Speed of Gravity

Einstein and Relativity
Albert Einstein

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What is the speed of gravity? It’s 299,792,458 m/s. Seem familiar? Yep, it’s the speed of light (in a vacuum)!

How do we know that that’s the speed of gravity? Not by direct measurement, yet, but by the great success of Einstein’s theory of general relativity (GR).

In general, because it is so successful, and because the speed of gravity in GR is the same as the speed of light, we can say we know how fast gravity propagates.

In particular, observations of the Hulse-Taylor binary pulsar (and other binary pulsars) show the mutual orbit is decaying (the stars are slowly spiraling in, and will one day collide). The rate of decay is exactly as predicted by GR, and is due to the system radiating gravitational waves. The rate at which the system is losing energy tells us how fast that gravitational wave radiation is travelling … and it’s c, the speed of light, to within 1%!

Working out how gravity, as geometry in GR, makes planets in our solar system orbit the Sun is somewhat tricky, and misunderstanding of the details is what’s behind an erroneous claim you might come across on many websites (that the speed of gravity is many millions of times c, or even infinite).

A very long baseline radio interferometric observation of a quasar as it passed near Jupiter, in 2002, lead two researchers to claim to have directly measured the speed of gravity (they found it to be c, plus or minus about 20%). However, this claim is controversial, with several GR experts claiming the analysis contains subtle flaws, and that what was actually measured is the speed of light. The method Fomalont and Kopeikin used might allow a direct estimate of the speed of gravity to be made in future, in the view of their critics, with big improvements in precision.

More to explore: Speed of Gravity (NASA), What is the speed of gravity? (Cornell University), and Does Gravity Travel at the Speed of Light? (University of California Riverside).

Gravity Moves at the Speed of Light is an interesting Universe Today story on the speed of gravity; Warp Drives Probably Impossible After All is a very different take!

And check out the Astronomy Cast September 18th, 2008 Questions Show episode for more on the speed of gravity.

Sources:
Nobel Prize Press Release
Living Reviews in Relativity
UC-Riverside
NASA
Cornell Astronomy

Universe Puzzle No. 6

As with last week’s Universe Puzzle, something that cannot be answered by five minutes spent googling, a puzzle that requires you to cudgel your brains a bit, and do some lateral thinking. This is a puzzle on a “Universal” topic – astronomy and astronomers; space, satellites, missions, and astronauts; planets, moons, telescopes, and so on.

Name three well-known astronomers – or physicists whose work contributed to astronomy – and whose names are constellations. For a gold star, say why your three are more prize-worthy than anyone else’s!

UPDATE: Answer has been posted below.

There are no prizes for the first correct answer – there may not even be just one correct answer – posted as a comment (the judge’s decision – mine! – will be final), but I do hope that you’ll have lots of fun.

Hon. Salacious B. Crumb, Charles A. Musca, David Virgo, and V.R. Phoenix are indeed possible answers, but they are not particularly well-known. You definitely get an extra point for going to “defunct constellations”, but it is creativity too far.

Navneeth, Leó Szilárd (Leo) is an excellent answer!

renoor, Francis Drake (Draco) is a wonderful, left-field answer!

Gadi Eidelheit, Henrietta SWAN Levitt (Cygnus) is good, not least because I had that on my list. And LEOnard Euler is also excellent! However, you get only half marks for Maximillian WOLF (Vulpecula) – Vulpecula is ‘Fox’; Lupus is ‘Wolf’; and no marks for Charles Augustione de COLUMBO (you mean Charles Augustin de Coulomb; the constellation Columba, the Dove, is not related to Coulomb).

In addition to Henrietta Swan Levitt (Cygnus), I had the following:
* William Swan (he left his name in astronomical spectroscopy, google Swan bands)
* Bill Keel (Carina; Bill is extremely active in his support of amateurs, Galaxy Zoo, etc, etc – ‘ngc3314’ is his handle – and also has done excellent work on dust in spiral galaxies)
* Arthur Wolfe (Lupus; his name is in the cosmologically important Sachs-Wolfe effect)
* Tim Hunter (Orion; co-founded the International Dark Sky Association, in 1987)
* Charles Wolf (Lupus again; together with Georges Rayet he discovered the Wolf-Rayet stars)

Check back next week for another Universe Puzzle!

