In either late November or early December I saw a prompt in one of the LinkedIn groups I belong to that I couldn’t resist. Suppose you are in a conversation with someone and you tell them that you’re an amateur astronomer and they ask you to tell them something interesting, what would you tell them?
Most of the group members facts revolved around distance scales, like If the distance between Sol and Earth was represented by a football field, how far would it be to the next star, Alpha Proxima? Or if you shrank the sun down to the size of a basketball, how big would Earth be?
My ‘interesting’ fact? “If the sun suddenly disappeared, we would wouldn’t know for about 9 minutes. During those 9 minutes, we would still see the sun shining, and the Earth would continue orbiting it as though it were still present.
Only after the 9 minutes are up, would the sky go dark and the Earth with fly off in a straight line, deep into space.”
Mostly, this was unobjected. However, I checked my email before bed on new years day, 2015. That may have been the worst idea I had all day. I saw that I had a response to my post:
“As I understand it, the force of gravity is instantaneous and doesn’t “travel” at the speed of light or any other finite speed. If this weren’t the case, orbital mechanics would be much more complex and stable orbits may not even be possible. This article is very interesting http://www.metaresearch.org/cosmology/speed_of_gravity.asp. So, if you think of gravity as a string holding the earth in orbit around the sun, if you cut the string, the earth will, at exactly the same time, stop traveling along the curve of its orbit and fly off in a straight line. Would we notice the effects immediately? Given the huge mass and inertia involved, possibly not. But I wouldn’t want to be around to find out 😉“
Great, how am I going to sleep now?
Almost immediately, I began thinking of ways that I can experimentally prove that gravity is not an instant force felt everywhere in the universe faster than the speed of light. My first thought was that I can use the tides.
This thought experiment kept me awake for a few hours while I pretended to sleep. If light from the Sun takes 8.3 minutes to travel to the Earth, and gravity is also experienced at the speed of light, then high tide should happen at the moment of solar noon, or when the Sun is at it’s highest point in the sky. If the speed of gravity was instant, then the timing of the high tides would lead solar noon by about 8 minutes.
Since I have no way to accurately measure the tides myself, I will have to prove this by using data collected by other sources. I can find high tide data online quite easily. As I tossed and turned I made a check list of things to that I would have to do:
1) The data will need to be corrected to account for lunar influences on our tides.
2) I would need to find measurements from multiple stations around the country, and compare them to each other to find patterns. and help normalize the data.
3) I’d have to correct for wind and other factors attributed to weather.
Then it hit me – Because the tides are influenced by weather, and water currents, and air pressure and probably a hundred other factors I’m not even aware of, high tide doesn’t actually have to occur at solar noon.
I verified this hunch the next morning when I checked NOAA data for three stations around the country.
Port Isabell, TX will have a high tide at 4:59 pm local time on January 2, 2015. (10:59 am GMT)
Key West, FL will have a high tide at 7:51 pm local time on January 2, 2015. (2:51 pm GMT)
Wrightsville Beach, NC will have a high tide at 5:14 pm local time on January 2, 2015. (12:14 pm GMT)
What is interesting here, is that Port Isabell, TX and Wrightsville Beach, NC high tides happen almost an hour and 15 minutes apart, but Key West, FL (which lies between the two stations I picked) comes two and a half hours after the Wrightsville Beach, NC high tide. Conventional wisdom says that the tides should follow the sun, and as it moves from East to West, then the North Carolina station should encounter the high tide first, followed by Key West, and finally Texas. In reality, the high tide starts in Texas, than an hour and 15 minutes later it’s in North Carolina. Two hours and 37 minutes later, it does an about face, and heads back towards Key West…
Using the tides is not going to be a suitable way to prove the speed of gravity. The margin of error and other factors are far too great for me to account for.
I resigned myself to reading the article posted above, and found that it was compelling. I also found that the article was written in 1998. A lot has changed in the last 16 years, and I was curious to see what follow on studies had been done to either prove gravity was instant, or that the speed of gravity was equal to the speed of light.
As I read further, I saw that there are a few assumptions that I believe to be flawed. The biggest one being that Earth accellerates along its orbit to a position 20 arc seconds ahead of the apparent position of the Sun. This is equal to the ‘true’ or ‘real-time’ position of the sun because of the 8 minute light delay time necessary for the real position of the Sun to be reflected in our skies. In the authors own words: “How then does the direction of Earth’s acceleration compare with the direction of the visible Sun? By direct calculation from geometric ephemerides fitted to such observations (the author is referencing observations made using pulsars to triangulate the vector of Earths motion), such as those published by the U.S. Naval Observatory or the Development Ephemerides of the Jet Propulsion Laboratory, the Earth accelerates toward a point 20 arc seconds in front of the visible Sun, where the Sun will appear to be in 8.3 minutes. In other words, the acceleration now is toward the true, instantaneous direction of the Sun now, and is not parallel to the direction of the arriving solar photons now. This is additional evidence that forces from electromagnetic radiation pressure and from gravity do not have the same propagation speed.”
I concede that the Earth does in fact move exactly as is stated above. However, it is not evidence that the speed of gravity is not the same as the speed of light. In fact, it has nothing to do with the speed of gravity at all!
