[Bolvan (OP)]

The Sun converts some of its mass into energy to shine and some into solar wind.
Earth gets some mass increase due to space dust, meteors etc. fall, but loses some due to helium and hydrogen "escape".
How does it impact distance between Earth and the Sun?
Can it have impact on so called climate change?
Numbers I found while googling are taken out of the "blue", arbitrary and at best good for rotating straw in a cup of cappuccino.
Please recommend well made and empirically supported study.

[evan_au]

How does it impact distance between Earth and the Sun?

A change in Earth's mass does not affect Earth's orbit, provided it does not change the Earth's velocity significantly.

A significant change in the Sun's mass would have an impact on the Earth's orbit. However, the Sun is incredibly massive, and the effects you describe would not make a measurable change to the Sun's mass.

In 4 billion years or so, the Sun will enter a Red Giant phase, and will puff off some of its outer envelope. This will measurably reduce the Sun's mass, and will measurably increase the radius of Earth's orbit. However, the hugely inflated atmosphere of the Sun will fry the Earth's surface, despite the increased orbital radius. This won't start until the Sun starts burning helium, which is still a long way off.

Can it have impact on so called climate change?

No.

Human-induced climate change (the "hockey stick curve") focuses on the past 100 years. It started with burning coal in the Industrial Revolution, and really accelerated with the great increase in per-capita energy consumption in the past century, with individual motor vehicles, electricity, airplanes, aluminium cans, fertilizer, etc etc.

Changes in the mass of the Sun have not occurred on these timescales (astronomers would have noticed a Jupiter-sized planet plunging into the Sun - which would have made a tiny change to its mass).

If you want to grasp at other straws for why humans aren't causing climate change, you could try something with a more significant impact, like:
- The Maunder Minimum, a century-long reduction in the number of sunspots, which coincided with "the little ice age". This occurred before the start of the industrial revolution, but since then, the Sun has returned to something similar to its previous sunspot activity, so you can't blame that for recent climate change. 
- Milankovitch cycles, changes in the tilt of the Earth's rotation, which operate on timescales of thousands of years. The long duration of these cycles can't explain the rapid changes in the past 100-200 years.
- Then you still have to explain acid rain and ocean acidification, which are generally agreed to be due to increased smokestack emissions...

[Janus]

How does it impact distance between Earth and the Sun?

A change in Earth's mass does not affect Earth's orbit, provided it does not change the Earth's velocity significantly.
.

Not 100% true.    While it is true that, due to the Earth small mass relative to the Sun, it would take a huge change in the Earth mass to produce a measurable change in its orbit, this not the same as it  making no change.
The orbital velocity for a mass m can be found by
V= sqrt(G(M+m)/r)

Note that as m increases, V must go up for any value of r.  So if m were to suddenly increase without a change in r or v,  the orbiting object would find itself at a lower orbital speed than it should be at(for a circular orbit at that distance), and it would fall into an elliptical orbit with a closer average distance to M to compensate.

Having said that, even doubling the Earth's mass would only result is an difference of 5 cm/sec in its orbital speed.  This would in turn change the Earth's average distance from the Sun by much less than it varies due to its existing orbital eccentricity.

[PmbPhy]

According to legends Sun converts some of its mass into energy to shine and some into solar wind.

Contrary to popular belief, mass cannot be converted to energy. That's a common misconception. What happens is that energy and matter changes form. E.g. if you have a collision between an electron and a positron (aka anti-electron) then they will annihilate each other producing photons. What was originally kinetic energy and rest energy ends up being kinetic energy only (the energy of photons is all kinetic energy. The mass of the system remains unchanged as does the energy.

[Bored chemist]

Stonehenge still keeps pretty good time.
So the effects of these things (and everything else) over the last few thousand years  must be small.

[PmbPhy]

Not 100% true. ....

Yeah, but that's like saying that there's no such thing as a flat table.

[Bolvan (OP)]

Main question was : possible impact of mass change of Sun and Earth resolving into change of distance between them and as a result increase or decrease of energy Earth receives from the Sun.

[Bolvan (OP)]

Please recommend well made and empirically supported study.

[Bolvan (OP)]

Stonehenge still keeps pretty good time.

Please, provide well made and re-verifiable data. Or science is set of believes?

[evan_au]

Please recommend well made and empirically supported study.

Sorry if I sound a little annoyed, but it appears as if the promoter of a weak and unsupportable theory (about why humans aren't causing climate change) has had some of the more obvious flaws in his theory pointed out.

He then tries to defend an indefensible position by demanding solid proof that his theory is invalid.
- In fact, the supporter of this new theory should now come up with a "well made and empirically supported study" showing that this new theory has any credibility at all.

Or is science a set of beliefs?

Science does have beliefs. But it also has evidence.

Show us the evidence.

[Janus]

Main question was : possible impact of mass change of Sun and Earth resolving into change of distance between them and as a result increase or decrease of energy Earth receives from the Sun.

And the answer was given: insignificant.   I already showed how even a doubling of the Earth's mass would have a minimal effect on its orbit. ( and the Earth's mass has hasn't even increased its mass by a significant fraction in the last century)
As far as the Sun goes, it loses ~10^-13 solar masses per century due both fusion and solar wind.   Comparing the Earth's present orbit to the one it would have in one century as a result of that mass loss by the Sun results in an increase in distance by about 712 meters, an insignificant change when compared the the Earth's present 1.496e11 meter distance from the Sun.
While the Sun will move away from the Sun as the Sun loses mass, it will take much longer time scales than centuries for this to become significant.