This is Getting Boring: General Relativity Passes Yet another Big Test!

Princeton University scientists (from left) Reinabelle Reyes, James Gunn and Rachel Mandelbaum led a team that analyzed more than 70,000 galaxies and demonstrated that the universe - at least up to a distance of 3.5 billion light years from Earth - plays by the rules set out by Einstein in his theory of general relativity. (Photo: Brian Wilson)

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Published in 1915, Einstein’s theory of general relativity (GR) passed its first big test just a few years later, when the predicted gravitational deflection of light passing near the Sun was observed during the 1919 solar eclipse.

In 1960, GR passed its first big test in a lab, here on Earth; the Pound-Rebka experiment. And over the nine decades since its publication, GR has passed test after test after test, always with flying colors (check out this review for an excellent summary).

But the tests have always been within the solar system, or otherwise indirect.

Now a team led by Princeton University scientists has tested GR to see if it holds true at cosmic scales. And, after two years of analyzing astronomical data, the scientists have concluded that Einstein’s theory works as well in vast distances as in more local regions of space.

A partial map of the distribution of galaxies in the SDSS, going out to a distance of 7 billion light years. The amount of galaxy clustering that we observe today is a signature of how gravity acted over cosmic time, and allows as to test whether general relativity holds over these scales. (M. Blanton, SDSS)

The scientists’ analysis of more than 70,000 galaxies demonstrates that the universe – at least up to a distance of 3.5 billion light years from Earth – plays by the rules set out by Einstein in his famous theory. While GR has been accepted by the scientific community for over nine decades, until now no one had tested the theory so thoroughly and robustly at distances and scales that go way beyond the solar system.

Reinabelle Reyes, a Princeton graduate student in the Department of Astrophysical Sciences, along with co-authors Rachel Mandelbaum, an associate research scholar, and James Gunn, the Eugene Higgins Professor of Astronomy, outlined their assessment in the March 11 edition of Nature.

Other scientists collaborating on the paper include Tobias Baldauf, Lucas Lombriser and Robert Smith of the University of Zurich and Uros Seljak of the University of California-Berkeley.

The results are important, they said, because they shore up current theories explaining the shape and direction of the universe, including ideas about dark energy, and dispel some hints from other recent experiments that general relativity may be wrong.

“All of our ideas in astronomy are based on this really enormous extrapolation, so anything we can do to see whether this is right or not on these scales is just enormously important,” Gunn said. “It adds another brick to the foundation that underlies what we do.”

GR is one, of two, core theories underlying all of contemporary astrophysics and cosmology (the other is the Standard Model of particle physics, a quantum theory); it explains everything from black holes to the Big Bang.

In recent years, several alternatives to general relativity have been proposed. These modified theories of gravity depart from general relativity on large scales to circumvent the need for dark energy, dark matter, or both. But because these theories were designed to match the predictions of general relativity about the expansion history of the universe, a factor that is central to current cosmological work, it has become crucial to know which theory is correct, or at least represents reality as best as can be approximated.

“We knew we needed to look at the large-scale structure of the universe and the growth of smaller structures composing it over time to find out,” Reyes said. The team used data from the Sloan Digital Sky Survey (SDSS), a long-term, multi-institution telescope project mapping the sky to determine the position and brightness of several hundred million galaxies and quasars.

By calculating the clustering of these galaxies, which stretch nearly one-third of the way to the edge of the universe, and analyzing their velocities and distortion from intervening material – due to weak lensing, primarily by dark matter – the researchers have shown that Einstein’s theory explains the nearby universe better than alternative theories of gravity.

Some of the 70,000 luminous galaxies in SDSS analyzed (Image: SDSS Collaboration)

The Princeton scientists studied the effects of gravity on the SDSS galaxies and clusters of galaxies over long periods of time. They observed how this fundamental force drives galaxies to clump into larger collections of galaxies and how it shapes the expansion of the universe.

