We know that the speed of electromagnetic radiation can be derived from Maxwell’s equation[s] in a vacuum. What equations (similar to Maxwell’s - perhaps?) offer a mathematical proof that Gravity Waves must travel [at the] speed of light?
If you were to somehow make the Sun disappear, you would still see its emitted light for 8 minutes and 20 seconds: the amount of time it takes light to travel from the Sun to the Earth across 150,000,000 km of space. But what about gravitation? Would the Earth continue to orbit where the Sun was for that same 8 minutes and 20 seconds, or would it fly off in a straight line immediately?
There are two ways to look at this puzzle: theoretically and experimentally/observationally. From a theoretical point of view, this represents one of the most profound differences from Newton’s gravitation to Einstein’s, and demonstrates what a revolutionary leap General Relativity was. Observationally, we only had indirect measurements until 2017, where we determined the speed of gravity and the speed of light were equal to 15 significant digits!
Gravitational waves do travel at the speed of light, which equals the speed of gravity to a better precision than ever. Here’s how we know.
If you’ve ever looked at a hurricane forecast, you’re probably familiar with “cones of uncertainty,” the funnel-shaped maps showing a hurricane’s predicted path. Thirty years ago, a hurricane forecast five days before it made landfall might have a cone of uncertainty covering most of the East Coast. The result? A great deal of uncertainty about who should evacuate, where it was safe to go, and where to station emergency responders and their equipment.
Over the years, hurricane forecasters have succeeded in shrinking the cone of uncertainty for hurricane tracks, with the help of data from satellites. Polar-orbiting satellites, which fly nearly directly above the North and South Poles, are especially important in helping cut down on forecast error.
The orbiting electronic eyeballs key to these improvements: the Joint Polar Satellite System (JPSS) fleet. A collaborative effort between NOAA and NASA, the satellites circle Earth, taking crucial measurements that inform the global, regional and specialized forecast models that have been so critical to hurricane track forecasts.
The forecast successes keep rolling in. From Hurricanes Harvey, Irma and Maria in 2017 through Hurricanes Florence and Michael in 2018, improved forecasts helped manage coastlines, which translated into countless lives and property saved. In September 2018, with the help of this data, forecasters knew a week ahead of time where and when Hurricane Florence would hit. Early warnings were precise enough that emergency planners could order evacuations in time — with minimal road clogging. The evacuations that did not have to take place, where residents remained safe from the hurricane’s fury, were equally valuable.
The satellite benefits come even after the storms make landfall. Using satellite data, scientists and forecasters monitor flooding and even power outages. Satellite imagery helped track power outages in Puerto Rico after Hurricane Maria and in the Key West area after Hurricane Irma, which gave relief workers information about where the power grid was restored – and which regions still lacked electricity.
Flood maps showed the huge extent of flooding from Hurricane Harvey and were used for weeks after the storm to monitor changes and speed up recovery decisions and the deployment of aid and relief teams.
As the 2019 Atlantic hurricane season kicks off, the JPSS satellites, NOAA-20 and Suomi-NPP, are ready to track hurricanes and tropical cyclones as they form, intensify and travel across the ocean – our eyes in the sky for severe storms.
For more about JPSS, follow @JPSSProgram on Twitter and facebook.com/JPSS.Program, or @NOAASatellites on Twitter and facebook.com/NOAASatellites.
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“There are many ways to use a smartphone in the classroom, but it continues to be a touchy subject. Privacy, equity, bandwidth, lesson design, classroom management, theft, bullying, and scores of other legitimate concerns continue to cloud education’s thinking about how to meaningfully integrate technology in the learning process.”
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A gravitational lens is a distribution of matter (such as a cluster of galaxies) between a distant light source and an observer, that is capable of bending the light from the source as the light travels towards the observer. This effect is known as gravitational lensing, and the amount of bending is one of the predictions of Albert Einstein’s general theory of relativity.
