Galileo and an Astronaut in Family Room

Galileo and an Astronaut in My Family Room

By Damon Nomad



You're Blocking the TV!

I remember the day well in the summer of 1971. Standing in the family room waving my hand in the air, spouting off at my father with disrespect. "I told you so!"

The news was showing a clip of astronaut David Scott dropping a feather and hammer on the surface of the moon, Scott exclaiming that Galileo was right. My father was irritated, he could never understand my obsession with science and constant questions about the nature of things. He was a practical man. As a loud-mouthed adolescent and teenager, I thought he was stupid and closed-minded. I was ashamed years later when I realized how wrong I was. He saw the world differently than me, he did not care about the subatomic world or the world of the cosmos. He worried about paying the bills and taking care of a large family. Saving money for college educations, something he never had.

As I walked out of the family room I heard my father mutter to my mother. "Why is he so arrogant and stubborn?"

She did not argue but she confirmed my arrogant position. "Well he was right, wasn't he?"

The last thing I heard was my father's exasperated sigh as he grumbled. "Yes, that just makes his head even bigger."

They were referring to another episode in the family room about a year earlier. I had been reading about the history of the equivalence principle and Galileo, Newton, and Einstein. I stood in front of the TV one evening interrupting everyone's viewing pleasure, I did not care. I was sure they all needed a lesson to better understand the world around them. I had a large feather I had extracted from a pillow and a baseball. I held the two up at shoulder height and dropped them at the same time. The baseball plummeted quickly to the floor and the feather slowly drifted to the brown shag carpet.

I looked at my brothers and parents bug-eyed. "Why did the feather fall more slowly?" Knowing they would get it wrong.

My father waved for me to get out of the way. "You're blocking the TV! The ball is a lot heavier, now get out of the way!"

I smirked, of course the old man did not know. "It's not weight, it's air resistance. In a vacuum, they would hit the ground at the same time."

My father stood up. "Nonsense, the feather is nearly light as air. Now get out of the way, so we can watch Bonanza!"

About a year later at the end of a moonwalk for the Apollo 15 mission in 1971, astronaut David Walker proved me right, even though he mentioned Galileo and not me. You can find videos of this fun moment online. This story is still playing out on a satellite experiment where the results have been recently reported. From Galileo to Newton to Einstein, scientists are still testing the equivalence theory. So far, they are still proving me right . That's how I would have seen it fifty years ago.


Brief History of the Weak Equivalence Theory

The weak equivalence theory started with the equivalence between inertial and gravitational mass. A few simple steps of algebra from Isaac Newton can show pretty well what it's about. The story normally starts with the brilliant astronomer Galileo Galilei (1564-1642). Supposedly dropping two balls from the tower of Pisa, balls made of different materials exclaiming that they would strike the ground below at the same time. We will not dwell on this dubious story, he did not have the correct reasoning and among his many scientific accomplishments, this is not so important. It was Newton who laid the first real scientific basis for the theory.

Isaac Newton's (1642-1727) accomplishments in the world of mathematics and physics are well chronicled. Including his mathematical formulation for gravity that stood for three hundred years as what was expected to be the final word on the subject. It remains remarkably accurate but is only an approximation that was upended by another great mind, Albert Einstein. We will come to Einstein's role in this story in a bit. Newton famously admitted he did not know the origin of the gravity force essentially leaving that to the Provence of God. He developed elegant mathematics to explain the effects of gravity including this resulting formula for its strength.

Eq. 1 Fgravity = G x [Mass Body 1 x Mass Body 2/Distance between the bodies Squared]

We will use the earth, hammer, and feather as our bodies. G is the gravitational constant and we will use D for the distance. We will consider the force of gravity of the earth on the hammer and feather when they are dropped from the same height, D. We will use Newton's arguments about equivalence to show how fast each would accelerate in free fall when dropped from that distance, ignoring the effect of air resistance. Similar to if they were dropped in the near vacuum of space on the moon, falling to the surface of the moon under the gravitational pull of the mass of the moon.

For the hammer, we would have the force of gravity as:

Eq. 2 Fgravity = G x [mass earth x mass of hammer/D squared]

Next Newton used his second law of motion, the rate of acceleration of an object is directly proportional to the net force applied to the object. The constant of proportionality is the inertial mass of the object. Stated mathematically in equation 3.

Eq. 3 Force = mass x acceleration

Where the force is the net force and the mass is the inertial mass of the body. Newton asserted that the inertial mass in equation 3 is equal to the gravitational mass in equation 2. This is a classical statement of weak equivalence, the equivalence of the inertial and gravitational masses. Equation three cast for the hammer gives us equation 4.

