Gravity in Science – What is It?

Gravity is invisible. You can’t see it, you can’t touch it, you can’t taste it nor can you hear it – but you can sure as hell feel it. Are you sitting on a chair right now? What would happen if that chair suddenly dissolved into thin air? Or what if just one of its legs gave in? Yes, you’d find yourself on the floor in a matter of a second. Gravity pulls you towards the center of the Earth. Just focus on your buttocks and your thighs for a second. Can you feel gravity pulling them downward? You should feel as if something is pushing you onto your chair, or rather as if something tried to pull you through your chair. It’s time to get a grip on gravity!

Gravity and Classical Mechanics

Gravity, a Force that Attracts

Gravity attracts objects towards each other. Gravity is one of nature’s fundamental forces besides the weak force, the electromagnetic force and the strong nuclear force. In our everyday lives, we are hardly ever aware of the weak force (responsible for particle decay) and the strong nuclear force (responsible for binding the fundamental particles of matter together). We do notice the influence of the electromagnetic force, though, as it is necessary for our electric devices to work, but gravity is even more noticeable. Just think of the chair example above, or whenever you drop something.

Gravity plays a huge part in why the world we live in is the way it is. Planets are kept in orbit around their central star due to gravity, and moons are kept in their orbit around a planet. Things fall onto the ground because of gravity. The more massive an object is, the stronger gravity is between two objects and the more it is capable of pulling them closer together. And: The closer an object gets to another one, the stronger gravity’s effects on both of them become.

You can see this, for example, when weighing an astronaut on Earth before a trip to the moon, and then measuring him again on our celestial companion. The moon’s gravitational pull is only about 16.5% of Earth’s gravity because it does not have as much mass as Earth does. Keep in mind, it is not about the size of an object, but about its mass. A football (soccer ball) is approximately the same size as a bowling ball, yet their mass is different. The bowling ball is heavier than the football because it has more mass, i.e. there is more matter packed into the same volume of space. But back to the moon: As the moon’s mass is smaller, its gravitational pull on an astronaut is smaller than on Earth. If the astronaut weighs 100 kilograms on Earth, he only weighs 16.5 kilograms on the moon.

How Can You Tell How Much Gravity Affects You?

Gravity is powerful. We can see that every day. Whatever we drop does not float around in the air, but falls to the ground. This is true also for things like feathers and sheets of paper when there is no other influence on them but gravity. Just watch the video of Commander David Scott of the Apollo 15 mission drop a hammer and a feather on the moon.

Apollo 15 Hammer & Feather Drop Video by NASASolarSystem (YouTube)

In a vacuum, without air resistance, you can see how the gravity of a massive object influences both “light” and “heavy” objects smaller than itself equally. Both the feather and the hammer in our case, also exert a force of gravity onto the moon. But as the moon is so much more massive than feather and hammer, their gravitational force does not have a significant effect on the moon.

Let’s look at how to calculate the force of gravity between two objects. The formula to do this is:

    \[ F_g = G\frac{m_1 m_2}{r^2} \]

Here, F_g is the force of gravity, m_1 and m_2 are the masses of two objects, and r, for radius, is the distance between them. Then there is also G, the fundamental gravitational constant. All constants in physics are empirical values. For G, the measurements taken in various experiments have led to:

    \[ 6.674\cdot10^{-11}m^3 \cdot kg^{-1} \cdot s^{-2} \]

which is the same as

    \[ 6.674\cdot10^{-11}N \cdot m^2 \cdot kg^{-2} \]

where N is “Newton”, the international unit of force (Newton was the first to develop a concept about gravity; rumour has it that the idea was sparked when an apple fell from the apple tree he was sitting beneath):

    \[ 1N = 1\frac{kg \cdot m}{s^2} \]

Let’s look at an example of what this means. Let’s assume we have two asteroids floating in space, 100 m apart from each other, one weighing 1,000 kg and the second one weighing 20 kg. With the formula above we can calculate the magnitude of the gravitational force between these two objects:

m_1 = 1,000kg
m_2 = 20kg
r = 100m

F_g = G\frac{m_1 m_2}{r^2}
F_g = (6.674 \cdot 10^{-11}N \cdot \frac{m^2}{kg^{-2}}) \cdot (\frac{1,000kg \cdot 20kg}{(100m)^2})
F_g = (6.674 \cdot 10^{-11}N \cdot \frac{m^2}{kg^{-2}}) \cdot (\frac{20,000kg^2}{(10,000m^2})
F_g = (6.674 \cdot 10^{-11}N \cdot \frac{m^2}{kg^{-2}}) \cdot (2\frac{kg^2}{m^2})
F_g = (6.674 \cdot 10^{-11}N) \cdot 2
F_g = 13.348 \cdot 10^{-11}N

