Focus

Confirming Einstein's Theory of Gravity

Instead of always tracing out the same ellipse, the orbit of Mercury pivots around the focus occupied by the Sun. "tte point of closest approach to the Sun, the perihelion, advances by a small amount, 43 seconds of arc per century, beyond that caused by planetary perturbations. Albert Einstein (1879-1955) invented a new theory of gravity, the General tteory of Relativity, which explains this anomalous advance ofMercury's perihelion.

According to this theory, space is distorted and curved in the neighborhood of matter, and this distortion is the cause of gravity, "tte result is a gravitational effect that departs slightly from Newton's expression, and the planetary orbits are not exactly elliptical. Instead of returning to its starting point to form a closed ellipse after one orbital period, the planet moves slightly ahead in a winding path that can be described as a rotating ellipse.

"tte observed advance of Mercury's perihelion is in almost exact agreement with Einstein's prediction, but this accord depends on the assumption that the Sun is a nearly perfect sphere. If the interior of the Sun is rotating very fast, it will push the equator out further than the poles, so its shape ought to be somewhat oblate rather than perfectly spherical. After all, even the solid Earth is slightly fatter at the middle because of its rotation, and the effect ought to be more pronounced for a rotating gaseous sphere like the Sun. "tte size of the oblateness, and the amount that it affects gravity, depend on how fast the interior is rotating.

"tte gravitational influence of the outward bulge, called a quadrupole moment, will provide an added twist to Mercury's orbital motion, shifting its orbit around the Sun by an additional amount and lessening the agreement with Einstein's theory of gravity. Fortunately, the slow rotation of the outer parts of the Sun, which is inferred from helioseismol-ogy, is not enough to produce a substantial asymmetry in its shape, even if the core of the Sun is rapidly rotating. So, we may safely conclude that measurements of Mercury's orbit confirm the predictions of General Relativity under the assumption that the Sun is a nearly perfect sphere.

In fact, the small quadrupole moment inferred from the oscillation data, about one ten millionth rather than exactly zero as Einstein assumed, is consistent with a very small difference between radar measurements of Mercury's orbit and Einstein's prediction. So, the Sun does have an extremely small, middle-aged bulge after all.

tte entire outer layer of the Sun, to a depth of at least 25,000 kilometers, is slowly but steadily flowing from the equator to the poles with a speed of about 20 meters per second. At this rate, an object would be transported from the equator to a pole in a little more than one year. Of course, the Sun rotates at more than 100 times this rate, completing one revolution at the equator in about 25 days.

Both types of internal flows are linked to the Sun's magnetism. Islands of intense magnetic fields, called sunspots, emerge at the poleward side of the faster zonal bands, marking belts of solar activity. Helioseismologists speculate that sunspots might originate at the boundaries of zones moving at different speeds, where the shearing force and turbulence might twist the magnetic fields and intensify magnetic activity, like two nearby speed boats moving at different velocities and churning the water between them.

Intermediate-latitude Shear Zone

FIG. 4.7 Interior flows Global helioseismology of internal flows in the Sun with rotation removed. Red corresponds to faster-than-aver-age flows, yellow to slower than average, and blue to slower yet. On the left side, deeply rooted zonal flows (yellow bands), analogous to the Earth's trade winds, travel slightly faster than their surroundings (blue regions). The streamlines in the right-hand cutaway reveal a slow meriodional flow toward the solar poles from the equator; the return flow below it is inferred. This image is the result of computations using one year of continuous observation, from May 1996 to May 1997, with the Michelson Doppler Imager, abbreviated MDI, instrument aboard the SOlar and Heliospheric Observatory, or SOHO for short. (Courtesy of Philip H. Scherrer and the SOHO SOI/MDI consortium. SOHO is a project of international cooperation between ESA and NASA.)

FIG. 4.7 Interior flows Global helioseismology of internal flows in the Sun with rotation removed. Red corresponds to faster-than-aver-age flows, yellow to slower than average, and blue to slower yet. On the left side, deeply rooted zonal flows (yellow bands), analogous to the Earth's trade winds, travel slightly faster than their surroundings (blue regions). The streamlines in the right-hand cutaway reveal a slow meriodional flow toward the solar poles from the equator; the return flow below it is inferred. This image is the result of computations using one year of continuous observation, from May 1996 to May 1997, with the Michelson Doppler Imager, abbreviated MDI, instrument aboard the SOlar and Heliospheric Observatory, or SOHO for short. (Courtesy of Philip H. Scherrer and the SOHO SOI/MDI consortium. SOHO is a project of international cooperation between ESA and NASA.)

tte magnetic activity belts and the zonal flow bands migrate together, moving slowly toward the solar equator during the Sun's 11-year cycle of magnetic activity, tte meriodional flows also vary with the solar cycle, and these flows may transport leftover magnetic flux to the polar regions, resulting in the reversal of the Sun's global, dipolar magnetic field.

Ms therefore brings us to a discussion of the magnetic fields that pervade the solar atmosphere.