Critically, because relativity calls for the curvature of space to be equal to the curvature of time, the researchers could calculate whether light was influenced in equal amounts by both, as it should be if general relativity holds true.

“This is the first time this test was carried out at all, so it’s a proof of concept,” Mandelbaum said. “There are other astronomical surveys planned for the next few years. Now that we know this test works, we will be able to use it with better data that will be available soon to more tightly constrain the theory of gravity.”

Firming up the predictive powers of GR can help scientists better understand whether current models of the universe make sense, the scientists said.

“Any test we can do in building our confidence in applying these very beautiful theoretical things but which have not been tested on these scales is very important,” Gunn said. “It certainly helps when you are trying to do complicated things to understand fundamentals. And this is a very, very, very fundamental thing.”

“The nice thing about going to the cosmological scale is that we can test any full, alternative theory of gravity, because it should predict the things we observe,” said co-author Uros Seljak, a professor of physics and of astronomy at UC Berkeley and a faculty scientist at Lawrence Berkeley National Laboratory who is currently on leave at the Institute of Theoretical Physics at the University of Zurich. “Those alternative theories that do not require dark matter fail these tests.”

Sources: “Princeton scientists say Einstein’s theory applies beyond the solar system” (Princeton University), “Study validates general relativity on cosmic scale, existence of dark matter” (University of California Berkeley), “Confirmation of general relativity on large scales from weak lensing and galaxy velocities” (Nature, arXiv preprint)

Universe Puzzle No. 5

As with last week’s Universe Puzzle, something that cannot be answered by five minutes spent googling, a puzzle that requires you to cudgel your brains a bit, and do some lateral thinking. This is a puzzle on a “Universal” topic – astronomy and astronomers; space, satellites, missions, and astronauts; planets, moons, telescopes, and so on.

What do the following have in common?

UPDATE: Answer has been posted below.

Alice, Hanny, Kate, Pamela

They are all featured in Galaxy Zoo’s She’s an Astronomer: Alice Sheppard, Hanny van Arkel (of the Hanny’s Voorwerp fame), Kate Land, and Pamela L. Gay (of Astronomy Cast fame!)

Check back next week for another Universe Puzzle!

World-wide Campaign Sheds New Light on Nature’s “LHC”

Recent observations of blazar jets require researchers to look deeper into whether current theories about jet formation and motion require refinement. This simulation, courtesy of Jonathan McKinney (KIPAC), shows a black hole pulling in nearby matter (yellow) and spraying energy back out into the universe in a jet (blue and red) that is held together by magnetic field lines (green).

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In a manner somewhat like the formation of an alliance to defeat Darth Vader’s Death Star, more than a decade ago astronomers formed the Whole Earth Blazar Telescope consortium to understand Nature’s Death Ray Gun (a.k.a. blazars). And contrary to its at-death’s-door sounding name, the GASP has proved crucial to unraveling the secrets of how Nature’s “LHC” works.

“As the universe’s biggest accelerators, blazar jets are important to understand,” said Kavli Institute for Particle Astrophysics and Cosmology (KIPAC) Research Fellow Masaaki Hayashida, corresponding author on the recent paper presenting the new results with KIPAC Astrophysicist Greg Madejski. “But how they are produced and how they are structured is not well understood. We’re still looking to understand the basics.”

Blazars dominate the gamma-ray sky, discrete spots on the dark backdrop of the universe. As nearby matter falls into the supermassive black hole at the center of a blazar, “feeding” the black hole, it sprays some of this energy back out into the universe as a jet of particles.

Researchers had previously theorized that such jets are held together by strong magnetic field tendrils, while the jet’s light is created by particles spiraling around these wisp-thin magnetic field “lines”.

Yet, until now, the details have been relatively poorly understood. The recent study upsets the prevailing understanding of the jet’s structure, revealing new insight into these mysterious yet mighty beasts.

“This work is a significant step toward understanding the physics of these jets,” said KIPAC Director Roger Blandford. “It’s this type of observation that is going to make it possible for us to figure out their anatomy.”

