C/2010 X1 (Elenin) is a comet which will pass by earth in Oct of 2011. What is the mass and size of this comet and will there be any gravitational effects on earth with this body passing so close?
Comet Elenin is a normal long-period comet, which means it has a long, skinny orbit that takes thousands of years to complete. Based on our best estimates, Elenin will pass about 35 million kilometers from Earth, which is about 0.23 times the distance between the Earth and Sun (or 90 times father than our Moon). This isn't especially close, so it probably won't be perturbed by the Earth's gravity heavily, though it would only take a slight nudge to make the difference between Elenin never coming back and it returning in thousands of years. Earth won't feel it at all.
Comet orbits are usually pretty certain, because they don't depend on the comet itself very much. What they do depend on are things like the planets, which we know very well. We can also tell how certain we are of a comet's orbit. If it passes close to a planet, then the orbit will be less known than if it stays far from planets. Luckily, Comet Elenin is one of the predictable ones that will be far from any of the planets, so will only get those slight nudges.
It's hard to know the mass of a comet directly because we'd need to have something fly by or orbit the comet. Even the size is tricky because comets are surrounded by clouds of gas and dust (the coma) put off as they warm up when they approach the Sun. But we've studied several comets, so can make some pretty good estimates about Comet Elenin. It's probably about 3-4 km in diameter based on how bright is now. Comets can be a bit fluffy -- at least the ones we've seen are too light to be made of solid ice, and definitely too light to be made out of the rock-ice mixture we see on their surfaces. So what happens is we think they've got a lot of empty space, and have a density that's about half that of water.
Under that estimate, Elenin probably masses around 1013 (that's 10 trillion) kilograms. That's about twenty times lighter than Comet Halley, for a point of reference. As far as celestial bodies go, Elenin is a real lightweight, like most comets.
Since long-period comets like Elenin are on their first few trips close to the Sun, it's hard to predict how much ice they have near the surface and how much of that is early-sublimating ices like methane and ammonia, and how much is water ice (which will put on a better show near Earth). Periodic comets like Halley have evened out and lost a lot of their most volatile ices, so are much more predictable (but not always, as Comet Holmes showed in 2007). Hence, long-period comets are watched for signs of being bigger/brighter than predictions, just in case they might end up being the next Hale-Bopp, Hyakutake or McNaught.
There is a lot of speculation on the internet about Comet Elenin ..Some say it is bigger than advertised others say it has a brown dwarf behind it. Is it possible that Comet Elenin is a satellite ( Moon) for a Brown Dwarf ?
Currently Comet Elenin is inside the asteroid belt (as of Summer 2011, when I'm writing this). At that distance, a brown dwarf would not only be visible to a naked-eye stargazer, it also would be playing merry havoc with the asteroid belt and orbits of the gas giants. Furthermore, Comet Elenin is moving around the Sun on its own path, rather than the orbital motion of something orbiting something else.
Most likely what happened is someone decided to throw a real comet into a recycled and fictional doomsday story about a brown dwarf. Given the size of such an object, scientists would know about it several years in advance (at least!) and it would make the papers before it got into the range of something one of millions of hobbyists with telescopes could discover.
Is it possible that it will impact the earth or Our moon?
Comet Elenin will not impact the Earth or Moon on this go-around -- as mentioned, it will be 90 times the distance to the Moon from us at its closest approach.
After the closest approach in 2011:
Indeed, as predicted, Comet Elenin had no impact on the Earth's orbit nor the Earth on Comet Elenin. The comet has disintegrated and stayed very faint. It is back on its trajectory to the outer parts of the Solar System until its next approach in some 12,000 years.
Updated by Everett Schlawin on July 18, 2015.