# Bringing The Apple to the Moon

## TL;DR

This paper introduces a teaching approach for Newtonian and Einsteinian gravity based on empirical phenomena and model construction, emphasizing the development of the universal gravitational constant as a conclusion.

## Contribution

It presents a novel didactic method that derives gravity laws from empirical data and discusses modern interpretations, contrasting with standard textbook approaches.

## Key findings

- Universal gravitational constant emerges as a conclusion.
- Empirical basis enhances understanding of gravity.
- Modern interpretation includes Einstein's general relativity.

## Abstract

Newtonian gravity can be regarded as a hypothetic-deductive system where the inverse square law is the starting point from which gravitational phenomena are deduced. This operational form of presenting gravity endorses problem solving and seems to be predominant in the teaching practice. In contrast, regarding phenomena as a source for the development of the theory is also possible, of course, and can be advantageous to scientific education since it deals with model conception and construction. This article intends to introduce undergraduates to Newtonian gravity using its empirical basis, i.e. the free fall and the planetary motion, to deduce the universal law of gravitation. Additionally, an elemental analysis of the theory's structure is presented. It also steps into the modern interpretation of gravitational phenomena i.e. Einstein's general relativity, including a discussion on the instantaneous action at a distance in this context. This didactic presentation of the theory of gravity differs from the standard approach usually found in common textbooks. It is designed to reach a threefold equality, similar to those applied in the method of separation of variables in partial differential equations, where G is treated as a separation constant. By doing so, the universality of the gravitation constant emerges as a conclusion rather than a statement. It is also meant to create a perception on how imagination can be helpful in discovering Physical laws.

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Source: https://tomesphere.com/paper/1903.10342