# Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

**Paper discussion**: Solar system expansion and strong equivalence principle as seen by the NASA MESSENGER mission. Antonio Genova, Erwan Mazarico, Sander Goossens, Frank G. Lemoine, Gregory A. Neumann, David E. Smith & Maria T. Zuber. Nature Communications volume 9, Article number: 289.

Students of physics learn some interesting facts about the sun, spread over different lessons and different classes. When learning about orbital mechanics, students are taught that the gravitational field of the sun exerts a long-range force proportional to its mass and causes planets to orbit in an elliptical path around it. When encountering “modern physics” for the first time, students are taught the sun in its interior is “converting mass to energy,” maintaining its temperature and pressure by fusion of hydrogen into helium and producing energy that is eventually radiated from its surface and eventually felt by us on the Earth. An astute student may ask if the sun is decreasing in mass to produce and radiate energy, is its gravitational influence on the planets getting weaker? For many years this has been handwaved away as a negligibly small effect, but now a probe orbiting the planet Mercury has made the first measurements of the sun’s loss of mass.

Before we discuss this recent finding, let’s estimate what kind of effect this would have. The sun’s luminosity is on the order of ##10^{26}## Watts. If we apply Einstein’s relation and divide this by ##c^2## this luminosity is consistent with a rate of mass loss of a million tons per second, which through energy conservation can be thought of as the rate that “mass is converted to energy” by fusion. For context, this is a reduction of about twice the mass of the largest ship ever built every second. The fusion-radiation process is not the only way that the sun loses mass; there is also the protonic outflux that forms the solar wind, as well as more coherent losses such as coronal mass ejections. The sun, however, is very big, and this is a few parts per quadrillion per year. From Kepler’s laws we know that with a given axis, the orbital period is proportional to the reciprocal square-root off the central mass, and even after billions of years we would not expect a noticeable difference in the orbit. Measuring something at the parts per trillion scale is extremely difficult, so it would have been a safe bet to assume that the gravitational effect of the sun’s shrinkage would never be observed.

Mercury is a well-known participant in the sun’s gravitational antics. Its over-eager perihelion precession of an extra 43 arc-seconds per century was a mystery at the end of the nineteenth century and was famously figured out by Einstein with the general theory of relativity. From 2011 to 2015, Mercury had a visitor from Earth, an orbiting probe called “Mercury Surface, Space Environment, Geochemistry, and Ranging” which totally randomly and coincidentally spells out **MESSENGER**. Its goal was to make measurements of Mercury’s surface topography and gravitational field to determine its internal structure. During that time, it gave us some stunning images of our smaller sibling.

A number of papers were published by the MESSENGER collaboration about, as I mentioned, Mercury’s surface and interior, e.g. here and here and here. The probe was deliberately crashed into the surface of the planet on April 30, 2015, but unfortunately did so on the side that was not facing Earth, so we couldn’t watch. Since then, the various members of the collaboration have been busy analyzing all the data and learning the most they can. In their recent paper in Nature Communications (Nature’s journal for freely-readable papers), they used seven years of data to measure various parameters related to general relativity and its potential violations. This was done by carefully tracking the position of the probe with respect to Mercury, to see how well its orbit corresponded to what we know about gravity.

One of these violations is the Nordtvedt effect, which would exist if gravity gravitated differently from mass (meaning, if the contribution to the mass of a body due to its gravitational binding energy coupled differently to an external gravitational field). This would violate the equivalence principle, and objects would orbit differently depending on their internal composition. If this were real but small enough to have eluded previous measurements, it would have lead to a discrepancy in the relative position of Earth and Mercury by about three meters. MESSENGER data showed that the strength of this effect is consistent with zero, constraining it to less than one part in ten-thousand. While we already knew it was consistent with zero by tracking the distance to the moon (using the reflectors left there by Apollo astronauts), now we know it’s consistent with to zero with like three times the precision.

The most interesting result in the paper, in my opinion, was the measured decrease in the sun’s gravitational parameter. As readers may be aware, the equations of orbital mechanics all have the product of the mass and Newton’s gravitational constant, together with GM. Each parameter cannot be separately analyzed by examining orbits. This is why Cavendish measured the deflection of a pendulum between giant lead spheres to separately measure G and Earth’s mass in 1798. By very precisely tracking the distance to MESSENGER from Earth, the collaboration was able to measure the change in the Earth-Mercury distance over the several years of observation. This amounted to about two meters, and this was the first nonzero measurement of the changing gravitational parameter of the sun (keeping in mind the distance between them is at least 77,000,000,000 meters). They found that the sun’s gravity was getting proportionally weaker by ##6.13 \pm 1.47 \times 10^{-14}## per year (61 parts per quadrillion), and thus the solar system is slowly expanding as well.

