Sun-Earth Distance: Inaccurate?

[sirjon]

I am just wondering if it only took "eight minutes" (in some references, it is seven minutes), for the light coming from the sun to reach the earth? I think, if my hypothesis is valid, " It will take more than eight minutes for the light from the sun to reach the earth, if based on Einstein's theory that gravity affects light, (in case, gravity is indeed, a force)."

According to page 31 (lines 11-12), Stephen Hawking's book,'A Brief History of Time' (1988 edition) and I quote, "...so general relativity predicts light should be bent by gravitational field". While on that same book too, page 32 (lines 23-30), it is written and as I quote,"...another prediction of general relativity is that time should appear slower near a massive body like the earth...this prediction was tested in 1962...the clock at the bottom, which was nearer the earth was found to, run slower, in exact agreement with general relativity."

If my data is correct, the sun's mass is about 330,000 times more than the earth, (Therefore, its gravitational pull, in direct proportion is also, 330,000 times?). The gravity of the sun at its surface is 28 times greater (www.universetoday.com). Would you think with such tremendous pull of gravity, light could still travel at the speed of 186,000 miles per second? Is the 'eight-minute light-distance of the earth to the sun, the "net" result of computation in which other factors were taken into consideration? Or is it only an assumption (an approximate calculation)? If it is only an assumption, the sun could either be nearer or farther away from us by a light-distance of eight minutes. Should it will be wiser for us to think it over, to take note of Einstein's theory before we can conclude that the sun-earth distance is indeed, accurate?

[Jens]

I'm not absolutely sure, but I don't think the gravity of the sun is strong enough to make a very large difference. Certainly not in terms of how many minutes it takes.

[Shaula]

Plugging numbers randomly into an equation googled from Wiki gives the time dilation factor at the Sun's surface as 0.9999989.

Plus to get the distance to the Sun the general method was to use Venus. We can bounce radar signal from Venus to get its distance. Doing this when the Sun/Venus/Earth system was laid out so that the angle SVE was 90 degrees (when Venus is furthest from the Sun in the sky) you can use basic trig to get an accurate measure of the distance to the Sun. No photons from the Sun are involved at all in this method.

[Jeff Root]

sirjon,

The delay you are talking about is called "Shapiro delay". You can
look it up on Wikipedia to get a formula, from which you can calculate
its magnitude in any specific situation. From memory, I believe the
Shapiro delay for light travelling from the surface of the Sun to the
surface of the Earth is a few nanoseconds. A few billionths of a
second.

The mean center-to-center distance between the Sun and Earth is
149,597,870,000 m. The speed of light is 299,792,458 m/s. That
gives a light travel time of 499.00478 seconds.

Considering the variation in the distance between the Sun and Earth,
the diameters of the Sun and Earth, the curvature of the surfaces of
the Sun and the Earth, and the thickness of the Sun's photosphere,
a few nanoseconds isn't anything you are likely to notice. And we
might as well call the light travel time 500 seconds, a nice, round
number, which is 8 minutes 20 seconds, or 8 1/3 minutes.

-- Jeff, in Minneapolis

[sirjon]

sirjon,

The delay you are talking about is called "Shapiro delay"....might as well call the light travel time 500 seconds, a nice, round number, which is 8 minutes 20 seconds, or 8 1/3 minutes.
-- Jeff, in Minneapolis

Thanks for your replies Jeff, Shaula and Jens...

[RussT]

sirjon,

The delay you are talking about is called "Shapiro delay". You can
look it up on Wikipedia to get a formula, from which you can calculate
its magnitude in any specific situation. From memory, I believe the
Shapiro delay for light travelling from the surface of the Sun to the
surface of the Earth is a few nanoseconds. A few billionths of a
second.

The mean center-to-center distance between the Sun and Earth is
149,597,870,000 m. The speed of light is 299,792,458 m/s. That
gives a light travel time of 499.00478 seconds.

