It might not be noticeable to anyone but every time a DART pulls out of a station, it has an effect on the Earth.
"Every action has an equal and opposite reaction."
Isaac Newton is one of the most famous scientists who ever lived. His book, Philosophi Naturalis Principia Mathematica, revolutionised science when it was published in 1687 and became the foundation of how we describe how things move. We call this classical mechanics. After its publication, his views on the laws of motion and gravitation went largely unchallenged by mainstream science for the next 300 years.
Newton invented calculus (for which he shares credit with Leibniz), began a theory of light and colour, and figured out many of the concepts that would eventually become the Principia over the course of just two summers, in 1665 and 1666 when Cambridge University was closed because of the Black Death.
Newton is commemorated in the unit used to measure force, which of course is the 'newton'.
Therefore you accelerate far more than the Earth does. So, while you might jump a metre in the air (if you're lucky), the Earth only moves by an infinitesimal amount.
The engine causes the wheels on the train to move off from the station. The wheels push on the track and the track pushes back with an equal and opposite force. So the Earth moves a tiny, tiny bit.
An object will stay still or will continue to move until a force acts on it. In simple terms: you'll stay as you are until some force is applied to you. This might be a stationary football that doesn't move until it’s kicked, or a bullet that flies through the air until air resistance (a force) causes it to slow down.
The amount of acceleration an object experiences depends on the mass of an object and the force that's being applied to it. Consider the example of a person jumping given above – the force of the jump is applied equally to the person as to the Earth. The Earth is big and massive so it’s acceleration is tiny, meaning it won’t be affected much. But the person has far less mass, and so accelerates more, in this case, upwards.
As we've been looking at above, the third law states that for every action, there is an equal and opposite reaction. Whatever the action is – pushing, pulling, throwing – there are a pair of forces working on the interacting objects. The forces are equal in size, but opposite in direction. These laws form the basis of our understanding of how the physical world operates.