Can solar flares affect gravity?

Can a large eruption of solar flares on our sun change the effects of its gravity ever so slightly, and is it possible to measure these changes with the equipment we have today.

There are two questions in this question.

Question 1:

Can a large eruption of solar flares on our sun change the effects of its gravity ever so slightly ...

Question 2:

and is it possible to measure these changes with the equipment we have today?

The answers are "theoretically, yes" and "absolutely not", respectively. In theory, even the tiniest change in the mass of the Sun will affect how the planets orbit the Sun (question #1). Whether this is observable (question #2) depends on the magnitude of the loss of mass. The answer to this question is an emphatic "NO".

Even the largest CME represents but a tiny fraction of the Sun's yearly loss of the mass due to everyday solar flares, and even more importantly, photons. On average, the Sun loses about 1.5×106 metric tons of mass per second due to CMEs, solar flares, and normal everyday outgassing. A very large CME comprises about 1.5 billion metric tons of mass, or about 1000 seconds worth of that average mass loss rate. That figure on the average loss rate is a rather uncertain, perhaps by a factor of two (either way). In either case, the mass loss from a large CME is tiny compared to the mass loss due to everyday outgassing and solar flares.

There is an even larger mass loss from the Sun that results from the fusion of hydrogen into helium. This is an easily calculable number. The solar constant is 1.361 kilowatts per square meter, which corresponds to a mass loss of 4.3 billion metric tons of mass per second, or 6.7×10-14 solar masses per year.

Accounting for the additional mass loss due to outgassing, solar flares and CMEs brings this up to about 10-13 solar masses per year. Note very well: Over the span of fifty years, that known mass loss rate is equivalent to about 10 million CMEs. That fifty years is about the span of time during which people have been making extremely accurate models of the solar system. Models prior to that were markedly less accurate. The vastly improved accuracy over the last fifty years is a consequence of sending satellites and probes into space.

The people who do that modeling do not yet account for the loss of mass of the Sun, period. There is, or at least there was, a good reason for that. Until fifty years ago, the uncertainty in the solar mass (expressed in units of length3/time2) was on the order of one part per million. That uncertainty has dropped by five+ orders of magnitude in the last fifty years (the satellite era).

As a fraction of the Sun's mass, the accumulated mass loss of the Sun over fifty years expressed as a fraction of the Sun's mass is very close to the uncertainty in the Sun's mass (once again expressed in units of length3/time2). This correspondence has caught the attention of those who do that modeling. In estimation theory, modeling a parameter that is orders of magnitude below the noise floor is worse than stupid. This is why the people who model the solar system have treated the Sun's mass as being as constant, even though they know that it isn't constant. The accuracies are getting to the point where treating the Sun's mass as constant is no longer a valid assumption.

Now let's look at an extremely large CME. A large CME is on the order of 10-19 solar masses. An extremely large one might be an order of magnitude larger. While over-the-top extreme, that represents about one ten millionth of the uncertainty of the mass of the Sun. The gravitational consequences of over-the-top CME are not observable.

• Cool! I didn't know we are coming close to measuring the mass loss directly (within one order of magnitude?). That's amazing. Feb 20, 2016 at 0:24
• Generally, a solar flare is not a source of mass loss except for the beams of energetic particles (though the fluences are very high compared to background, they are orders of magnitude below the thermal fluences). Solar flares are not always associated with CMEs. They are really just defined by a localized enhancement in x-ray flux, not a large burst of mass loss. Feb 20, 2016 at 20:01

Yes, a solar flare or a coronal mass ejection will have a gravitational effect, but it's tiny. The mass contained in a mass ejection is said to be on the order of $10^{12}kg$ (roughly equivalent to a 1km cube of solar material), which compared to the sun's entire mass of $2\times 10^{30}kg$ is completely negligible. Even if we assume that the flare has many times the mass of the actually ejected mass the resulting change in gravity on Earth would be unmeasurably small.

As impressive as these events are... they are caused by extremely rarified gas in the sun's atmosphere, not by what we would call "liquid material". That it looks somewhat like liquids being thrown up is because of the incredible size of these things and because they are being contained by solar magnetic fields, but the densities in flares are actually very low, just one billionth of the density of air.

• I'm curious if large flares from an active young red dwarf star would affect the tides of a planet (with ocean) orbiting within the habitable zone? There a planet orbits much closer to its sun and large flares would have a higher relative mass (?) But if I'm following your math then 10^12kg (solar flare) is one billionth the mass of our moon 10^22kg so not much chance of that happening, right? Mar 6, 2018 at 5:19