Over a full year of observations, the researchers focused on one particular blazar jet, 3C279, located in the constellation Virgo, monitoring it in many different wavebands: gamma-ray, X-ray, optical, infrared and radio. Blazars flicker continuously, and researchers expected continual changes in all wavebands. Midway through the year, however, researchers observed a spectacular change in the jet’s optical and gamma-ray emission: a 20-day-long flare in gamma rays was accompanied by a dramatic change in the jet’s optical light.

Although most optical light is unpolarized – consisting of light with an equal mix of all polarizations – the extreme bending of energetic particles around a magnetic field line can polarize light. During the 20-day gamma-ray flare, optical light from the jet changed its polarization. This temporal connection between changes in the gamma-ray light and changes in the optical polarization suggests that light in both wavebands is created in the same part of the jet; during those 20 days, something in the local environment changed to cause both the optical and gamma-ray light to vary.

“We have a fairly good idea of where in the jet optical light is created; now that we know the gamma rays and optical light are created in the same place, we can for the first time determine where the gamma rays come from,” said Hayashida.

This knowledge has far-reaching implications about how a supermassive black hole produces polar jets. The great majority of energy released in a jet escapes in the form of gamma rays, and researchers previously thought that all of this energy must be released near the black hole, close to where the matter flowing into the black hole gives up its energy in the first place. Yet the new results suggest that – like optical light – the gamma rays are emitted relatively far from the black hole. This, Hayashida and Madejski said, in turn suggests that the magnetic field lines must somehow help the energy travel far from the black hole before it is released in the form of gamma rays.

“What we found was very different from what we were expecting,” said Madejski. “The data suggest that gamma rays are produced not one or two light days from the black hole [as was expected] but closer to one light year. That’s surprising.”

In addition to revealing where in the jet light is produced, the gradual change of the optical light’s polarization also reveals something unexpected about the overall shape of the jet: the jet appears to curve as it travels away from the black hole.

“At one point during a gamma-ray flare, the polarization rotated about 180 degrees as the intensity of the light changed,” said Hayashida. “This suggests that the whole jet curves.”

This new understanding of the inner workings and construction of a blazar jet requires a new working model of the jet’s structure, one in which the jet curves dramatically and the most energetic light originates far from the black hole. This, Madejski said, is where theorists come in. “Our study poses a very important challenge to theorists: how would you construct a jet that could potentially be carrying energy so far from the black hole? And how could we then detect that? Taking the magnetic field lines into account is not simple. Related calculations are difficult to do analytically, and must be solved with extremely complex numerical schemes.”

Theorist Jonathan McKinney, a Stanford University Einstein Fellow and expert on the formation of magnetized jets, agrees that the results pose as many questions as they answer. “There’s been a long-time controversy about these jets – about exactly where the gamma-ray emission is coming from. This work constrains the types of jet models that are possible,” said McKinney, who is unassociated with the recent study. “From a theoretician’s point of view, I’m excited because it means we need to rethink our models.”

As theorists consider how the new observations fit models of how jets work, Hayashida, Madejski and other members of the research team will continue to gather more data. “There’s a clear need to conduct such observations across all types of light to understand this better,” said Madejski. “It takes a massive amount of coordination to accomplish this type of study, which included more than 250 scientists and data from about 20 telescopes. But it’s worth it.”

With this and future multi-wavelength studies, theorists will have new insight with which to craft models of how the universe’s biggest accelerators work. Darth Vader has been denied all access to these research results.

Sources: DOE/SLAC National Accelerator Laboratory Press Release, a paper in the 18 February, 2010 issue of Nature.

Universe Puzzle No. 4

As with last week’s Universe Puzzle, something that cannot be answered by five minutes spent googling, a puzzle that requires you to cudgel your brains a bit, and do some lateral thinking. This is a puzzle on a “Universal” topic – astronomy and astronomers; space, satellites, missions, and astronauts; planets, moons, telescopes, and so on.

What’s the next number in the sequence? 401, 172, 85.2

There are no prizes for the first correct answer – there may not even be just one correct answer – posted as a comment (the judge’s decision – mine! – will be final), but I do hope that you’ll have lots of fun.

