# The relationship between mathematics and astronomy

## Introduction

Astronomy is the science of all celestial objects (Earth, solar system, the Milky Way, the moon, the sun, etc.), space, and the universe in general. On the other hand, mathematics is the science of numbers, space, and the amount of matter, especially as abstract concepts. It can also be applied to other fields of study such as biology and architecture as applied mathematics. Traditionally, mathematics and astronomy have been closely intertwined. In present times, the names of Euler, Gauss, Poincare, and Newton among others are celebrated in both mathematical and astronomical sciences. This recognition reveals the commonality of these disciplines. This research then seeks to place more emphasis on this intimate relationship between the two sciences (LoPresto, 2016).

## Astronomy

Historically, astronomers were interested in mathematical principles, and the reverse was also correct. Consequently, the line between the two concepts was blurred, and it was difficult to tell the shared effect that each had on the other. However, astronomical demands were, in one case, the inspiration behind the development of a mathematical concept. A renowned Greek astronomer, Hip-Parchus came up with the theory of trigonometry, as a mathematician and as a practical observer. The astronomer had problems that he needed to solve that made it vital for him to come up with the principles of trigonometry.

Hip-Parchus had a significant impact in the astronomy field of study. He evaluated the yearly length fittingly to approximately within six minutes of its accurate value and ecliptic obliquity to roughly five minutes of arc. Hip-Parchus later determined the annual precession of the equinoxes to within nine seconds of arc. In addition, he determined the length of distance to the moon to approximately one percent of its value. Also, he also evaluated the sun’s, moon’s, and planets’ mean motions, assessed changes in the moon’s movement, and was also responsible for making a catalogue of fixed stars. Continuity of his work was led by Gauss after 2000 years while trying to find solutions to the same problems (Fleisch and Kregenow, 2013).

Generally, astronomical problems have occasioned discrete or continuous mathematics. The physical universe is made up of distinct matter such as atoms which change from one state to another continuously. A large portion of the problems associated with natural sciences is caused by changes in position or state, e.g. change in planetary motion. This continuity is laid bare in the foreground in the use of mathematics to provide solutions to real questions. In consequence, in trying to discover the areas where astronomy has made considerable and profound contributions to mathematical principles, we should restrict our search to discrete mathematics (Pantin, 2006).

Astronomy is the oldest of the natural sciences, and it played a part in the development of mathematical theories. Physics is the other natural science that is behind vital mathematical concepts such as the kinetic theory of gases. The additional benefit that has made astronomy famous is the delicate character of its numerous observations and the high precision levels of its many methods. Other fields that have utilized the same principles are tangents and areas in geometry. It can be safely concluded consequently that astronomical problems have led to the development of theories of discrete mathematics.

## Application of Mathematics in Astronomy

Calculus invention was one of the milestone events in mathematics. Calculus was a brainchild of Newton and was later improved by Leibnitz. The two founding fathers laid a good foundation with their combined efforts for what has followed since they invented the sub-discipline. Newton’s thoughts for the concept were, to a large extent inspired by physical phenomenon consideration. This is shown by terminologies and notations employed by Newton and the problems to which he applied his methods. Time was used as an independent variable. This was not vital, however. He also used terms as* fluents* and *fluxions*. This shows the reasons behind his ideas. Leibnitz, on the other hand, used the geometry term and arrived at derivatives conclusion through the use of tangents and curves. This proves the independence of work of the two founding fathers of calculus (LoPresto, 2016).

### Calculus

Calculus application in the years to follow demonstrated the accomplishments of the human mind. Mathematicians now possessed immense power and greatest generality with their new invention. The laws of gravity and motion would be the key that would unlock the universe as well as countless possibilities for them. A succession of triumphs was occasioned by the works of Euler, Clair-aut, d’Alembert, and Lagrange. The highly improved the actions of both Newton and Leibnitz. It is safe to reiterate that physical and astronomical problems gave rise to calculus and aided its evolution into broader domains of analysis in the years to follow. It is doubtless that the significant standing that analysis enjoys in mathematics is mainly due to its astronomic application.