There are two potential causes for this decreasing gravity: the M of GM is changing and the mass of the sun is decreasing as it fuses, radiates, and spews, or the G of GM is changing and the whole universe’s gravity is getting weaker. To separate these two, we can consider how the measured value compares to our expectations. Solar physicists can make a more precise estimate than my “luminosity over c-squared” calculation, and the expected mass-loss rate due to fusion is about 68 parts per quadrillion per year, and the mass loss due to the solar wind was estimated at 10 parts per quadrillion per year (this was harder to pin down due to the fact that the observation window didn’t span a full sunspot cycle). Together, the predicted mass-loss rate is consistent with the measured decreasing gravitational parameter given its uncertainty.

The curious skeptic might ask how we know that the laws of physics are unchanging over time. To answer that, we can examine what the effect would be *if* they varied over time, and go look for those effects. One possibility is that the strength of gravity changes over time, and looking for a time-varying Newton’s constant would verify or constrain that. Given our confidence in the physics of the sun and the measurements from MESSENGER, they were able to use the data to constrain this to below 40 parts per quadrillion per year and consistent with zero. There have been previous attempts to look for a changing gravitational constant, also consistent with zero, but less constraining. Before this study, the best estimate was based on long-term observation of binary neutron stars, constraining it to about 600 parts per quadrillion per year. So, we still have no evidence that gravity is changing (my intuition says it isn’t), and now we know that if it is, it decreases proportionally like 400 times slower than the universe is expanding.

So, now we have empirical evidence that the sun is decreasing in mass (even though it is very slowly increasing in volume as well), and that it leads to a change in the orbital axis of Mercury consistent with a few meters over a few years.

Ph.D. McGill University, 2015

*Assistant Professor, California State University, Long Beach*

My research is at the interface of biological physics and soft condensed matter. I am interested in using tools provided from biology to answer questions about the physics of soft materials. In the past I have investigated how DNA partitions itself into small spaces and how knots in DNA molecules move and untie. Moving forward, I will be investigating the physics of non-covalent chemical bonds using “DNA chainmail” and exploring non-equilibrium thermodynamics and fluid mechanics using protein gels.

Just as a sanity check, I took the figures given in your reference for the total energy dissipated by tidal forces:

"P = 110 ± 25 GW. For comparison this is 22 times smaller than the M% dissipation rate in the oceans (Cartwright & Ray 1991), but an order of magnitude greater than the rate in the atmosphere (Platzman 1991)."

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20000072440.pdf

I multiplied 110 GW by 23, to combine losses from solid and liquid friction, which gives an estimate of the total amount of energy dissipated by all tidal forces on Earth:

http://www.wolframalpha.com/input/?i=110+*+10^9+*23+W

This gives 2.53 TW, about the same as total electrical power consumption on Earth.

I then used 1/2 * (G * Mass_earth * Mass_sun / Orbital radius of Earth):

http://www.wolframalpha.com/input/?…sun)*(mass+of+Earth))/(2*(astronomical+unit))

This gives 2.649 x 10^33 Joules for the orbital kinetic energy of Earth. Wolfram helpfully adds that this figure is 98% of

theirnumber for the "Earth's orbital kinetic energy around the Sun", so it looks right.Divide the second number by the first number:

http://www.wolframalpha.com/input/?…/(2*(astronomical+unit))+/+(110+*+10^9+*23+W)

The result is that the Earth will stop orbiting the Sun due to its loss of orbital kinetic energy from tidal friction in a mere 33 trillion years.

If we rather cavalierly assume constant tidal friction over time, the age of the Earth is 4.5 billion years, so we have lost about

http://www.wolframalpha.com/input/?i=(age+of+the+earth)+/+33+trillion+years

or 1.38 * 10 ^ -4 = 0.000138 of the initial kinetic energy.

Call it about one percent of one percent.

That's also tossing all lunar tidal friction into the equation, which is not accurate for our solar distance calculation, as that mostly slows down the moon, rather than the Earth.

So, yeah … it's not a big factor.

The tidal effects are negligible.

