# 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

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 $$12\,000\,\text{km}$$.