Let me break this down into terms as simply as possible, but no simpler. Because the Sun is made of matter, it has mass. Mass warps space. This warping of space is what we commonly refer to as gravity. Said another way: Matter tells space how to curve. The curvature of space propagates away from the center of mass at the speed of light. the shape of the curvature remains the same unless the mass changes. For all intents and purposes, the solar system’s mass is unchanging. The Sun contains over 99.8% of the matter (and thus mass) in the solar system. Space-time is then curved, and unchanging in the direction of the sun. The Earth follows this curvature which is always centered around the real time/instantaneous position of the Sun. Because the sun doesn’t move relative to the solar system in any dramatic way (it does wobble, but that motion is very very slow), then the curvature of space around the Sun is also moving from our perspective, but in the same slow, and non-dramatic way. Notice that I explained our orbit as Earth following a curve around the Sun, and not the Sun pulling on Earth as though it were a string tied to us. This string analogy is a massive misunderstanding by most people, and it does not explain how gravity works at all. The Sun is not pulling on Earth. The Sun is pulling on space, and Earth moves through this distorted space. Said another way, Space tells matter how to move.
In the above article, and in many other texts, we are told that when we calculate the motions of the planets, we are to take gravity as an instant force, not a propagating force. There is then the assumption that gravity is moving faster than light speed. As I pointed out above, we assume that gravity is instant, because the Suns curvature of space already exists around every body in the solar system. As Earth moves along the curved gravity well of the Sun, any position along our orbit that we have yet to cross is already curved. The effects of gravity are already there, waiting for us to catch up, and for space to gently nudge us along.
While googling around today to find newer articles on the subject, I found one authored back in 2002, which actually provides the evidence I was looking for that the speed of gravity to be equal to the speed of light.
This experiment involved using Jupiter’s gravity to study the lensing of a bright radio source in the sky with enough accuracy to determine if it’s gravitationally lensed position changed ahead of Jupiter’s apparent position in the sky (meaning that the lensed light was seen because of the real time gravitational effects of Jupiter) or did the object lens with the apparent position of Jupiter.
The experiment pinned down the lensing of the radio bright quasar to three times the precision of anything done up to that point. The position was so accurately determined that they would be able to detect the minimum amount of change necessary to calculate how fast gravity was acting on the light coming from the quasar. What they found was that the speed of gravity was 1.06 times faster than the speed of light, with a margin of error +/- .21%.
What these Kopeikin and Fomalont proposed doing was to look for a way to measure how the light of something that originated from outside our solar system moved when it encountered the two largest gravity fields in our solar system: the Sun and Jupiter. Based on the equations that they derived, the theorized that as Jupiter moved near this bright object, it would bend the light on it’s way to Earth. This is a phenomenon called gravitational lensing. It had originally been predicted by Albert Einstein when he published his theory of General Relativity. We’ve since found this prediction to be true and use it all of the time when looking for the oldest, faintest galaxies in the universe. Kopeikin and Fomalont knew that Jupiter would have enough mass to also create gravitational lensing if an object were close enough to it.
If the speed of gravity were instant, then the curvature of space, as seen from Earth, would actually be in front of the apparent position of Jupiter. The light moving through our solar system would encounter this ‘offset’ curvature, and it would bend in a predictable way. If gravity were moving at the speed of light, then the lensing effect would have a completely different outcome. What is most important about this experiment, is that the two outcomes are different enough to be detectable by Earth based radio telescopes. They detected that the position of the quasar shifted the way that was predicted by the equations that placed the speed of gravity equal to the speed of light.
But wait, there’s more! Since 2005, scientists have been watching a binary pulsar system. As the orbits of these two pulsars star decay, astronomers are able to calculate the amount of energy and angular momentum carried away by gravity waves. They have calculated that the orbits decay by 7 mm each day, and that number is what General Relativity predicts it should be. And because pulsars make awesome clocks, and this unique system offers the only opportunity to use two of them for testing Einsteins predictions in an extremely high gravity environment, we can study the warping of space with the highest precision yet. These two pulsars have different pulse timings, which allows observations of each pulsar to be made at different points along the orbit. In fact, when one pulsars orbit takes it behind the foreground pulsar, it’s signal is delayed because of the warping of space around the closer pulsar!
So there you have it, folks. The effects of gravity are felt ‘instantly’ by any object that is already within a gravity field. However, changes to that field are propagated away from the center of mass at the speed of light towards outside objects. If the Sun suddenly disappeared, the curvature of space that it creates would ‘flatten out’. This flattening would start at the center of mass (where the Sun was) and move towards the orbit of Earth at the speed of light. For 8.3 minutes, our region of space, and all of the space we will move through during the intervening time, will remain curved. Once the space around us flattens, we will continue to move at about 30 km/s in a straight line. What’s interesting about this, is that we would continue to observe the planets beyond Earth’s orbit moving along curved space for quite some time. The average light distance to Jupiter is 33 minutes. We would witness Jupiter continue along its orbit as though space were still curved for an hour and six minutes. That is because it takes 33 minutes for the curvature of space to update for Jupiter after it has been updated for Earth, and another 33 minutes for that update to be seen by us.