This illustration shows how gravitational lensing works. The gravity of a large galaxy cluster is so strong, it bends, brightens and distorts the light of distant galaxies behind it. The scale has been greatly exaggerated; in reality, the distant galaxy is much further away and much smaller. Credit: NASA, ESA, L. Calcada
1° Strong lensing: where there are easily visible distortions such as the formation of Einstein rings, arcs, and multiple images.
Einstein ring. credit: NASA/ESA&Hubble
2° Weak lensing: where the distortions of background sources are much smaller and can only be detected by analyzing large numbers of sources in a statistical way to find coherent distortions of only a few percent. The lensing shows up statistically as a preferred stretching of the background objects perpendicular to the direction to the centre of the lens. By measuring the shapes and orientations of large numbers of distant galaxies, their orientations can be averaged to measure the shear of the lensing field in any region. This, in turn, can be used to reconstruct the mass distribution in the area: in particular, the background distribution of dark matter can be reconstructed. Since galaxies are intrinsically elliptical and the weak gravitational lensing signal is small, a very large number of galaxies must be used in these surveys.
The effects of foreground galaxy cluster mass on background galaxy shapes. The upper left panel shows (projected onto the plane of the sky) the shapes of cluster members (in yellow) and background galaxies (in white), ignoring the effects of weak lensing. The lower right panel shows this same scenario, but includes the effects of lensing. The middle panel shows a 3-d representation of the positions of cluster and source galaxies, relative to the observer. Note that the background galaxies appear stretched tangentially around the cluster.
3° Microlensing: where no distortion in shape can be seen but the amount of light received from a background object changes in time. The lensing object may be stars in the Milky Way in one typical case, with the background source being stars in a remote galaxy, or, in another case, an even more distant quasar. The effect is small, such that (in the case of strong lensing) even a galaxy with a mass more than 100 billion times that of the Sun will produce multiple images separated by only a few arcseconds. Galaxy clusters can produce separations of several arcminutes. In both cases the galaxies and sources are quite distant, many hundreds of megaparsecs away from our Galaxy.
Gravitational lenses act equally on all kinds of electromagnetic radiation, not just visible light. Weak lensing effects are being studied for the cosmic microwave background as well as galaxy surveys. Strong lenses have been observed in radio and x-ray regimes as well. If a strong lens produces multiple images, there will be a relative time delay between two paths: that is, in one image the lensed object will be observed before the other image.
As an exoplanet passes in front of a more distant star, its gravity causes the trajectory of the starlight to bend, and in some cases results in a brief brightening of the background star as seen by a telescope. The artistic concept illustrates this effect. This phenomenon of gravitational microlensing enables scientists to search for exoplanets that are too distant and dark to detect any other way.Credits: NASA Ames/JPL-Caltech/T. Pyle
Explanation in terms of space–time curvature
Simulated gravitational lensing by black hole by: Earther
In general relativity, light follows the curvature of spacetime, hence when light passes around a massive object, it is bent. This means that the light from an object on the other side will be bent towards an observer’s eye, just like an ordinary lens. In General Relativity the speed of light depends on the gravitational potential (aka the metric) and this bending can be viewed as a consequence of the light traveling along a gradient in light speed. Light rays are the boundary between the future, the spacelike, and the past regions. The gravitational attraction can be viewed as the motion of undisturbed objects in a background curved geometry or alternatively as the response of objects to a force in a flat geometry.
A galaxy perfectly aligned with a supernova (supernova PS1-10afx) acts as a cosmic magnifying glass, making it appear 100 billion times more dazzling than our Sun. Image credit: Anupreeta More/Kavli IPMU.
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Image Credit:NASA/JPL-Caltech
In this large celestial mosaic, our Spitzer Space Telescope captured a stellar family portrait! You can find infants, parents and grandparents of star-forming regions all in this generational photo. There’s a lot to see in this image, including multiple clusters of stars born from the same dense clumps of gas and dust – some older and more evolved than others. Dive deeper into its intricacies by visiting https://go.nasa.gov/2XpiWLf
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HE IS THE WORD OF GOD.