The Solar System


Conservation of Angular Moment

The Origin

Solar System in the Making?

Binary Stars




Our theory for the origin of the Solar System is a very old one with some modern innovations called the Nebular Hypothesis. A crucial ingredient in the nebular hypothesis is the conservation of angular momentum.

Conservation of Angular Moment

Objects executing motion around a point possess a quantity called angular momentum. This is an important physical quantity because all experimental evidence indicates that angular momentum is rigorously conserved in our Universe: it can be transferred, but it cannot be created or destroyed. For the simple case of a small mass executing uniform circular motion around a much larger mass (so that we can neglect the effect of the center of mass) the amount of angular momentum takes a simple form. As the adjacent figure illustrates the magnitude of the angular momentum in this case is L = mvr, where L is the angular momentum, m is the mass of the small object, v is the magnitude of its velocity, and r is the separation between the objects.

Ice Skaters and Angular Momentum

This formula indicates one important physical consequence of angular momentum: because the above formula can be rearranged to give v = L/(mr) and L is a constant for an isolated system, the velocity v and the separation r are inversely correlated. Thus, conservation of angular momentum demands that a decrease in the separation r be accompanied by an increase in the velocity v, and vice versa. This important concept carries over to more complicated systems: generally, for rotating bodies, if their radii decrease they must spin faster in order to conserve angular momentum. This concept is familiar intuitively to the ice skater who spins faster when the arms are drawn in, and slower when the arms are extended; although most ice skaters don't think about it explictly, this method of spin control is nothing but an invocation of the law of angular momentum conservation.

The Origin

The Nebular Hypothesis in its original form was proposed by Kant and Laplace in the 18th century. The initial steps are indicated in the following figures.

Collapsing Clouds of Gas and Dust

A great cloud of gas and dust (called a nebula) begins to collapse because the gravitational forces that would like to collapse it overcome the forces associated with gas pressure that would like to expand it (the initial collapse might be triggered by a variety of perturbations---a supernova blast wave, density waves in spiral galaxies, etc.).

In the Nebular Hypothesis, a cloud of gas and dust collapsed by gravity begins to spin faster because of angular momentum conservation

It is unlikely that such a nebula would be created with no angular momentum, so it is probably initially spinning slowly. Because of conservation of angular momentum, the cloud spins faster as it contracts.

The Spinning Nebula Flattens

Because of the competing forces associated with gravity, gas pressure, and rotation, the contracting nebula begins to flatten into a spinning pancake shape with a bulge at the center, as illustrated in the following figure.

The collapsing, spinning nebula begins to flatten into a rotating pancake

Condensation of Protosun and Protoplanets

As the nebula collapses further, instabilities in the collapsing, rotating cloud cause local regions to begin to contract gravitationally. These local regions of condensation will become the Sun and the planets, as well as their moons and other debris in the Solar System.

As the nebula collapses further, local regions begin to contract gravitationally on their own because of instabilities in the collapsing, rotating cloud

While they are still condensing, the incipient Sun and planets are called the protosun and protoplanets, respectively.

Evidence for the Nebular Hypothesis

Because of the original angular momentum and subsequent evolution of the collapsing nebula, this hypothesis provides a natural explanation for some basic facts about the Solar System: the orbits of the planets lie nearly in a plane with the sun at the center (let's neglect the slight eccentricity of the planetary orbits to simplify the discussion), the planets all revolve in the same direction, and the planets mostly rotate in the same direction with rotation axes nearly perpindicular to the orbital plane.

The nebular hypothesis explains many of the basic features of the Solar System, but we still do not understand fully how all the details are accounted for by this hypothesis. As we discuss in the next section, we now have some direct observational evidence in support of the nebular hypothesis.

Solar System in the Making?

The nebular hypothesis for the origin of our Solar System has been bolstered by a variety of recent observations that look very much like star and planetary systems in various stages of formation.

New Solar Systems

Recent Hubble Space Telescope observations shed considerable light on the birth of stars and associated planetary systems. The following image shows regions in the Orion Nebula where solar systems may be forming.

Regions in the Orion Nebula where solar systems appear to be forming

The Orion Nebula is approximately 1500 light years from Earth. It is visible to the naked eye as the middle "star" in the sword of the constellation Orion. These images were taken with the Wide Field Planetary Camera 2 of the Hubble Space Telescope (C.R. O'Dell, Rice University). Details of the images show several protoplanetary disks ( proplyds ), including a single dark disk surrounding a central star (Ref). The lower left inset figure shows a drawing giving the approximate scale of our Solar System relative to the proplyd.

Here is a HST movie (650 kB MPEG) illustrating these protoplanetary disks in the Orion Nebula (original movie source), here is a further discussion of these planetary systems now forming in Orion.

More Star-Forming Regions

Many other star-forming regions are known. In addition to the Eagle Nebula discussed below, here are images and discussion of

In each of these examples there is strong evidence that stars are being born in the region shown in the image; presumably, at least in some of the cases, attendant solar systems are being formed also.

Star Formation in the Eagle Nebula

The following images show examples in the Eagle Nebula of regions where stars (and possibly solar systems) appear to be forming.

Star-Birth Clouds in M16 (Eagle Nebula). J. Hester and P. Scowon (Arizona St. Univ.), November 2, 1995. Taken with NASA Hubble Space Telescope, WFPC2

The scale of the image on the left is about 1 light year. The blowup on the right shows finger-like structures that are thought to be regions in which new stars are being formed. The tips of these finger-like objects are about the size of our Solar System! Here is a spectacular movie (780 kB) of these star-forming regions in the Eagle Nebula made with the Hubble Space Telescope (Source). This movie is about as close as you are ever going to get to the bridge of the Starship Enterprise!

Planets Around other Stars

In recent years rather conclusive evidence has accumulated for planets orbiting other stars. This evidence comes from the gravitational perturbations exerted on the star by the unseen companion planet that can be exposed by very accurate measurement of the radial velocity of the star (see the related discussion of detecting unseen companions in binary star systems). These measurements require that variations in the radial velocity of order 10 meters per second be detected relative to a total radial velocity typically of order 10-100 kilometers per second. Here is more information about the newly discovered planets, and here is an online Extrasolar Planets Encyclopedia.

Binary Stars

Our Solar System may not be the norm for stars in the Universe. The observational evidence is that most stars are parts of multiple star systems, not single stars like our Sun.

Formation of Binary Star Systems

The most common occurrence of stars appears to be as parts of binary (two-star) systems. This suggests an alternative to the nebular hypothesis illustrated in the following figure.

Alternative to the nebular hypothesis that leads to binary star formation

Although planets might still form in such binary systems by a similar mechanism as discussed before, it is an open question whether they would have stable orbits that would keep them bound in the system without running into the stars. Another question, assuming such planets were on stable orbits, is whether they could have temperature ranges favorable for the formation of life.

If Jupiter Had Become a Star . . .

We note in this connection that if Jupiter had been about 100 times more massive than it is, it would have formed a star instead of a planet. Thus, maybe the Solar System very nearly became a binary star system instead of a single star with planets. We may speculate that in that case the Earth might not even exist, or even if it existed would be in an orbit giving surface conditions not favorable to the evolution of life.