Chapter 9: Planet Formation and Exoplanets

Two bodies with a major difference in mass orbiting around a common barycenter (red cross) with circular orbits.

When Newton realized that planets orbit due to gravitational forces, our picture of the Solar System changed from one of the planets orbiting the Sun, to planets and the Sun all orbiting their mutual center of mass. As the planets travel round and round the Sun, their masses pull the Sun toward them. If the planets are positioned such that their mass is more or less evenly distributed about the Sun, the Sun will sit squarely on the Solar System's center of mass. This came close to happening in both 1951 and 1990. If, conversely, all the planets were to arrange themselves on the same side of the Sun in a straight line, then the Sun would be pulled 500,000 km away from the center of mass, more than half its diameter. Throughout most of the 1980s and from the mid-1950s to the mid-1960s, the center of mass of the Solar System was outside the surface of the Sun. Due to the motions of the planets, the Sun is constantly moving in a gentle spiral about the center of mass of the Solar System. This type of motion is called reflex motion.

A star orbited by an exoplanet, viewed in line with the plane of the system.

The size of this wobble would be greater if Jupiter were larger or if Jupiter were closer to the Sun, and thus exerted a greater gravitational pull. Were we able to rise above the Solar System, and perch near a nearby star to look down on the Sun and planets, it might be possible to perceive the Sun's slight motion. It's possible in principle, but in practice, it's an extremely challenging observation. The angular size of the wobble is set by the physical diameter of the wobble and the distance to the star. The total amount of wobble is twice the distance from the center of the Sun to the center of gravity, or 1.6 × 10⁶ kilometers. We can use the small angle equation to calculate that this would be visible as 0.01 seconds of arc from a neighboring star system. This is an incredibly small angle. It's like the wobble of a hula hoop seen 10,000 miles away! The correct term for the wobble is reflex motion, and the technique used to detect it is astrometry. The next generation of planet-searching telescopes is designed to be able to detect reflex motions even this small. As you can imagine, the reflex motion is even tinier for an Earth-like planet. Even though the Earth is closer to the Sun, it's 300 times less massive than Jupiter, so it has a much smaller gravitational force on the Sun.

The radial velocity method to detect exoplanet is based on the detection of variations in the velocity of the central star, due to the changing direction of the gravitational pull from an (unseen) exoplanet as it orbits the star. When the star moves towards us, its spectrum is blueshifted, while it is redshifted when it moves away from us. By regularly looking at the spectrum of a star - and so, measure its velocity - one can see if it moves periodically due to the influence of a companion.

Since the 1990s, astronomers have been monitoring nearby stars looking for evidence of Doppler shifts caused by orbiting planets. Much to the astronomy communities amazement, the first planet discovered via this technique was roughly half the size of Jupiter, but on an orbit significantly smaller than Mercury's! The star was 51 Peg, the 51st brightest star in the constellation of Pegasus, and its planet was whipping around the star every 4.3 days. This planet — termed a hot Jupiter for its mass and proximity to its host star — defied all solar system formation models of the time. What's more, for nearly a decade, many planets found around normal stars were also hot Jupiters. This forced astronomers to rework their models to allow gas planets to migrate close to their host stars. This technique for detecting exoplanets is called the radial velocity method or the Doppler method, and it continues to be used today. From the motions that it detects, astronomers can place lower limits on planetary masses and measure the size and period of the planet's orbits.