In our day-to-day life, we can weigh an object using a scale to find its mass. However, it’s not practical to weigh the earth using this method because we cannot place it on a scale. Therefore, scientists had to calculate the mass of the earth which is approximately 60 trillion tons. So, how did they do it? Let’s discuss below.
Key points of this article that can be understood in 3 lines in number
- To calculate Earth’s mass, scientists measure gravitational force. They use Newton’s law of universal gravitation. The law needs knowing the gravitational constant.
- During the 18th century, Henry Cavendish conducted an experiment called Cavendish’s Torsion Balance Experiment. He used a torsion balance with a mirror to accurately measure the weak gravitational force between two masses.
- Cavendish found out how Earth weighs using gravity. He figured out the gravitational constant. Then, he calculated Earth’s mass to be about 5.965 x 10^24 kg or 60 trillion tons. This number is almost the same as current estimates.
To calculate an object’s mass, measure its volume and density. However, this method doesn’t work for the earth. We can measure the earth’s radius to calculate its volume, but not its density. To find the earth’s mass, we can use gravity as a starting point.
Newton proposed the law of universal gravitation. It says that objects have gravitational force between them. The formula for this force is F = G*m1*m2/r^2. Here, G is a constant value, m1 and m2 are the mass of each object, and r is the distance between the two objects.
1. To determine the weight of the earth, a series of steps must be taken.
2. Obtain an object with a known weight (m1).
3. Measure the force of gravity (F) acting on the object while on the surface of the earth.
4. To find the weight of the earth (m2), use the gravitational constant (G) and the distance (r) between the object and the center of the earth.
The distance from the earth’s surface to its center is the same as its radius. Newton’s law of universal gravitation needed to know the gravitational constant, which was unknown at the time. To calculate the mass of the earth using this method, you need to find the gravitational constant value first. There is a way to determine it.
Newton said things with mass have a force between them. We need two objects of known mass to measure force. Then we can use a formula to calculate the gravitational constant.
This is a simple method to explain, but hard to perform. Why? Because gravity is weak. For instance, a magnet can pull an iron paper clip off the ground. It means that the entire Earth’s gravitational pull on the clip is weaker than a tiny magnet’s electromagnetic force on it.
After Newton’s law of universal gravitation was proposed, people struggled to calculate the exact value for the gravitational constant. Consequently, determining the mass of the Earth became a tricky scientific problem to solve.
In the 18th century, people made a way to measure force called the “torsion balance”. To explain it easily, they hung a thin wire on a slender rod. We can call the rod a “torsion bar” and the wire a “twisted wire”. When you push one end of the “torsion bar” sideways, it will bend and twist the “wire”. You can calculate how much force was used by measuring how much the “wire” twisted.
Physicist Henry Cavendish used a method to measure small forces that couldn’t be measured before. He used this method to calculate the specific gravitational constant’s numerical value.
It seems that he wants to put two small iron balls on both sides of a “torsion bar”. Then, he’ll use two big iron balls to attract the two ends of the “torsion scale” equally. When the small iron balls are under the gravitational force between them, it will twist the “twisting scale”. This twisting will also happen to the “twisting wire”. By measuring how much it twists, we can calculate the gravitational force between the balls.
When Cavendish tried his initial experiment, it didn’t work. This is because the iron balls’ gravitational force was very weak. As a result, the “twisted wire” did not twist enough to measure accurately. However, he didn’t give up and thought for a long time. Finally, he came up with a smart solution: using mirrors.
As children, many of us played a game where we held a mirror and adjusted its angle under the sun. This caused a light spot to appear on the wall. By shaking the mirror slightly, the light spot could be made to move around the wall.
Cavendish made the “torsion balance” better by using a mirror and light. He put the mirror on the “twisted wire” and shone a beam of light on it. By moving the mirror, he made the light shine on a scale. This made it easier to see how much the wire was twisted. Even a small twist could be seen on the scale, making it possible to measure changes accurately.
Several experiments were conducted to confirm this method’s feasibility. To get accurate measurements, we need to avoid external factors like air flow, sound, and temperature changes. The experiments of Cavendish took several years due to these requirements.
In 1798, he found out the specific value of gravitational constant. It was around 6.754 x 10^-11 (N·m^2/kg^2). Using it, he calculated that the earth’s mass was roughly 5.965 x 10^24 kg, which is equal to around 60 trillion tons.
It’s important to note that Cavendish figured out how much the Earth weighs over 200 years ago. His calculation was almost identical to the weight we agree on today (5.972 times 10 to the power of 24 kilograms). This is why he’s called “The man who calculated the mass of the Earth”. He improved a device called a “torsion balance”, which is now known as the “Cavendish torsion balance. Many advanced experiments still use it these days.