The size of the tides is proportional to mass/distance[sup]3[/sup]. For tides on Earth the Sun has a weaker effect than the Moon already because the larger distance wins over the larger mass. For changes in Earth's orbit, you are now looking into feedback of these tides on the Earth/Sun gravitational interaction – so you get another factor 1/distance[sup]3[/sup], another factor of a few million relative to the Earth's influence on the Moon. In addition you want to change the orbit of Earth, not the orbit of the Moon. Another factor 80 from the larger mass. Completely negligible.

Mercury is closer to the Sun but it is still negligible for it.

This paper has a formula to estimate the effect: ##langle dot a rangle = -frac{4}{3} n a^{-4} hat s left( (1+23e^2) + 7 e^2 D)right)## where ##D=frac{hat p}{2 hat s}## and ##hat s = frac{9 k_0 m_1}{4 Q_0 m_0}R_0^5## and ##hat p = frac{9 k_1 m_0}{2 Q_1 m_1}R_1^5##. Here index 0 is the star, index 1 is the planet, m and R are mass and radius, k is the Love number and Q is the dissipation function. e is the orbital eccentricity. n is not described but as far as I understand it is the orbital frequency. It has to have units of 1/time, in the worst case I get it wrong by a factor 2 pi.

For Earth Wikipedia has a value of the Love number – about 0.3. Constraints on energy dissipation in the earth's body tide from satellite tracking and altimetry (PDF) tells us Q=280 for the Earth. I didn't find values for the Sun. Q in the Solar System (PDF) gives ##geq 10^4## for the gas giants, I'll use that value. Note that larger values lead to smaller tides. Let's use k=1, this is just an order of magnitude estimate anyway.

For Earth e=0.017 and n=1/year and a=1 AU.

Let's plug that in:

##hat p## = 1.7*10[sup]37[/sup] m[sup]5[/sup] for Earth

##hat s## = 1.1*10[sup]35[/sup] m[sup]5[/sup] for Sun

D = 77

Finally ##langle dot a rangle = -frac{4}{3 year} (1 AU)^{-4} cdot 1.1 cdot 10^{35} m^5 cdot left( (1+23cdot(0.017)^2) + 7 (0.017)^2 cdot 77)right)##

##langle dot a rangle = -3.4cdot 10^{-10} frac{m}{year}##

It is probably optimistic to assume that Mercury has the same k and Q as Earth. In that case ##hat p = 2.5cdot 10^{36} m^5## and ##hat s = 6cdot 10^{33} m^5## and ##langle dot a rangle = -0.18 frac{mu m}{year}##. Way too small to measure.

We've had probes in orbit for extended periods of time around Mercury, Venus, Mars, Jupiter, and Saturn.

Has anyone tried to use the data accumulated by these probes to measure the change in distance between Earth and each of these planets over long period of time?

I've only seen data for the change in the Earth-Mercury distance. Why can't we do the same for the other four planets?

After further thought, if the Earth is moving away from the Sun over over long periods of time, that might also help to solve the "faint young Sun" paradox, as it implies that Earth was closer to the Sun three or four billion years ago and thus received more sunshine. Same idea would apply to a wet early Mars.

https://en.wikipedia.org/wiki/Faint_young_Sun_paradox

The article states that the quantity that was measured was the distance from the Earth to Mercury:

"By very precisely tracking the distance to MESSENGER from Earth, the collaboration was able to measure the change in the Earth-Mercury distance over the several years of observation. This amounted to about two meters, and this was the first nonzero measurement of the changing gravitational parameter of the sun (keeping in mind the distance between them is at least 77,000,000,000 meters). They found that the sun’s gravity was getting proportionally weaker by 6.13±1.47×10−146.13±1.47×10−14 per year (61 parts per quadrillion), and thus the solar system is slowly expanding as well."

However, we know that tidal effects from friction will gradually slow down the orbit of a small body orbiting around a larger body, even if the small body is a solid mass such as the Earth's moon.

For example, quoting from https://phys.org/news/2015-09-moon.html :

"Gravitational coupling between the moon and the bulge nearest the moon acts as a torque on Earth's rotation, draining angular momentum and rotational kinetic energy from Earth's spin. In turn, angular momentum is added to the moon's orbit, accelerating it, which lifts the moon into a higher orbit with a longer period.

As a result of this, the distance between Earth and moon is increasing, and Earth's spin is slowing down. Measurements from lunar ranging experiments with laser reflectors (which were left behind during the Apollo missions) have found that the moon's distance to Earth increases by 38 mm (1.5 in) per year."

The equations for orbital mechanics always assume that there is conservation of energy in the system, but over long periods of time tiny effects such as heat dissipated by tidal friction make this assumption incorrect.

