Summary of How to measure mass of the Earth using Arduino
This article outlines an indirect method to calculate Earth's mass using Newton's laws and Arduino-based experiments. By measuring the acceleration due to gravity (g) with a free-fall setup, the author derives Earth's mass using the formula M = (gr²)/G. The project involves constructing an IR timing circuit and assembling electronic components on a breadboard to capture precise fall times.
Parts used in the Measure Mass of the Earth Project:
- Arduino board (Uno/Duomilanove)
- USB cable
- 560 Ohm resistors (4 units)
- 100 Ohm resistors (2 units)
- Piezoelectric sensors (4 units)
- IR Tx (IR LED) and Rx (Photodiode) pair
- Potentiometer
- Opamp (UA741C)
- Breadboard
- Three 1.2 meter long wires
- 5cmx5cm general purpose PCB
- Tape
- Cardboard sheet
One fine day, I was weighing my self on a weighing scale. Suddenly a thought came to my mind, ‘How much would be the mass of Earth?’. Leave that apart ‘How can we even measure it?’. There is no such weighing scale on which, Earth can be placed. There has to be some indirect way to measure mass of the Earth. Here I present implementation of one such indirect method to measure mass of the Earth.
Step 1: The Indirect Method
In early nineteenth century scientists used Newton’s second law and Newton’s law of universal gravitation to measure mass of the Earth. These equations are F = ma and F=(GmM)/(r2) respectively(m=mass of the object, a=acceleration, G=Gravitational Constant, M=mass of the Earth, r=Radius of the earth). If we substitute g i.e. acceleration due to gravity for the ‘a’ acceleration term and combine these two equation we get.
mg = GmM/r2
This equation can be solved for M i.e mass of the earth.
M = (gr2)/G.
We will assume that we know the value of G and r. We will find g i.e. acceleration due to gravity using a small experiment, involving arduino and a few sensors. Finally we will put all things together to find the value of M.
If equations seems a bit awkward , look at the attached image.
Let’s get started with the experiment.
Step 2: Things We Will Need
Here is the list of things we will need for experiment to measure acceleration due to gravity.
- Any arduino board, preferably uno/duomilanove (no specific reason just that I have used this board for this experiment)
- USB cable for connecting arduino to PC
- 560 Ohm resistors (4 in quantity), 100 Ohm resistors (2 in quantity)
- piezoelectric sensor (4 in quantity)
- One pair of IR Tx (IR LED) and Rx(Photodiode)
- One potentiometer
- One opamp (like UA741C)
- One breadoard
- Three 1.2 meter long wires
- small 5cmx5cm general purpose PCB for assembling IR circuitry
- Tape
- Cardboard sheet
In case of any doubt look at the attached Images.
Step 3: Schematic 1: the IR Circuitary
This circuit will be used to time-stamp the starting time of free fall for an object used to measure ‘g’. Here are the important points about the fritzing schematic image.
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How can we measure the mass of the Earth?
We use an indirect method combining Newton's second law and universal gravitation to solve for mass using the formula M = (gr²)/G. -
What is the formula to find the mass of the Earth?
The derived equation is M = (gr²)/G, where g is acceleration due to gravity, r is the radius of the earth, and G is the Gravitational Constant. -
Can we place the Earth on a weighing scale?
No, there is no such weighing scale large enough to place the Earth on, so an indirect method is required. -
Which Arduino boards are suitable for this experiment?
Any Arduino board is acceptable, though Uno or Duomilanove are preferred as they were used for this specific experiment. -
How do we determine the value of g in this project?
We find g by conducting a small experiment involving an Arduino, piezoelectric sensors, and an IR circuit to time the free fall of an object. -
What is the function of the IR circuit in this setup?
The IR circuit is used to time-stamp the starting time of the free fall for the object being measured. -
Which opamp is recommended for the circuit assembly?
The UA741C opamp is suggested for use in the project's circuitry. -
How many piezoelectric sensors are needed?
Four piezoelectric sensors are required for the experiment.