Astronomy not only made analysis vital in mathematics, but it also gave direction to the forms mathematical theories should take. For instance, the analytic differential equations have five varied ways of finding their solutions. The solutions are all developed on account of the pressure of problems of an astronomical nature. These distinct methods were successfully used several years before mathematical methods established conditions of their validity.

#### Differential Equations

In recent memory, Hill’s treatment of the linear differential equations comes to mind. Hill infers characteristics of the moon’s motion to solutions of properties of the linear differential equation. Problems associated with an infinite number of concurrently uniform linear equations were also realized in the lunar theory by Hill (Fleisch and Kregenow, 2013).

Studies by Poincare into the problem of several bodies resulted in findings that show many new attributes of the solutions of differential equations. Using this background, Poincare arrived at vital discoveries. These discoveries show how to construct functions that provide the resolution of the general problem of *n *bodies given no collisions involved. For the developments to be valid indefinitely, the forces would have to be repulsive and not attractive. “Nature does not care about analytical difficulties,” Laplace asserts. As if to provide compensation for the problem it poses, it often gives ways of solving them (LoPresto, 2016).

Another use of mathematics was through the observation of the sun and planetary motion by Appolonius of Perga. Apollonius demonstrated the movement of celestial objects successfully. He used epicycles rather than heliocentric spheres. He also satisfactorily explained the evolution of the sun along an eccentric circle. The center did not at all coincide with that of the Earth. Discoveries and findings of Appolonius were improved by Ptolemy, who introduced the notion of equant through which he explained the orbit around the sun. His theory proposed that the sun’s center deferent was located at the Earth’s center. The movement of the sun along the deferent was not considered homogeneous hence it was visible from the Earth.

The theories by Appolonius were augmented quantitatively by Ptolemy. Ptolemy’s theory became the mathematics standpoint which gave sufficient details and quantitative amounts of all the celestial motions. What made Appolonius’s theory lack any feet to stand on is that it did not provide any mathematical explanation for planetary movement. The approach proposed by Ptolemy surmounted this challenge, and it is widely regarded as the most prominent scientific accomplishment of that time (Pantin, 2006).

### Use of Mathematics to Estimate Routes

Presently, mathematics is employed in astronomy to compute routes used by rockets, satellites, and probes in space. Moreover, mathematics is imperative in calculations involved in the global positioning system, for transmitting messages in the event of compression of data. It is also utilized in the coding of pixels in images and modeling elements to assemble a space shuttle. Furthermore, astronomy uses mathematics in the computations of directing space crafts to rendezvous locations where they link up with space stations. The meeting involves complex calculations that are solved for the two objects to rendezvous successfully without accidents. Other mathematical concepts used to correct the trajectories of space shuttles are analysis of error and maximum principle (Fleisch and Kregenow, 2013).

Geometry assists astronomers to determine the characteristics associated with celestial bodies such as stars and space objects. It is essential in the computation of the area, velocity, length, and volume of bodies in the universe. It also determines the scope and location of celestial bodies in the sky. The science of space measuring is known as trigonometric parallax. Trigonometry is essential in the determination of the distance between stars in the heavens and how the motion of stars compares with other distant stars (LoPresto, 2016).

# Conclusion

The many examples have shown the close relation that exists between the sciences of astronomy and mathematics. Hence, there is no need to cite any more to demonstrate their interdependence.

References

Fleisch, D. and Kregenow, J. (2013). *A Student’s Guide to the Mathematics of Astronomy*. Cambridge University Press.

LoPresto, M. C. (2016). The mass-luminosity relation in an introductory astronomy lab. *The Physics Teacher*, *54*(8), 506-507.

Pantin, I. (2006). Teaching mathematics and astronomy in France: the Collège Royal (1550–1650). *Science & Education*, *15*(2-4), 189-207.