Has anyone estimated the effects of tidal friction on the Sun and the eight major planets?

Mercury would experience a greater effect because it's deeper in the gravitational field of the Sun, but the fact that Earth has oceans and an atmosphere and Mercury does not might well create much more friction. Liquids and gases dissipate tidal energy faster than solids. IOW, the Sun-Earth distance might increase faster than the Sun-Mercury distance, thus explaining the increasing gap between the two planets without requiring any changes to the way that gravity works.

The fact that Earth also has a large Moon would also affect the amount of dissipation of the total kinetic energy of the Earth, although that may not be affect the distance from Mercury to Earth directly.

Both Jupiter and Saturn contribute notably to the position of the Sun relative to the barycenter of the Solar System. Saturn has a smaller mass but the larger distance means it still plays a relevant role.

Wikipedia has an image – the 12 year period comes from Jupiter and the perturbation of that cycle comes from Saturn, with smaller contributions from other planets.Never heard about this before but its interesting

Very interesting. There's a minor LaTeX error after "77,000,000,000".

And last but not least a good reference to quote on the FAQ "Do constants change over time or space?"Yes it is interesting. Infact I thought to link between dark energy and this phenomenon by the information from the link about amazing facts about the universe and god- https://dailyjunkies.com/15-amazing-facts-about-the-universe-and-god/.If you could link the phenomenon it would be greatful

Certainly the sun is losing some of its heat, by time, so that it has become somewhat cooler than before .. and so it has become smaller by contraction, and because it gets cooler, its electromagnetic field will be less (and its gravity is less.)

http://www.quran-ayat.com/universe/new_page_2.htm#Cause_of_the_Gravity_

Both Jupiter and Saturn contribute notably to the position of the Sun relative to the barycenter of the Solar System. Saturn has a smaller mass but the larger distance means it still plays a relevant role.

Wikipedia has an image – the 12 year period comes from Jupiter and the perturbation of that cycle comes from Saturn, with smaller contributions from other planets.

that's not what I was asking or talking about.It appears that I did address what you were asking and talking about. So the rest of the argument about this subthread is pointless, and I am deleting it.

Oh nonsense. Peter was simply expanding on what you posted to make sure you and anyone else reading this thread understood that all the objects in the solar system pull on the Sun (and each other) and affect its position. I can almost guarantee you that someone reading this thread would see your post and then wonder if the same was true for objects other than Jupiter. Now they have their answer.You choose to start a comment that does not address my initial post with, "Oh nonsense."

If you don't understand what aspect of his comments I am addressing, then opening with, "Oh nonsense." isn't adding anything beneficial.

Ok, it's nonsense.

For your consideration:

Definition of pedantic1: of, relating to, or being a pedant

2: narrowly, stodgily, and often ostentatiously learned

3: unimaginative, dull

Number 2 fits well to my point regarding his first comments.

And now this has gone way off topic.

Time to go.

Thanks.

His reply is directly on topic. So now that you know the ratio of the mass of the Sun and Jupiter, can you comment on where the Barycenter of our Solar System lies? :smile:I understand your position.

Taken as a whole, I disagree with your conclusion on "his reply".

The second part of his comments addressed my questions, and I thanked him for those.

No, I can't Mr. Berkeman.

I didn't know there was going to be a quiz.

The dog ate my paper. My car wouldn't start. I couldn't find my keys.

I have a doctors note that I can't take a quiz today, or any day. :)

I know, some people just have a need to add, counter, or otherwise add in things just because they feel the need to appear more knowledgeable.

"Pedantic" is the word that fits.Oh nonsense. Peter was simply expanding on what you posted to make sure you and anyone else reading this thread understood that all the objects in the solar system pull on the Sun (and each other) and affect its position. I can almost guarantee you that someone reading this thread would see your post and then wonder if the same was true for objects other than Jupiter. Now they have their answer.

Perhaps staying on topic to teach and learn is not as meaningful to some.His reply is directly on topic. So now that you know the ratio of the mass of the Sun and Jupiter, can you comment on where the Barycenter of our Solar System lies? :smile:

This is true of all the planets, not just Jupiter. Jupiter's effect is by far the largest, but I don't think it's the only detectable one. The strictly correct statement is that all of the objects in the Solar system orbit its barycenter, which can be thought of as the "center of mass" of the system as a whole, and this barycenter does not coincide with the center of any of the objects, including the Sun.Well now, of course Jupiter's gravity affects all the planets, as all the planets can affect each other. But now, that wasn't the point, and that's not what I was asking or talking about.