Eq. 4 F = (mass of hammer) x (hammer acceleration)

Newton further argued that if he ignored other forces, especially air resistance. Then the force of gravity, pulling the hammer to the ground would be the net force acting on the hammer to accelerate it toward the ground when dropped from a height D. That meant the force of equation 4 equaled the gravity force of equation 2.

Algebraically, Equation 2 = Equation 4, yielding equation 5

Eq. 5 (mass of hammer) x (hammer acceleration) = G x [mass earth x mass of hammer/D squared]

You can see that the mass of the hammer is on both sides of the equation, so they cancel out, leaving the key result:

Eq. 6 Acceleration of hammer = G x [Mass of Earth/D squared]

The rate of fall of the hammer does not depend on the hammer's mass or its weight, weight is mass times the acceleration of gravity roughly a constant. The same set of steps for the feather would yield the same result.

Eq. 7 Acceleration of feather = G x [Mass of Earth/D squared]

The accelerations of the hammer and feather are equal. Without air resistance, the rate of the fall of the feather and hammer toward the earth only depends on the height from which they are dropped. If you were to consider doing the experiment on the moon, the only difference would be exchanging the mass of the moon for the mass of the earth in equations 6 and 7. The hammer and feather will fall accelerating at the same rate and since they were dropped from the same height, they will strike the ground at the same time. Exactly what astronaut David Scott proved on television in 1971, well at least to most people.

Up to now, the story is quite easy to understand and rather intuitive, but there is a plot twist of sorts. Albert Einstein (1879-1955) came along about three hundred years after Newton and turned the world of gravity upside down. Not exactly, but it was revolutionary and not so intuitive. Einstein claimed he knew where gravity came from. In essence from the curvature of space-time. He also argued space and time could not be separated, hence the four-dimensional world of space-time. The extent to which space-time is warped is a function of the amount of energy or mass present. Space-time would be flat in the absence of any mass or energy. This is a whole complex story, but suffice it to say that it has rocked the world of physics since 1915 when he published the general theory of relativity.

As part of general relativity, he further refined the weak equivalence theory by showing mathematically that gravity cannot be distinguished from the apparent force of an accelerating framework. He used some of his classic thought experiments to demonstrate. He described an observer in an elevator in space who does not know where the elevator is located. The observer would not be able to discern whether the force pushing him to the floor was due to the gravity of the massive earth below the floor or because the elevator was accelerating upward in the deep void of space. If the acceleration in space matched the gravitational acceleration on earth. The observer would even see the same value for his weight standing on a scale as he zipped through the cosmos as he would standing on the elevator back on earth.


Continuing Experiments

The concept of equivalence as expressed by Einstein continues to be tested especially due to more recent discoveries, regarding dark energy and dark matter. Subjects for another essay. As a reminder, the use of the term dark in both cases is a synonym for, poorly understood, things scientists do not understand. Dark matter was "discovered" to account for the rate of movement of stars about their galactic centers, unseen mass. Dark energy was an answer to the shock when scientists discovered that the rate of expansion of the universe was not slowing or constant. Those were the two competing theories, instead in 1998 it was determined and repeatedly confirmed since then the rate of expansion is accelerating. The reason, some unknown energy, "dark energy" was postulated to exist. Scientists estimate that the universe is roughly made up of seventy percent dark energy and twenty-five percent dark matter. Yes, only five percent of the universe is made up of the stuff we understand.

Both of these "discoveries" revolve, so to speak around theories of gravity. Since 1915 all observations predicted by Einstein from his formulation of gravity in the general theory of relativity have confirmed his predictions. However, the surprises of these dark phantoms are one reason people continue to test his formulation of the equivalence theory. Recently results have been reported from the analysis of data collected by a satellite experimental platform known as MICROSCOPE, orbiting around 700 kilometers above the earth.

The satellite contains two pairs of nested cylinders, essentially floating inside the satellite and held in place by electrostatic charges. The amount of charge is a measure of the acceleration of the cylinders, and the force against the electric field is precisely measured. One pair is made of platinum and the other titanium, measurements were carried out for nearly two years. There have been reports of a recent detailed analysis of that data. The results showed no difference in accelerations to a few parts in a thousand trillion. That is pretty darn accurate, sounds like the equivalence principle is on solid footing for now.

Next time you come across this question, about the rate things fall to the earth think of a parachute. It's strapped to your back as you plummet to earth, you pull the cord. You know the weight does not change, you and the parachute weigh the same as you did moments before, but the air resistance of the large surface area of the deployed chute produces a counteracting drag force to slow your descent. Or you can imagine me arrogantly preaching to my family, interrupting one of my father's favorite TV shows as if I was the only person in the world who understood this.