This means the gravitational force of the two asteroids is F_g = 13.348 \cdot 10^{-11}N when they are 100 meters apart. This equals 1.36 kilogram-force, whereas a kilogram-force is the magnitude of force applied to one kilogram of mass (that is, on Earth – things are a bit different in outer space, but let’s ignore this here for the sake of simplicity). So, the force between these two asteroids is not very strong, but the closer they are to each other, the stronger the force gets. When they are only 50 meters apart, the gravitational force is already at F_g = 53.392 \cdot 10^{-11}N or 5.44 kilogram-force – this is 4 times bigger by only half the distance. This is because the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of their distance to each other. So, the closer the two objects get to one another, their gravitational pull on each other grows exponentially and the stronger the force of gravity becomes.

What about 9.81?

You may have come across the number 9.81 concerning gravity on Earth. The concept behind this number is called gravitational acceleration and it tells us how fast a freely falling body accelerates in a vacuum towards another object. Here again, the masses of the two objects in question are of relevance. If one object is much larger than the other, usually this is the reference object from which gravitational acceleration is calculated. In the case of planet Earth, for example, it wouldn’t make any sense to use a human being as a reference object as Earth’s mass is so much greater.

Then, what does 9.81 tell us? It means that objects falling towards Earth accelerate with 9.81 m/s2, or more precisely, with 9.80665 m/s2 when they are in free fall towards Earth, provided that no other forces come into play. This number is only an average, though. Freefall acceleration ranges from 9.764 m/s2 to 9.834 m/s2, depending on where you are. Here, both altitude and latitude affect acceleration. Earth is not a perfect sphere but has both a varied topography (mountains, valleys, oceans etc.) as well as flattened poles. Thus, Earth’s mass is not distributed evenly everywhere around the (imperfect) globe and thus gravity varies.

If you would like to know how to calculate a body’s gravitational acceleration (g), this is the formula:

g = \frac{-GM}{r^2} \hat r

Here, M is the mass of the larger object and \hat r is a unit vector directed from the larger body to the smaller one. It is negative because it is an attractive force, pointing towards the larger object as the source of the force. This tells you how fast objects “fall” towards each other.

Gravity and the Theory of Relativity

Einstein's Take on Gravity

While Newton assumed that matter itself gave rise to gravity as if it were emitting the force, Einstein came up with a new idea: Space and time are woven into each other and together form the fabric of spacetime. Every object is located somewhere within spacetime, and the heavier the object, the more it curves and bends the area of spacetime around it. Gravity emerges from this curvature of spacetime. It is hard to imagine in a 3d environment, but it works like this example in a 2d plane:

Imagine you have an elastic piece of cloth, held in place by a stable frame on all four sides. Now place an orange onto it. The fabric will give in, forming a “valley” all around the orange. Now take a plum and do the same thing. It will also affect the fabric, but the “valley” will be less prominent because the plum has less mass than the orange. Now take a pea and first place it onto the fabric as well. The pea might not put a visible dent at all into the fabric as it might be too light. Now put the pea onto the edge of one of the valleys the other pieces of fruit have created (never mind here that peas aren’t fruit). What happens? The pea rolls into the valley and towards the heavier piece of fruit.

The same thing happens in 3d. Take our solar system, for example. The planets are pulled into the sun’s “valley”. The only reason they are not falling onto or rather into the sun is that each planet has a velocity, a speed with which it crosses space. And if it weren’t for the sun, this is exactly what Earth and the other planets would do: Fly through space in a straight line. So, both a planet’s velocity and the sun’s gravitational “valley” are the reasons why planets and moons are kept in orbit as long as gravity and velocity keep balancing each other.

© Composition: Julia Haunschild | Individual elements by designed by Freepik

Black Holes – the Universe's Drain Holes?

When Einstein formulated his theory of relativity, something emerged in its equations which Einstein thought to be only theoretical, without an equivalent in the real world: A gravitational singularity. This is a point in spacetime whit zero volume but infinite density. All the mass of the singularity is concentrated in this one single point, peculiarly curving spacetime. The physical laws of normal spacetime break down in a singularity, giving rise to an infinite gravitational field.

Einstein thought this to be impossible and thought it was simply a quirk in his calculations. But ever since black holes have been detected and have been confirmed to be a real thing in our universe, it is strongly suspected that a singularity is what is at the heart of a black hole. There is just no way to prove it (yet).