I know, some people just have a need to add, counter, or otherwise add in things just because they feel the need to appear more knowledgeable.

"Pedantic" is the word that fits.

Perhaps staying on topic to teach and learn is not as meaningful to some.

My time here will likely be very short.

Thanks for playing just the same. :)

This is true of all the planets, not just Jupiter. Jupiter's effect is by far the largest, but I don't think it's the only detectable one. The strictly correct statement is that all of the objects in the Solar system orbit its barycenter, which can be thought of as the "center of mass" of the system as a whole, and this barycenter does not coincide with the center of any of the objects, including the Sun.

Never. The rate of mass loss of the Sun is much, much too small. The sun is over 1100 times as massive as Jupiter, and the mass loss rate is roughly 6 parts in ##10^{14}## per year, so even after 5 billion years more, when the Sun is expected to become a red giant, the Sun will have lost only about 1 part in 100,000 of its current mass, so it will still be over 1100 times as massive as Jupiter.Soooo, you're sayin there's a chance!? LOL.

Thanks for the answer.

Due to the gravitational force of Jupiter it actually affects the Sun's position in our solar system, such that the Sun is not in a constant epicenter where all the planets form their orbits around that constantThis is true of all the planets, not just Jupiter. Jupiter's effect is by far the largest, but I don't think it's the only detectable one. The strictly correct statement is that all of the objects in the Solar system orbit its barycenter, which can be thought of as the "center of mass" of the system as a whole, and this barycenter does not coincide with the center of any of the objects, including the Sun.

As the Sun's mass lessens, and with that it's gravitation force lessens, then at what point in the future will Jupiter's gravity have a greater effect on the planets between it and the Sun?Never. The rate of mass loss of the Sun is much, much too small. The sun is over 1100 times as massive as Jupiter, and the mass loss rate is roughly 6 parts in ##10^{14}## per year, so even after 5 billion years more, when the Sun is expected to become a red giant, the Sun will have lost only about 1 part in 100,000 of its current mass, so it will still be over 1100 times as massive as Jupiter.

Some of you likely already know some of the following, but it was a very interesting point, about the Sun, when I heard it.

Jupiter is massive, and so is the Sun. Given the mass of Jupiter it has great total gravitational force. That force also is exerted noticeably on the Sun itself.

Due to the gravitational force of Jupiter it actually affects the Sun's position in our solar system, such that the Sun is not in a constant epicenter where all the planets form their orbits around that constant point. Rather, Jupiter's gravity pulls on the Sun such that the Sun also has an "orbit", and it's orbit is around an imaginary point that the sun orbits around. So, the Sun itself is also pulled towards Jupiter as Jupiter is pulled towards the sun, and their respective gravity creates both Jupiters's orbit as well as giving the Sun an "orbit" that is around the "center" of the solar system.

Very cool. And it demonstrates the massive gravitational power of Jupiter.

Question:

As the Sun's mass lessens, and with that it's gravitation force lessens, then at what point in the future will Jupiter's gravity have a greater effect on the planets between it and the Sun? IOW, at some future point, will Jupiter's gravitational effect become stronger on the Earth as the Sun's gravitational effect becomes lesser? And, when, or if, that happens, will the Earth's orbit change? Will the effect of Jupiter's gravitational pull slow the Earth's orbit around the sun? Or, can it create an effect of a slow orbit during certain Earth to Jupiter orbiting positions, and then speed up the orbit during different relative positions?

This of course is predicated on the idea that the Sun's mass is lessened due mainly to fusion and mass coronal ejections, while Jupiter's mass remains constant over this same period.

About 200 W for Earth/Sun, a bit more for Jupiter. Wikipedia has formulas where you can just plug in masses, distances and eccentricities (use e=0 for a good approximation).

Has anyone calculated the loss of energy from the gravitational waves emitted by the Sun and Jupiter, or the Sun and the other gas giants?

For the Sun and Jupiter,

m1 = 1.989 × 10^30 kg (Sun) ~ 2 × 10^30 kg

m2 = 1.898 × 10^27 kg (Jupiter) = 0.0009543 m1 ~ 2 × 10^27 kg

R = 778.5 million km = 7.785 x 10^11 m ~ 8 x 10^11 m

The best reference I could find with a quick Google search was:

http://www.physics.usu.edu/Wheeler/GenRel2013/Notes/GravitationalWaves.pdf

but I'm not familiar enough with the formulas to be confident that I'm applying them correctly.