Post your guesses in the comments section, and check back on Wednesday at this same post to find the answer. Good luck!

UPDATE: Answer has been posted below.

42.5 is the answer; it’s the mean orbital period of Io, in hours; the first three members of the sequence are the mean orbital periods of Callisto, Ganymede, and Europa (source)

Well done scibuff!

Check back next week for another Universe Puzzle.

Universe Puzzle No. 3

As with last week’s Universe Puzzle, something that cannot be answered by five minutes spent googling, a puzzle that requires you to cudgel your brains a bit, and do some lateral thinking.

Which is the ‘odd one out’? And why?

aragonite, diamond, ice, olivine

This is a puzzle on a “Universal” topic – astronomy and astronomers; space, satellites, missions, and astronauts; planets, moons, telescopes, and so on.

So “ice” is certainly one answer (it’s the only one-syllable word), but not, perhaps, the best answer!

If you think the answer to this puzzle is a cline, rather than a single choice, then try this:

What is the best order to arrange these four in? And why?

Of course, the order they are already in is OK (alphabetical); but is it the best?

aragonite, diamond, ice, olivine

There are no prizes for the first correct answer – there may not even be just one correct answer! – posted as a comment (the judge’s decision – mine! – will be final!), but I do hope that you’ll have lots of fun.

Post your guesses in the comments section, and check back on Wednesday at this same post to find the answer. Good luck!

Update: Answer now posted below

Odd one out: aragonite

This is the only one not yet found beyond the Earth. It’s also the only one which is definitely the result of biological processes (although it can be produced by non-biological ones too).

Cline: there are several good answers, and it is difficult to choose among them.

For example: aragonite, diamond, ice, olivine … found on Earth only, found on Earth and in meteorites only, found/detected in the solar system only, only one detected beyond the solar system.

Check back next week for another Universe Puzzle!

Small Asteroids, Bread Flour, and a Dutch Physicist’s 150-year Old Theory

Itokawa, a dusty asteroid (Credit: JAXA)

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No, it’s not the Universe Puzzle No. 3; rather, it’s an intriguing result from recent work into the strange shapes and composition of small asteroids.

Images sent back from space missions suggest that smaller asteroids are not pristine chunks of rock, but are instead covered in rubble that ranges in size from meter-sized boulders to flour-like dust. Indeed some asteroids appear to be up to 50% empty space, suggesting that they could be collections of rubble with no solid core.

But how do these asteroids form and evolve? And if we ever have to deflect one, to avoid the fate of the dinosaurs, how to do so without breaking it up, and making the danger far greater?

Johannes Diderik van der Waals (1837-1923), with a little help from Daniel Scheeres, Michael Swift, and colleagues, to the rescue.

Rocks and dust on asteroid Eros (Credit: NASA)

Asteroids tend to spin rapidly on their axes – and gravity at the surface of smaller bodies can be one thousandth or even one millionth of that on Earth. As a result scientists are left wondering how the rubble clings on to the surface. “The few images that we have of asteroid surfaces are a challenge to understand using traditional geophysics,” University of Colorado’s Scheeres explained.

To get to the bottom of this mystery, the team – Daniel Scheeres, colleagues at the University of Colorado, and Michael Swift at the University of Nottingham – made a thorough study of the relevant forces involved in binding rubble to an asteroid. The formation of small bodies in space involves gravity and cohesion – the latter being the attraction between molecules at the surface of materials. While gravity is well understood, the nature of the cohesive forces at work in the rubble and their relative strengths is much less well known.

The team assumed that the cohesive forces between grains are similar to that found in “cohesive powders” – which include bread flour – because such powders resemble what has been seen on asteroid surfaces. To gauge the significance of these forces, the team considered their strength relative to the gravitational forces present on a small asteroid where gravity at the surface is about one millionth that on Earth. The team found that gravity is an ineffective binding force for rocks observed on smaller asteroids. Electrostatic attraction was also negligible, other than where a portion of the asteroid this is illuminated by the Sun comes into contact with a dark portion.