Considering the variation in the distance between the Sun and Earth,
the diameters of the Sun and Earth, the curvature of the surfaces of
the Sun and the Earth, and the thickness of the Sun's photosphere,
a few nanoseconds isn't anything you are likely to notice. And we
might as well call the light travel time 500 seconds, a nice, round
number, which is 8 minutes 20 seconds, or 8 1/3 minutes.

-- Jeff, in Minneapolis

Jeff...sirjon is definitely talking about 'gravitational time dilation' (if it exists), as Jens picked up on, and I know you understand the difference between that and the 'Shapiro Effect' (which was the 'first' reference he quoted from Hawking)...so you might want to explain that to sirjon real quick so he doesn't go away confused by the two.

He may also be getting confused because this link in the OP is to a "Neutron Star"...

The gravity of the sun at its surface is 28 times greater (www.universetoday.com).

[sirjon]

Thank you Russ for that follow-up. Yes, although I accepted that the eight minutes distance could be correct (there is a billionth second difference is negligible) , I'm still wondering if 'light', coming from the sun is not being delayed (time dilation) by the sun's gravity, provided that in certain experiment, the sun's gravitational field deflected light. How much more a light coming directly away from the sun? Does this means that light's speed is too high that it can overcome the sun's 'escape velocity'?

[Jens]

Does this means that light's speed is too high that it can overcome the sun's 'escape velocity'?

Yes. Light's speed is so high that it has absolutely no trouble whatsoever escaping the sun. For light, the difference between escaping from the earth and from the sun is a fairly trivial one. It's only when you get to much, much higher gravity that light starts having trouble. The way I interpret it is kind of like this: could a 747 take off with a fly on board? Yes. How about with 28 flies on board?

[sirjon]

It's only when you get to much, much higher gravity that light starts having trouble.

A black hole? Any way, thanks a lot for the reply

[RussT]

Thank you Russ for that follow-up. Yes, although I accepted that the eight minutes distance could be correct (there is a billionth second difference is negligible) , I'm still wondering if 'light', coming from the sun is not being delayed (time dilation) by the sun's gravity, provided that in certain experiment, the sun's gravitational field deflected light. How much more a light coming directly away from the sun? Does this means that light's speed is too high that it can overcome the sun's 'escape velocity'?

Yes, I should have stipulated that all of this that Jeff posted was correct...sorry Jeff,,,I figured you would know I meant that!
(I guess I should add the stipulation...since we are talking about "Our Perspective" Or "Earth Rest Frame" observer wth no SR 'rest frame' or observer motion involved )

The mean center-to-center distance between the Sun and Earth is
149,597,870,000 m. The speed of light is 299,792,458 m/s. That
gives a light travel time of 499.00478 seconds.

Considering the variation in the distance between the Sun and Earth,
the diameters of the Sun and Earth, the curvature of the surfaces of
the Sun and the Earth, and the thickness of the Sun's photosphere,
a few nanoseconds isn't anything you are likely to notice. And we
might as well call the light travel time 500 seconds, a nice, round
number, which is 8 minutes 20 seconds, or 8 1/3 minutes.

I'm still wondering if 'light', coming from the sun is not being delayed (time dilation) by the sun's gravity, provided that in certain experiment, the sun's gravitational field deflected light. How much more a light coming directly away from the sun? Does this means that light's speed is too high that it can overcome the sun's 'escape velocity'?

Again, you are mixing two different effects...The Shapiro Effect and Gravitational Time Dilation...but I am going to leave that to others to explain.

[sirjon]

I did searched it in wikipedia... "The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar system tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than it would if the mass of the object were not present." Are the 'The Shapiro Effect and Gravitational Time Dilation' you mentioned are two different things or the same as wikipedia defined 'gravitational time delay effect' as another term for Shapiro time delay effect ?".

[Andrew D]

Correct me if I'm wrong here, but I was under the impression that always travelled at light speed (what's in a name?), but the wavelength changed. It sounds to me like the OP is suggesting that the velocity of the photons is changed as they exit the sun's gravity well.