Does this mean that if the Sun was, say, so shiny that the outward force more than counteract the gravitational force between the Earth and the Sun, the Earth would still have its orbit intact?No, of course not. These particles are not in an orbit at all. That only affects particles smaller than ~500 nm, however.

A uniform outwards force does not increase orbits, it gives them a different period. It acts like a slightly lower (but constant) solar mass. What is left is some sort of friction, which decreases the orbital radius of objects over time.Does this mean that if the Sun was, say, so shiny that the outward force more than counteract the gravitational force between the Earth and the Sun, the Earth would still have its orbit intact?

I do not understand how the Earth could stay with the same orbit if the photons hitting them from the Sun were so much more numerous than they are now that the outward force would be so great that there should not be any stable orbit. Am I missing something?

It is very difficult to draw any meaningful conclusions about individual factor variance based on the product of individual factors across cosmological time scales.

I'm curious if they took into account the momentum of the EM field (or photons) created by the Sun exerted on the planets (and the black body radiation of the planets and cosmic background blackbody radiation). By intuition, even though Mercury is a small planet, it's very close to the Sun and might be the most affected to it.This is covered by @mfb's post #8 here (even though that was stated in the context of the solar wind).

I'm curious if they took into account the momentum of the EM field (or photons) created by the Sun exerted on the planets (and the black body radiation of the planets and cosmic background blackbody radiation). By intuition, even though Mercury is a small planet, it's very close to the Sun and might be the most affected to it.

Yes. So what?

What astronomers measure is not the gravitational constant, but the product of the gravitational constant and the mass of objects, GM. This product can be measured much more precisely than either G or M.Yes. So in principle, the title of this thread is misleading: The product is decreasing, but (a) it could be either or (b) it could be both or (c) one could be increasing slightly but the other decreasing more.

Yes. So what?

What astronomers measure is not the gravitational constant, but the product of the gravitational constant and the mass of objects, GM. This product can be measured much more precisely than either G or M.

Isn't sixty parts per quadrillion decrease in gravity per year smaller than the uncertainty in the gravitational constant given by CODATA?

A uniform outwards force does not increase orbits, it gives them a different period. It acts like a slightly lower (but constant) solar mass. What is left is some sort of friction, which decreases the orbital radius of objects over time.

A uniform outwards force does not increase orbits, it gives them a different period. It acts like a slightly lower (but constant) solar mass. What is left is some sort of friction, which decreases the orbital radius of objects over time.

To one point: The Solar System — the orbital radii of the planets and other bodies — could be getting larger as the Sun's mass slowly shrinks. However, it could also be getting

smaller, due to friction from the solar wind. (Also radiation pressure, in the case of tiny bodies, especially dust.) The getting-larger effect should apply equally to all bodies, and the increase should be a simple proportionality with distance. But the getting-smaller effect(s) should be greater at smaller solar distances and for less dense bodies. Which effect is dominant, and for which bodies?Well isn't the momentum of the solar wind directed, for the most part, directly away from the sun? So it would contribute to an expansion overall, yes? Perhaps when the charged particles interact with magnetic fields of (some) planetary bodies and they're deflected? But still seems like an "outward" directed force.Some would hope the Earth's gravity is getting weaker. It would certainly make people feel better after the end of year holiday dinners. :biggrin:

Very interesting. There's a minor LaTeX error after "77,000,000,000".

And last but not least a good reference to quote on the FAQ "Do constants change over time or space?"There is also one at "10[sup]2[/sup]6 Watts"

> Together, the predicted mass loss rate is consistent with the measured decreasing gravitational parameter given its uncertainty.

So… we expect a mass loss, and we see the effect of the mass loss in the expected amount. Nothing surprising, unlike the topic would suggest.

Really enjoyed this Insight!

Greg Bernhardt submitted a new PF Insights post

Either the Sun Is Getting Smaller or Gravity Is Getting Weaker

View attachment 223610To one point: The Solar System — the orbital radii of the planets and other bodies — could be getting larger as the Sun's mass slowly shrinks. However, it could also be getting

smaller, due to friction from the solar wind. (Also radiation pressure, in the case of tiny bodies, especially dust.) The getting-larger effect should apply equally to all bodies, and the increase should be a simple proportionality with distance. But the getting-smaller effect(s) should be greater at smaller solar distances and for less dense bodies. Which effect is dominant, and for which bodies?Very interesting. There's a minor LaTeX error after "77,000,000,000".

And last but not least a good reference to quote on the FAQ "Do constants change over time or space?"