanding it right, gravitational acceleration is constant regardless of the size of the object, so the main thing determining orbital period is the speed of the object, not the size.
Essentially if a satellite in an orbit is constantly falling *past *the object it’s orbiting, then going faster translates into both a higher orbit and a longer orbital period.