Fast backward to the mid-19th century, a time when the existence of molecules was controversial, and inter-molecular forces pure science fiction (except, of course, that there was no such thing then). Van der Waals’ doctoral thesis provided a powerful explanation for the transition between gaseous and liquid phases, in terms of weak forces between the constituent molecules, which he assumed have a finite size (more than half a century was to pass before these forces were understood, quantitatively, in terms of quantum mechanics and atomic theory).

Van der Waals forces – weak electrostatic attractions between adjacent atoms or molecules that arise from fluctuations in the positions of their electrons – seem to do the trick for particles that are less than about one meter in size. The size of the van der Waals force is proportional to the contact surface area of a particle – unlike gravity, which is proportional to the mass (and therefore volume) of the particle. As a result, the relative strength of van der Waals compared with gravity increases as the particle gets smaller.

This could explain, for example, recent observations by Scheeres and colleagues that small asteroids are covered in fine dust – material that some scientists thought would be driven away by solar radiation. The research can also have implications on how asteroids respond to the “YORP effect” – the increase of the angular velocity of small asteroids by the absorption of solar radiation. As the bodies spin faster, this recent work suggests that they would expel larger rocks while retaining smaller ones. If such an asteroid were a collection of rubble, the result could be an aggregate of smaller particles held together by van der Waals forces.

Asteroid expert Keith Holsapple of the University of Washington is impressed that not only has Scheeres’ team estimated the forces in play on an asteroid, it has also looked at how these vary with asteroid and particle size. “This is a very important paper that addresses a key issue in the mechanics of the small bodies of the solar system and particle mechanics at low gravity,” he said.

Scheeres noted that testing this theory requires a space mission to determine the mechanical and strength properties of an asteroid’s surface. “We are developing such a proposal now,” he said.

Source: Physics World. “Scaling forces to asteroid surfaces: The role of cohesion” is a preprint by Scheeres, et al. (arXiv:1002.2478), submitted for publication in Icarus.

Eccentricity

The eccentricity in Mars' orbit means that it is . Credit: NASA

When it comes to space, the word eccentricity nearly always refers to orbital eccentricity, or the eccentricity of the orbit of an astronomical body, like a planet, star, or moon. In turn, this relies on a mathematical description, or summary, of the body’s orbit, assuming Newtonian gravity (or something very close to it). Such orbits are approximately elliptical in shape, and a key parameter describing the ellipse is its eccentricity.

In simple terms, a circular orbit has an eccentricity of zero, and a parabolic or radial orbit an eccentricity of 1 (if the orbit is hyperbolic, its eccentricity is greater than 1); of course, if the eccentricity is 1 or greater, the ‘orbit’ is a bit of a misnomer!

In a planetary system with more than one planet (or for a planet with more than one moon, or a multiple star system other than a binary), orbits are only approximately elliptical, because each planet has a gravitational pull on every other one, and these accelerations produce non-elliptical orbits. And modeling orbits assuming the theory of general relativity describes gravity also leads to orbits which are only approximately elliptical (this is particular so for binary pulsars).

Nonetheless, orbits are nearly always summarized as ellipses, with eccentricity as one of the key orbital parameters. Why? Because this is very convenient, and because deviations from ellipses can be easily described by small perturbations.

The formula for eccentricity, in a two-body system under Newtonian gravity, is relatively easy to write, but, unfortunately, beyond the capabilities of the HTML coding of this webpage.

However, if you know the maximum distance of a body, from the center of mass – the apoapsis (apohelion, for solar system planets), ra – and the minimum such distance – the periapsis (perihelion), rp – then the eccentricity, e, of the orbit is just:

E = (ra – rp)/( ra+ rp)

Eccentricity of an Orbit (UCAR), Eccentricity of Earth’s Orbit (National Solar Observatory), and Equation of Time (University of Illinois) are websites with more on eccentricity.

Universe Today articles on eccentricity? Sure! For example: Measuring the Moon’s Eccentricity at Home, Buffy the Kuiper Belt Object, and Lake Asymmetry on Titan Explained.

Two Astronomy Cast episodes in which eccentricity is important are Neptune, and Earth; well worth listening to.