There are several types of black holes. The most widely known type are stellar black holes. A stellar black hole forms when a very heavy star collapses in on itself once it runs out of “fuel”. It blows some of its mass out into the universe, and the rest of it concentrates in a single point in space. This point in space is surrounded by a spherical area called the Schwarzschild radius, and its outer edge is called the event horizon. It marks the boundary from where nothing can escape once it crosses it, not even light. Matter doesn’t even have to get as close as the event horizon to get pulled into the black hole. How close something or someone can get to a black hole without being sucked in strongly depends on how much energy it can produce to overcome the gravitational field of the black hole, which gets weaker the farther it extends from its center. But what happens to the matter which is drawn into the black hole? This is still a mystery so far. Maybe it just stays inside the black hole, concentrated in that zero-volume singularity, maybe it is “drained” through it like through a drain in your sink and comes back out on the other side of it, from a so-called white hole, which could theoretically give birth to a whole new universe. Or maybe something completely different happens of which nobody has thought of yet. So far, we have no way of finding out.

If black holes aren’t visible directly because their gravitational pull is so strong that not even light can escape from them, then how can we tell they exist? We can only tell that they are there by how other things behave or by observing how light bends in ways it would usually not do. There is a massive black hole at the center of our own galaxy, and scientists have been able to tell this by how stars orbit around this center. Regarding light, light always follows the shortest path of spacetime, and if spacetime is curved by a very massive object such as a black hole, the light follows the bent path and produces an effect known as gravitational lensing. The so-called Einstein cross shows this pretty clearly, not with a black hole as its cause, but a very heavy galaxy:

We can see the exact same quasar (a certain type of galaxy core) four times, left, right, above and below the heavy galaxy, due to light taking the shortest way – along the curvature of spacetime.

As you can see, gravity produces the strangest phenomena in space, such as black holes and gravitational lensing. And it is responsible for what happens when two people sleep in the same bed: There is just no cure against rolling towards the dent that forms in the middle of the bed.

When Black Holes Collide

When massive objects meet in space, they tend to pull each other into each other’s orbit. This can happen to two massive black holes crossing each other’s path. They start to circle each other with great velocity, and over time, their orbits decay and they fall “into” each other and merge. This is such a major event that it affects spacetime itself. It causes ripples in its fabric, sending out waves like waves on the surface of water when you drop in a rock. Scientists are able to measure these so-called gravitational waves with very, very sensitive experiments such as LIGO (Laser Interferometer Gravitational-Wave Observatory). Isn’t it amazing that we can measure something like that, even if it happens so incredibly far away from us? It shows that we all are embedded within the fabric of spacetime and that everything is interconnected, even over very long distances.

Quantum Gravity

Gravitons as Force Carriers of Gravity?

Gravity is the only force that cannot be explained by quantum mechanics. A proposed particle, called a graviton, has not been discovered yet and finding it might be impossible. Although gravity can influence other objects even in great distances, we can only observe its effects when we look at very large objects, which makes gravity hard to study in a laboratory. So far, we have no clue what gravity is or what it is caused by on a quantum level. Maybe gravitons exist, maybe they don’t, but whether they do or don’t exist, science will surely find the answer at some point.

How is Gravity Different from the Other Fundamental Forces?

Besides the fact that gravity is the only fundamental force whose force-carrying particle has not been discovered yet, gravity seems to be the only force which doesn’t seem to have a strong (or any) influence on an atomic and subatomic level, but it can be felt over very long distances.

Compared to the other fundamental forces, gravity is not very strong, although it has the power to hold together large solar systems. You would think that a paper clip lying flat on the surface of the Earth would be pulled down with an immense gravitational force. And although it is, all you need is a magnet to pull it up. Gravity is 1040 times weaker than electromagnetism – this is a 10 followed by 40 zeros. Would you have guessed it? We, too, can apply a force greater than Earth’s gravitational pull to the paper clip – we can pick it up with our hands.

Gravity is very elusive compared to the other three forces when it comes to analyzing it. Even its universal constant has not been measured with such great precision as the other forces’ constants. It is simply too difficult to design experiments sensitive enough. We can easily observe gravity on a scale of galaxies, solar systems, stars and planets, but between objects of everyday life gravity is so weak that we can rarely notice any effects. Two books don’t pull each other closer, and when you drop one and it falls to the ground, it is because of our planet’s mass.

What can we conclude from this? Gravity is unique, as are the electromagnetic, the weak and the strong nuclear force. All four of them hold everything together, gravity on a large scale and the other three fundamental forces on a small scale. All four of them are fascinating in how they interact with matter and give rise to the material manifestation of our universe.