[cjameshuff]

Correct me if I'm wrong here, but I was under the impression that always travelled at light speed (what's in a name?), but the wavelength changed. It sounds to me like the OP is suggesting that the velocity of the photons is changed as they exit the sun's gravity well.

It is always locally c, no exceptions. There are deviations due to the geometry of space-time around massive objects though, light going through a gravity well travels a longer path and appears delayed to an outside observer.

[WayneFrancis]

Seems Jen, cjameshuff, RussT, and JeffT have it all under control. I can see where sirjon's question is coming from but as RussT points out it is more from mixing 2 different effects. Though I'm questioning my sanity lately, I accused RussT of making claims about a year ago that he didn't and now I could have sworn that sirjon was a respected member of Order of Kilopi...maybe I've slipped into a parallel universe :P

[sirjon]

Seems Jen, cjameshuff, RussT, and JeffT have it all under control. I can see where sirjon's question is coming from but as RussT points out it is more from mixing 2 different effects. Though I'm questioning my sanity lately, I accused RussT of making claims about a year ago that he didn't and now I could have sworn that sirjon was a respected member of Order of Kilopi...maybe I've slipped into a parallel universe :P

"Order of Kilopi?"...I don't know what you mean but if it means good...thanks a lot. Well, let me put it this way. The sun is a very big body, 330,000 times the mass of the Earth. All planets circles around it...giving the impression that its pull of gravity is indeed, 'strong'. Now, if a light pass through near it, it has the ability to deflect that passing light. I learn from elementary physics, the nearer you are to the very center of a body (like here on earth), the greater the gravitational pull (same confusing question as if a person is inside the very center of the earth. what is the gravitational pull of the earth?)... I do not have an idea of the experiments or observations done before but I am just wondering how far the light's rays from the sun in those experiments? Is it curving more, the nearer it comes to the sun? The 1962 experiment, 'detected' a slight delay of time here on earth due to the earth's pull of gravity. I am just wondering, how much more 'on' the sun? If we consider only 'the gravitational pull at its surface (28times greater than the earth's gravity), I believe it would be more 'detectable'. Yes, part of Roobydo's question (similar to it), is the light coming out from the sun, is it still traveling at the speed of 186,000 mi/sec?Or let me rephrase my question...if light is 'constant', light could escape from the sun's gravity, delayed only in few 'nanoseconds'?

[Jeff Root]

sirjohn,

You will become a member of the Order of Kilopi when you have
posted your 3,142nd post.

The delay will certainly be more for light leaving the Sun than for
light leaving the Earth. My recollection appears to have been wrong
that it amounts to only a few nanoseconds. Make that quite a few
microseconds. Still less than a millisecond. I haven't calculated it,
though.

After Russ's post, I am unsure whether there are really two separate
effects or whether the Shapiro delay is simply a manifestation of
gravitational time dilation. My inclination is toward the latter. I do
not see two separate effects at work here, but I may be forgetting
something.

Light always travels at c relative to any nearby observer. Light
climbing out of the Sun's gravity well is travelling at c relative to
an imaginary observer at rest relative to the Sun's surface. That is
slower than c relative to an observer on Earth, but an observer
on Earth cannot measure the speed of the light as it leaves the Sun.
All an observer on Earth might be able to tell is that the light has
been redshifted, if he knew the original wavelength or frequency.

If the observer on Earth arranges things so that he can measure the
longer travel time required because of the Sun's gravity, he will also
note that the distance is longer, too, so the speed is unchanged.

Because Earth gets denser toward the center, if you were go down
several hundred miles, the gravitational field strength would continue
to increase. But eventually you get far enough down that the pull
of matter above you counteracts the pull of matter below you, and
the gravitational field strength begins to decrease. When you reach
the center, it becomes zero. Ideally, if you could hollow out an empty
chamber at Earth's center, you could float in it, weightless. Several
things prevent that from being possible, of course. One of them is
the enormous pressure of the entire mass of Earth pressing down
on the center. Even if there is practically zero gravitational field
strength right at the center, there is a little bit of gravity above that,
and more above that... so a column of rock and metal 3963 miles
high makes for an awful lot of weight -- way more than enough to
collapse any chamber.

