Expert: Courtney Seligman - 12/12/2010

Question
Hello, Mr Seligman.

My question has two parts.

First, it concerns Jupiter. I understand that the planets' orbits are eccentric because of several factors and, in the case of Earth (and I suppose Mars and Venus), one of those factors is Jupiter's gravity. So, if Jupiter suddenly 'disappeared', would the Earth's (and Mars's, and Venus's) orbit become less eccentric?

Secondly, I understand that the asteroids in the Asteroid Belt never got around to aggregating into a planet because of Jupiter, which besides that kicked off most of the asteroids in the original belt. So, if Jupiter 'disappeared', would the asteroids start aggregating? Even if they could only form an object with 4% of the Moon's mass (according to one internet page I've read). And if the answer is yes (over the course of millions and billions of years, naturally), would the first step be the formation of a more compact cloud of asteroids around Ceres?

Thank you for your insights,
Sara

Answer
The eccentricity of an orbit is due to a planet's current motion. If outside influences (anything other than the Sun) were removed, the orbit would stay exactly the same as now, until the Sun gets old and loses mass (as a red giant). So "disappearing" Jupiter wouldn't change the eccentricity of other planets' orbits; it would just make their current orbits less changeable.

However, although Jupiter is certainly one of the largest causes of such changes, it is not the only one. For instance, the Earth and Venus affect each other's orbits, so their orbits would continue to change, almost the same as now. And even though Mars' orbit would be less changeable, the Earth would continue to affect it -- just on a longer time scale than when Jupiter's effects are also taken into account.

So no, the orbits wouldn't become less eccentric. They would stay as they are for a little longer, but continue to change, back and forth (sometimes more eccentric, and sometimes less eccentric; sometimes larger and sometimes smaller), over long periods of time.

As far as the asteroids are concerned, there are too few of them left to aggregate in any short period of time. Eventually most of the smaller ones will end up as part of larger ones, or broken into rubble too small to notice. But the target area for Ceres and the other large asteroids is simply too small for the asteroids to easily aggregate, so it will take tens or hundreds of billions of years for it/them to "sweep up" the smaller asteroids and rubble left over from their breakup.

Still, they should eventually end up as more nearly one object, as opposed to the current collection of thousands or millions (depending on how small you're willing to go, before you stop counting). But perhaps surprisingly, it will take longer for that to happen if Jupiter disappears, because if the orbits remain as they are, the larger ones will never have a chance to run into the smaller ones. Although, by removing mass from the area, Jupiter made it more difficult for them to form into a single large object (early on), its gravity is now the main thing "randomizing" their orbits, and by changing the orbits, allowing ones that cannot run into each other now a chance to run into each other in the future. So if Jupiter didn't exist, the tens or hundreds of billions of years needed to sweep everything into one object might become hundreds or thousands of billions of years.

I should note that they wouldn't cluster near Ceres toward the end, as your question suggests. As time goes on, and there are more and more of them in Ceres and fewer and fewer not in it, the rate at which Ceres runs into them will decrease. If, for instance, it took X billion years for Ceres to sweep up 90% of the current crop of asteroids, then it would take the best part of another X billion years for it to sweep up 90% of what was left, and a similar amount of time for it to sweep up 90% of what was left at that time. So, for instance, to sweep up 99.9999% of the current crop of asteroids, it would take the best part of 6X billion years (since there are six 9's in the percentage). So over time, instead of things clustering around Ceres, the asteroid belt as a whole would simply become emptier and emptier, until there was nothing worth noticing save for Ceres.

Finally, there is a presumption in this discussion that the process of accreting (building up by collision) Ceres will go smoothly. But although it is the largest asteroid, there are a number of them big enough that if they hit Ceres at a high velocity, a substantial number of fragments would be created, greatly increasing the number of asteroids left to run into. For example, when Vesta runs into Ceres (at some very distant date), Ceres will only gain a fraction of Vesta's mass, and so sweep up the rest of Vesta's mass will take an immense period of time. How long would be anyone's guess, but we are certain that when the Sun dies, in about 6 or 7 billion years, the asteroids will have made insignificant progress toward becoming a single object; and if Jupiter disappeared, 6 or 7 trillion years might not be long enough to reach that "goal".