Kuiper Belt - Mass and Size Distribution

Mass and Size Distribution

Despite its vast extent, the collective mass of the Kuiper belt is relatively low. The total mass is estimated to range between a 25th and 10th the mass of the Earth with some estimates placing it at a thirtieth an Earth mass. Conversely, models of the Solar System's formation predict a collective mass for the Kuiper belt of 30 Earth masses. This missing >99% of the mass can hardly be dismissed, as it is required for the accretion of any KBOs larger than 100 km (62 mi) in diameter. If the Kuiper belt had always had its current low density these large objects simply could not have formed. Moreover, the eccentricity and inclination of current orbits makes the encounters quite "violent" resulting in destruction rather than accretion. It appears that either the current residents of the Kuiper belt have been created closer to the Sun or some mechanism dispersed the original mass. Neptune's current influence is too weak to explain such a massive "vacuuming", though the Nice model proposes that it could have been the cause of mass removal in the past. While the question remains open, the conjectures vary from a passing star scenario to grinding of smaller objects, via collisions, into dust small enough to be affected by solar radiation.

Bright objects are rare compared with the dominant dim population, as expected from accretion models of origin, given that only some objects of a given size would have grown further. This relationship N(D), the population expressed as a function of the diameter, referred to as brightness slope, has been confirmed by observations. The slope is inversely proportional to some power of the diameter D.

where the current measures give q = 4 ±0.5.

Less formally, there are for instance 8 (=23) times more objects in 100–200 km range than objects in 200–400 km range. In other words, for every object with the diameter of 1,000 km (621 mi) there should be around 1000 (=103) objects with diameter of 100 km (62 mi).

The law is expressed in this differential form rather than as a cumulative cubic relationship, because only the middle part of the slope can be measured; the law must break at smaller sizes, beyond the current measure.

Of course, only the magnitude is actually known, the size is inferred assuming albedo (not a safe assumption for larger objects).

Since January 2010, the smallest Kuiper belt object discovered to date spans 980 m across.