# The Precession of the Perihelion of Mercury 43'' / century or 12000 km / century difference to Newton's Laws

I was reading Foundations of Astronomy by M Seeds and was wondering about the precession of Mercury. There he says it is 43''/century or about 29 km per revolution past the position predicted by Newton’s laws or in total 12,000 km — more than twice its own diameter per century.

Mercury's angular diameter is between 4.5″ – 13.0″ depending on the positions of Earth and Mercury at a particular moment so 43''/4.5'' = 9.5 and 43''/13'' = 3.3

The angular diameter shift observed would be between 3.3 and 9.5 times Mercury's diameter but 12000 km / 4880km (Mercury's diamater) would result in a 2.45 diameters shift.

Do you know what information I am missing here?

Many thanks

Here is the link in the book

• Have you taken into account Newtonian gravity from other planets? Apr 27 '20 at 23:03
• Yes I did, Newtonian mechanics takes into account all the effects from the sun and other planets and predicts a precession of 5557 arcseconds. The one observed is 5600 arcseconds so the difference is 43 arcseconds. What I don't understand is why in the book it says 43'' which is about 3.3 to 9.5 times Mercury's angular diameter depending on the Earth-Mercury configuration but at the same time the book says its 12000km per century which is 2.45 times its diameter. I don't know where the error is. All the information is in the book where I've put the link. Many thanks for the reply Apr 27 '20 at 23:39

## 1 Answer

The angular measure isn't the size of Mercury from Earth, it's the fraction of Mercury's orbit.

The radius of Mercury's orbit is about $$57\,909\,050\,\text{km}$$ and 43 arcseconds is about $$2.085 \times 10^{-4}\text{radians}$$. Multiply that together and you get about $$12\,000\,\text{km}$$.

• Yes, this was the answer. Many thanks. One question, when the measurements were done first by Urbain Le Verrier they were angular measurements as observed from Earth and then translated as fractions of Mercury's orbit? Apr 27 '20 at 23:59
• I haven't studied the techniques used at the time. I presume that the location of perihelion wasn't detected from observation directly, but calculated from multiple observations of the orbit. But that's just my speculation. Apr 28 '20 at 5:50