-- Jeff, in Minneapolis

[CaptainToonces]

While the Sun's gravity may seem strong relative to other bodies in our solar system, the Sun's gravity is not nearly strong enough to have much effect on something travelling as fast as the speed of light.

Now, if a light pass through near it, it has the ability to deflect that passing light.

Yes, it can deflect the light, but it does not change its speed. Light always travels at the same speed. This is the basis of relativity. If one accepts that the speed of light is always constant, regardless even of the speed the observer is travelling, relativity follows.

Light escaping the sun is not slowed by the sun's gravity because light cannot be slowed. It is red-shifted by the Sun's gravity though. The amount of redshift is actually very small because again the Sun's gravity is puny compared to the velocity of light.

is it still traveling at the speed of 186,000 mi/sec?

Yep! And as such, it does not experience the passage of time. Its trajectory in spacetime lies completely in the space directions and none in the time direction.

[sirjon]

Thanks a lot, I am now 'enlighten'. Good day everybody.

[Andrew D]

It is always locally c, no exceptions. There are deviations due to the geometry of space-time around massive objects though, light going through a gravity well travels a longer path and appears delayed to an outside observer.

I don't really understand what you mean, because using terms like "deviations" and "delayed" makes it seem like you are contradicting yourself. I think what you mean to say is that a message sent at light speed in one frame will arrive at light speed in another, but the content of the message will be stretched or contracted.

[Jeff Root]

Every observer sees light pass by them at c. Where space is
distorted by mass-energy, the light takes a longer path than
it otherwise would, so it takes longer to get from point A to
point B. But the speed is unchanged.

-- Jeff, in Minneapolis

[jfribrg]

The escape velocity from the surface of the sun is about 617 kilometers per second. Light is traveling about 300000 kilometers per second which is 486 times faster.

One thing to remember about the gravity of a solid sphere such as the sun and Earth is that as you get closer to the surface, the gravity increases, but once you start digging in, the gravity doesnt increase. This is because when you are at the surface, all of the mass is below you and is sort of pulling in the same direction. As you go deeper into the object, more and more mass is above you and it offsets some of the gravitational pull. The math is kind of complicated, but if you assume that the object is a sphere and the cross section of the mass is symmetrical, then the gravitational pull you feel is entirely from the mass that is closer to the center than you are. If you are at the center, there is no gravitational pull at all from the object. The pressure may be phenomenal, but that is from the electromagnetic force, not the gravitational force.

In short, the gravitational pull is greatest on the surface of the sun. Going farther into the Sun does not increase the gravity, so light never has to deal with an escape velocity greater than 617 kilometers per second. There is a tiny gravity effect that is explained by General Relativity, but nothing even close to the 16 second seasonal variation due to the fact that the Earth is 3 million miles closer to the sun in January than it is in July.

[Hornblower]

The escape velocity from the surface of the sun is about 617 kilometers per second. Light is traveling about 300000 kilometers per second which is 486 times faster.

One thing to remember about the gravity of a solid sphere such as the sun and Earth is that as you get closer to the surface, the gravity increases, but once you start digging in, the gravity doesnt increase. This is because when you are at the surface, all of the mass is below you and is sort of pulling in the same direction. As you go deeper into the object, more and more mass is above you and it offsets some of the gravitational pull. The math is kind of complicated, but if you assume that the object is a sphere and the cross section of the mass is symmetrical, then the gravitational pull you feel is entirely from the mass that is closer to the center than you are. If you are at the center, there is no gravitational pull at all from the object. The pressure may be phenomenal, but that is from the electromagnetic force, not the gravitational force.
In short, the gravitational pull is greatest on the surface of the sun. Going farther into the Sun does not increase the gravity, so light never has to deal with an escape velocity greater than 617 kilometers per second. There is a tiny gravity effect that is explained by General Relativity, but nothing even close to the 16 second seasonal variation due to the fact that the Earth is 3 million miles closer to the sun in January than it is in July.

