6: Exploring Gravity

Last updated
Save as PDF

Page ID: 25247

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Gravity is one of the most fundamental, and most mysterious, forces in our universe. There is an adage in astronomy that “Gravity controls everything.” Gravity was first explored mathematically and scientifically by Galileo in the early 1600’s. It was Galileo who first realized that gravity acts on all things equally and that everything falls at the same rate regardless of its mass. Galileo also explored gravitation using ramps and pendulums – something that even the youngest students can experience and begin to understand in school today.

The function of gravity on the solar system was largely unknown until Isaac Newton proposed his theory of universal gravitation in 1665. Newton’s theory says that all things possess gravity and attract each other across space. Therefore while the Earth’s gravity attracts you and holds you on the surface, your gravity also attracts the Earth! Newton also proved mathematically that gravitational force controlled all the orbits in our solar system – both those of planets going around the Sun as well as the orbits or moons around various planets. In fact, it was the falling apple that led Newton to prove that the Moon is really falling in its orbit around the Earth. Newton used his ideas to propose that artificial satellites were actually possible some 300 years before anyone actually launched one into Earth orbit.

The concept of what gravity actually is remained mysterious until Albert Einstein figured it out in his Theory of Relativity which was developed between 1905 and 1915. Einstein argued that space and time are actually one unified thing called spacetime. According to Einstein, it was the curvature of this spacetime that really creates the gravitational force that produces the effects studied by Newton and Galileo. While Einstein’s theory is well beyond most of us mathematically speaking, it is perfectly possible for young students to build simple Einsteinian models and explore the concepts of spacetime and gravity in the classroom!

In this unit, the activities we attempt will be arranged historically; that is, we will try some of Galileo’s ideas first, then explore Newton, and finally Einstein. What? You didn’t think you could teach 21^st century science to elementary school children!? Yes, you can! Let’s get started!

6.1: Galileo Explores Gravity with Pendulums
Legend has it that a young Galileo observed the swinging of a censer in church one day and noted that the incense burners kept swinging in time with each other as long as the chains that held them were of the same length. Galileo constructed his own pendulums and continued to experiment with them for much of his life. Like Galileo, we have much to learn from a swinging weight on the end of a length of string!
6.2: Hooke’s Pendulum
When Newton published his theory of gravity in the book Principia Mathematica, he struggled and failed to develop a simple and convincing demonstration for the mathematical concept that only a center-seeking force (gravity) and the straight line motion of a mass (momentum) are needed to create an orbit. Robert Hooke’s simple pendulum experiment achieved this and was considered a great triumph.
6.3: Galileo’s Falling Bodies
Aristotle’s scientific model stated that things fell to Earth because the ‘wanted to reach their natural place’, and that the heavier an object was, the faster it would fall. Aristotle’s fame was such that no one seriously challenged his assertions for over 2,000 years. Galileo’s experiment shows us the utility of gathering accurate observational data and comparing it to the predictions of scientific models. This is the very mechanism through which science corrects its own errors.
6.4: Packard’s Acceleration Ramp
Newton’s theory of gravity is no less complex and subtle than the concept of the curvature of spacetime and Einstein’s concept of gravity, yet we feel comfortable with it through long association. Einstein’s gravitational model is also powerful and mathematically subtle, but like Newton’s ideas of gravity, we can demonstrate it simply with a classroom model that students can grasp cognitively without troubling them (or you!) with the higher mathematics of the subject.