[evan_au]

The effect of doubling the Earth's mass would be insignificant. And we know that the Earth's mass hasn't doubled because athletes are still matching or exceeding records for high-jump, weight-lifting, running and javelin. Pendulum clocks still keep pretty good time, and aeroplanes aren't falling out of the sky.

The effect of small changes in the Sun's mass are more significant than large changes in the Earth's mass. But ever since Newton's theory of gravity was established, astronomers have been able to predict the date of eclipses, the exact time, and the path of totality, centuries ahead. If the Sun's mass had changed by even 0.01%, the Earth's orbit around the Sun would change by about an hour per year, and the path of totality would be totally wrong compared to predictions made just 1 year earlier. But these predictions were made much more than 1 year before.

If the Earth's mass had changed by even 0.01%, the Moon's orbit around the Earth would change by a similar amount, which would also make the path of totality totally different.

There is a total eclipse predicted for North America on August 21, 2017 - see for yourself whether the mass of the Sun or the Earth has changed.

Bolvan, time to provide some evidence for your wishful thinking!

[PmbPhy]

Please recommend well made and empirically supported study.

Contrary to popular belief there aren't studies of all the facts that we know to be true. In this case we know that the length of the year hasn't changed in recorded history and that means that the effect of the Sun loosing mass hasn't measureable effected the Earths orbit within experimental error. But to find a study to measure the length of the year is like looking for something you don't know exists. However there is zero reason to suspect that it has and its an empirical fact (ask any astronomer) that  the Earth is in the same place in its orbit every 365 days (plus a fraction of a day). That means that at midnight every January 1st the same stars will be over head that were there last year. If you have the patience you an observe this for yourself. But there hasn't been people around for the millions or billions of years to confirm this to be so. Hence the lack of empirical data.

What do I mean by "facts we know to be true" you may ask? If you went on to the roof of your house and jumped of we know that that you will fall down and hit the ground. That's a "fact". Other facts are harder to accept since we don't have direct experience of them but they are facts nonetheless.

[PmbPhy]

Main question was : possible impact of mass change of Sun and Earth resolving into change of distance between them and as a result increase or decrease of energy Earth receives from the Sun.

This question has already be answered, The Sun is losing mass and there is an increase in mass of the Earth due to meteor impacts. The percentage change is extremely small. As far as the change of mass regarding loss of atmospheric gases I'd say that there's a balance between what is lost to space with what is gained due to gravitational attraction.

The position of the center of mass of the Sun is so constant that you can think of it as being stationary. Please keep in mind that there are other planets in the solar system which all tug on the Sun. The formula that Janus posted only applies to a system in which there is only the Sun and Earth present.

The orbit of Earth around the Sun is so constant that there has never been any observed change in recorded history.

[evan_au]

Please recommend well made and empirically supported study.

An analysis of astronomical records in the 1850s was able to detect a variation in Mercury's orbit of 43 arc-seconds per century.

Similar astronomical sleuthing detected very subtle changes in the orbits of the known planets, allowing detection of the outer planets of our solar system (and one ex-planet).

These incredibly precise astronomical measurements are able to detect extremely small changes in the mass of the Sun. But any changes have been too small to measure with current techniques. So we can say with confidence that they are negligible.

By the way, the slightly peculiar orbit of Mercury was eventually explained by Einstein's General Relativity, which has been very well tested.
See: https://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury

[PmbPhy]

These incredibly precise astronomical measurements are able to detect extremely small changes in the mass of the Sun. But any changes have been too small to measure with current techniques.

Evan - Can you please clarify this response for me? These two statements seem to me to contradict each other. In the first sentence you state that we are able to detect extremely small changes in the Sun's mass while the second states that they're too small to be detected by current techniques. Huh?

[Bolvan (OP)]

To make last question clear = can we?

Note: Part of the discussion that diverged from measuring the mass of the Sun has been moved into a separate thread: "What is the cause of climate change?"

[evan_au]

In the first sentence you state that we are able to detect extremely small changes in the Sun's mass while the second states that they're too small to be detected by current techniques. Huh?

The OP was asking could there be gross changes in Earth's orbit that drew it closer to the Sun and explained away the alleged human-induced climate change.

I replied showing the exquisite sensitivity of telescope-based astronomical measurements that rule out any gross changes in the mass of the Sun, which would be easily measured by classical astronomers.

I could have mentioned the even more precise measurements of the Solar System which became possible with radar reflections from Venus, laser retroreflectors on the Moon, and are now routine with space probes dotted at numerous points around the Solar System (and at least one outside it). These radar measurements are so precise that with the Pioneer anomaly, NASA was able to detect and investigate a gravitational attraction by the Sun that differed by 10^-9 m/s² from what they were expecting. (Spoiler alert: it was not caused by a change in the Sun's mass.)

These routine measurements put very strict limits on any change in the mass of the Sun, the Earth and the other planets.

But these incredibly sensitive measurements have not shown any measurable change in the mass of the Sun (that I have heard of).

So we can confidently rule out the strawman argument implicit in the OP (and now explicit in today's post) that "The Earth is now warmer because the mass of the Sun has suddenly increased in the past century and Earth is now orbiting closer to the Sun; therefore climate change obviously has nothing to do with human activities on Earth.".