General Relativity and Astronomy

Previously, we discussed how mass can curve space(time) due to general relativity. Why is this important?

The curvature of mass leads to interesting phenomena. The first is it causes the perihelion of a planet orbiting the Sun to precess. Secondly, it causes light actually to bend - yes, gravity affects light - and this leads to really weird stuff.

Let's look at the first one. The best example of the precession of a planet at it orbits the Sun is the path of Mercury. This was discussed back in the post about Mercury and General Relativity. The highlight of the discussion was that as Mercury orbits around the Sun, at perihelion, Mercury is in the deepest part of the gravity well created by the Sun. As it continues to orbit, each successive perihelion moves farther ahead in its orbit. The perihelion of Mercury was noticed in the mid 1800s, but was thought to be caused by an inner planet. But after Einstein's Theory of General Relativity was developed, the equations were able to show why Mercury's orbit precessed around the Sun. Everything that orbits around another body shows this precession, with the amount of precession dependent on the mass of the central body.

The second one seems a little weirder. From Newton's equation for universal gravitation, we see that the force of gravity is dependent on mass. However, light and all electromagnetic radiation are massless. So how does gravity bend light?

In a nutshell - gravity wells.

If a star were behind the Sun, in Newtonian gravity, we would not be able to see it, because gravity only affects objects with mass. We would see something like this.

However, because of General Relativity, light will bend in the presence of a gravitational field. The light from the star will curve around the Sun and we can see it from Earth.

This was actually proven by Sir Arthur Eddington. In 1919, there was a solar eclipse that he observed and photographed. When the pictures were analyzed, they could see the effect of gravity on stars. This analysis only worked during an eclipse because otherwise, the Sun would be too bright and wash out the background stars. Eddington gave physical proof that General Relativity was correct!

Positive and Negative Image of Solar Eclipse of May 1919

Image Credit:



F. W. Dyson, A. S. Eddington, and C. Davidson

This phenomena of light bending around masses also is used to search for exoplanets. As a planet passes in front of star, that planet can bend the light towards us. This process is called lensing. Not only does it allow the light to reach us even if the source is behind the mass, it can also magnify the light, making it brighter. Most of the gravitational lensing seen are galactic in nature.

The curved arcs are the lensed (background) object. The centers are the lenses bending the light.

Image Credit:

NASA/Hubble Space Telescope

Einstein's Cross (Gravitation Lensing) - Quasar being lensed by a central dim galaxy

Image Credit:

ESA/Hubble/NASA

Einstein Ring - When the background object is perfectly aligned with lensing object and the Earth, a complete ring can be created

Image Credit:

NASA, ESA, A. Bolton (Harvard-Smithsonian CfA) and the SLACS Team

Hubble Site

Mercury and General Relativity

Albert Einstein proposed General Relativity in 1916. In it, he states that time and space re not separate geometric entities, but combined into one entity called space-time. Space-time is not flat, but curved and is heavily influenced by mass sitting in space-time. The larger a mass is, the larger its gravitational influence on space-time.

from Space.com

 

A consequence of General Relativity is that the apside of an object orbiting another object will move as the smaller object moves in its orbit. The apside in our Solar System can be thought of as being similar to the perihelion of a planet relative to the Sun. However, apsides are the point closest to the center of mass of a two-body system, like the Sun and a planet. Since the Sun is much more massive than any planet, we can equate the apside of a planet to the perihelion.

 

What we mean by the precession of the apside is that as the planet moves in its orbit, the planet goes deeper into the space-time well as shown above. This causes the planet's apside to move farther along as it orbits the Sun.

 

This is why full moons vary in size from month to month and why solar eclipses can vary from total, annular, or partial.  The apside of the Earth-Moon system precesses as the Moon orbits the Earth.

 

Since this post is about Mercury proving General Relativity, we should discuss how this is so. Back in 1859, French Mathematician Urbain Le Verrier discovered that Mercury's orbit had some strange anomalies. It was at first thought that the anomalies were due to a planet closer to the Sun than Mercury. This explanation helped in the discovery of Neptune by Le Verrier and two others: John Couch Adams and Johann Galle earlier in the century. But once Einstein's theory came out, the equations describing the precession of the asides calculated the anomalies present in Mercury's orbit.

 

There are other examples of observations proving the Theory of General Relativity. They can be found in the above Wikipedia link.