Does the Sun's spin have effect on the orbit of the Earth?
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$\begingroup$ The question in the question title differs substantially from what you've asked in the body of the question. Please edit your post to remove the confusion and provide more context and detail. For example, are you referring to the gradual change to the Sun's rate of spin over hundreds of millions of years, or a hypothetical scenario such as a collision that significantly changes the Sun's angular momentum? $\endgroup$– Chappo Hasn't ForgottenCommented Sep 22, 2020 at 4:49
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$\begingroup$ No. It has no effect. Only close to the event horizon of black holes, are there gravitational effects due to the rotation of the body. $\endgroup$– peterhCommented Sep 22, 2020 at 9:04
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$\begingroup$ @peterh-ReinstateMonica - Did you read my answer? While very small, the effect of the Sun's spin on the Earth's orbit most certainly does exist because the Sun's rotation makes the Sun slightly non-spherical. $\endgroup$– David HammenCommented Sep 22, 2020 at 23:34
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Does the Sun's spin have affect on the orbit of the Earth?
It has a very, very small effect. The Sun would have a larger equatorial bulge if it rotated faster, and a smaller equatorial bulge if it rotated slower. An equatorial bulge increases gravitational acceleration near the plane of the body's equator and decreases gravitational acceleration above below the body's poles.
Since the Sun is already rotating rather slowly, it doesn't have much of an equatorial bulge. Moreover, the effects of oblateness drop off as 1/R^4, as opposed to the 1/R^2 drop-off in Newton's law of gravitation for a point mass.
The combination of small oblateness, 1/R^4 drop-off, and large distances makes the effects of the Sun's oblateness on the planet's orbits very small.
The effect is very, very small, about three orders of magnitude smaller than the general relativistic effect on Mercury's precession (which is already very small, about 43 arc seconds per century). The primary effect of the Sun's oblateness is to make Mercury precess by 0.0286 arc seconds per century. That said, the extremely precise observations of Mercury's orbit about the Sun do make that tiny precession statistically important because the uncertainty in Mercury's precession rate is down to 0.0015 arc seconds per century, according to Park, Ryan S., et al. "Precession of Mercury’s Perihelion from Ranging to the MESSENGER Spacecraft." The Astronomical Journal 153.3 (2017): 121.
answered Sep 21, 2020 at 22:14
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1$\begingroup$ Is this too small to consider even for Mercury's apsidal precession measurement's error budget? $\endgroup$– uhohCommented Sep 22, 2020 at 0:04
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1$\begingroup$ @uhoh - I updated my answer to say "no" to your question. The effect is very small (over three orders of magnitude smaller than relativistic effects). But the error budget in Mercury's precession is smaller yet, over an order of magnitude smaller than the effect of the Sun's oblateness. $\endgroup$ Commented Sep 22, 2020 at 2:18
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