My bold for reference. You are mistaken here. The enormous pressure at the center of a star or a planet is indeed caused by the gravitational weight of the overlying material. The net lack of gravitational attraction of a central object toward the surrounding mass has distracted you from recognizing this fact. Everything not right at the center is tending to fall toward the center, and the resisting forces at the atomic level constitute the pressure that keeps the whole body from collapsing into a black hole.

The gravitational attraction would be greatest at the surface of a sphere of uniform density. This is not the case with the Sun, where the core density is over 100 times the mean value, and the density at the photosphere is that of a rarefied gas, meaning a small fraction of the mean value. The gravitational force would increase for a large fraction of the way to the core before starting to drop.

Unfortunately I do not have information readily available about the density distribution. I have seen it in Sky and Telescope, but it is buried somewhere in 40 years of back issues. When I try to find similar information online, I usually find a lot of garbage. Maybe someone in this forum has the magic touch for googling this stuff and can help.

[Shaula]

Hornblower - just to add: The pressure at the centre is at least partly resisted by the radiation pressure of the outgoing photons (thermal pressure). Google hydrostatic equilibrium of a star.

[Jeff Root]

Let me defend jfribrg: The ultimate cause of the pressure on the center
of the Earth is certainly the gravitational weight of the matter, but that
weight is converted into pressure by electromagnetic forces between
the atoms. The weight of an atom at Earth's surface is conducted to
the atoms at Earth's center via electromagnetic forces in all the atoms
between the surface and the center. If even one of those atoms refused
to pass along the force from the atoms above it via electromagnetism,
the chain would be broken and there would be no pressure on the atom
immediately below the rebellious atom, despite the gravitational weight
above it.

-- Jeff, in Minneapolis

[sirjon]

I don't really understand what you mean, because using terms like "deviations" and "delayed" makes it seem like you are contradicting yourself. I think what you mean to say is that a message sent at light speed in one frame will arrive at light speed in another, but the content of the message will be stretched or contracted.

I believe they are two different words...Isn't "deviates" light the same as to 'deflect' light? I know too the word 'delayed' means.. to be late as to the expected time ( am I right?). I do understand your explanations, indeed light could escape the sun's gravitational pull if your computation is correct (I believe it is correct). But what makes me feel strange is how come a light should be deflected by mere passing near the sun if light is not 'so affected' (sun's gravity is negligible), by directly moving away from its source? Is it due to the 'angle of direction' of light that makes the difference? (Patience, for being 'an order of kilopi')...in Pilipino, we call it "MAKULIT", too many annoying questions...(Hope I'm not that too 'makulit'...Good day to all!)

[Jeff Root]

There is no significant difference in how light light is delayed
or deflected whether it originates on the Sun or goes past the
Sun. In both cases, the amount of delay and deflection is
very, very small, requiring extremely precise measurements
to detect. Also, as far as I know there is no way to detect the
delay or the deflection of light from the Sun, since there is
nothing to compare a measurement to. With light going past
the Sun, the delay or the angle of deflection can be measured
by comparing the time or direction of a signal with the Sun
there and without the Sun there. No such comparison can be
done for light coming from the Sun's surface.

-- Jeff, in Minneapolis

[sirjon]

There is no significant difference in how light light is delayed
or deflected whether it originates on the Sun or goes past the
Sun. In both cases, the amount of delay and deflection is
very, very small, requiring extremely precise measurements
to detect. Also, as far as I know there is no way to detect the
delay or the deflection of light from the Sun, since there is
nothing to compare a measurement to. With light going past
the Sun, the delay or the angle of deflection can be measured
by comparing the time or direction of a signal with the Sun
there and without the Sun there. No such comparison can be
done for light coming from the Sun's surface.

-- Jeff, in Minneapolis

Now, I understand. Thank you to all who replied...God bless!