Very interesting response. Are there any public people who are doing work with cassini ovals? Also by pear earth. Did he mean as a 3D pear and we live on the surface? Or a flat earth but pear shaped?
I have one paper written by Charles A. Muses: A MORE EXACT THEORY OF GRAVITATION DEDUCIBLE IN PART FROM THE SOLAR OBSERVATIONS OF J.D.CASSINI ( Roma Consiglio nαzιonale Della Ricerche (1965).
As for Einstein's 'That there is no greater velocity than the speed of light through a vacuum,'Muses wrote:
'The phrase
in vacuo is a very doubtful assumption, for nowhere has been found any absolute vacuum. Thus for instance, if a compass needle is made to move by a magnet that does not touch it, even though both are in a vacuum with respect to the presence of other matter, there clearly exists a physical connection far more than merely geometric) between the magnet and the compass needle, for otherwise the magnet could not effect the observed rotation of the needle.'
Muses also wrote:‘The planets would thus ride in those energy grooves and the agreement between their semi-major axes and the zeros of the strongest (k = 0 or 1) cylindrical function is thus explained….. All in all, the theory of gravitation sketched here offers several new data, insights, and unifications for physical science and astronomy. There is no similar hypothesis that can explain all the data taken together or the parts taken separately.’--- Charles Muses.
As for a pear shape Earth,
Copernicus, Tycho de Brahe, Kepler, Newton and Cassini all took a global Earth for granted. Thus the shape of this global Earth was said by Newton to have a bulge around the Equator that caused the Earth to act as a gyroscope and cause precession. This was Newton's way to get the world to believe heliocentrism is proven. Cassini, a geocentrist was hated by the Newtonians because he proved them wrong about orbits and then about the shape of the Earth. Here is that science used to determine the shape of the Earth.
‘The period from Eratosthenes to Jean Picard can be called
the spherical era of geodesy. A new ellipsoidal era was begun by Sir Isaac Newton and Christian Huygens. In the Ptolemaic astronomy it had seemed natural to assume that the earth was an exact sphere with a centre that, in turn, all too easily became regarded as the centre of the entire universe. But, with a growing conviction that the Copernican system is true – the earth moves around the Sun and rotates around its own axis – and with the advance in mechanical knowledge due chiefly to Newton and Huygens, it seemed natural to conceive the earth as an oblate spheroid.’
King Louis XIV of France approved Cassini’s last great expedition. With the aid of his son Jacques Cassini (Cassini II) and others, he measured the arc of meridian (see above) from Paris north to Dunkirk and south to the boundary of Spain, and, in addition, he conducted various associated geodesic and further south astronomical operations that were reported to the Academy. Cassini knew that it would be virtually impossible to measure every kilometre of meridian from Pole to Pole at the time. At best, a northern measurement would confirm a probable shape of the Earth. Consequently, they decided to measure where it was most convenient, in Europe in the northern hemisphere.

In 1959 another measurement for the Earth was found, this time using a satellite called Vanguard. It found Newton’s ‘bulge’ was 25 feet (7.6 meters) higher south of the equator, and announced the Earth was shaped like a pear, that is, it has a bulgier bulge in the southern hemisphere. Seeking a few more details of this curious revelation we find that according to this latest measurement the South Pole is flatter by 50 feet and the North Pole higher (pointed) by 50 feet, as this illustration shows:

In the Journal of Surveying Engineering 1988, commenting on the current state of Astronomy and Space Geodesy, we find the following:
COORDINATE SYSTEMS USED IN GEODESY
BASIC DEFINITIONS AND CONCEPTS
By Tomás Soler and Larry D. Hothem, Member, ASCE
‘INTRODUCTION: The principal problem of geodesy may be stated as follows (Hirvonen 1960): “Find the space coordinates at any point P at the physical surface S of the Earth when a sufficient number of geodetic operations have been carried out along S.” Therefore, in order to know the position P, the definition of an appropriate frame to which these spatial coordinates refer is of primary importance. Due to the nature of the rotational motions of the Earth and to other geodynamic phenomena, a rigorously defined, Earth-fixing coordinates system at the degree of accuracy of our current observational capabilities is not presently available.’
‘Nothing under the sun is new, neither is any man able to say:
Behold this is new: for it hath already gone before in the ages that were before us.’

A simple study of the subject, however, as Ecclesiastes 1:10 tells us, seems to show us they were a people who had knowledge far greater than we would expect such an ancient race to have.
‘The perimeter of the Great Pyramid’s base is 3,023.16 feet and its height is 481.3949 feet…’ Now consider these calculations:
(1) Perimeter of 3,023.16 feet ÷ 5280 (feet per mile) = 0.572568181 miles multiplied by 43,200 = 24,734.94545 miles circuмference.
(2) Height of 481.3949 feet multiplied by 43,200 = 20796259.68 feet
÷ 5280 multiplied by 2 = 7877.71099 (the Earth’s diameter) multiplied by (3.14) = 24,748.55897 miles circuмference.
The Great Pyramid maths show, 24,734 miles is the distance around the equator, and 24,748 miles is the distance from pole to pole, then this shows us their Earth is a prolate - not an oblate - spheroid, not flattened at the poles but slightly elongated, with the equatorial circuмference 13.5 miles shorter than the polar circuмference, that is, slightly egg-shaped. Coincidentally, this is the general shape the Cassinis found and published in 1720.
As for the shape of the flat-Earth science, I do not know, I presume it is flat and they have a different way to confirm it.