Chapter 7: Newton & His Orbits

Abhinav Yadav
5 min readMar 5, 2022



Sir Isaac Newton was born on Christmas Day 1642 in England. The same year that Galileo passed away in Italy. Make what you will of that, but no one can deny the significant boost that Newton’s genius gave to Science. In some ways he picked up right where Galileo left. Most importantly, Newton proved to be a bridge between early natural philosophy and modern empirical science.

The range of subjects Newton touched are often overlooked, like his work on Alchemy and Theology. Though his work in mathematics, physics and astronomy elevated him to a whole other level. His three Laws of Motion, explanation of Gravity and work in Optics, are his monumental contributions to Physics. His development of Calculus, almost on a dare, gave mathematicians a powerful new tool. His seminal work in Optics, specifically with Prisms, led him to understand that light consists of colors of the visible spectrum and helped him in constructing the first practical reflecting telescope. His genius knew no bounds.

By giving us an universal gravitational law, Newton was able to explain how an apple falling on Earth is governed by the same law that makes Moon orbit the Earth. His mathematical mastery was used to understand trajectories of comets, the cycle of tides, and planetary motion. His work put to rest any doubts about our Sun being the center of every planetary motion, or Heliocentrism, the very idea that Galileo had been vilified for supporting.

In their entirety, Newton’s contributions increased the pace of scientific development and led to the Industrial Revolution. Only another genius was able to improve upon Newton’s gravitational law, and 200 years later at that. Even those improvements are only necessary when dealing with very high speeds or very large mass, something most of us Earthlings don’t deal with.

Newton’s own copy of his Principia, with hand-written corrections for the second edition, in the Wren Library at Trinity College, Cambridge.

To establish a universal law of gravity, Newton had to figure out why an apple fell straight down, while the Moon continues to orbit the Earth. So he did a thought experiment. Suppose you are holding a ball in your hand and you drop it. It should fall straight down, like Newton’s apple. Now you throw it in front of you with some force. It should go a little further out, before falling on the ground. Now suppose you want to throw it further out, maybe you are playing football and want to throw a Hail Mary pass. Obviously you’ll need to throw with lot more force, but the ball will follow a similar trajectory of an arc, where it will go up and eventually fall back down (hopefully in the hands of your receiver). So we have established that we need to use more force in order to throw the ball further out.

From Newton’s De mundi systemate (A Treatise of the System of the World). It is part of the image collection on the Voyager Golden Record that is being carried into deep space aboard the Voyager 1 and 2 spacecraft.

Newton obviously took it to the next level with his cannonball thought experiment. Suppose now you are on top of a mountain with a cannon and you fire that cannon dead straight. The cannonball will fall down after traveling a certain distance. Now let’s say you bring an even more powerful cannon and then fire another shot. This cannonball should travel a longer distance before falling down to the ground. So some force is pulling this cannonball down. But you can begin to overcome it by throwing projectiles at greater speeds. So the question that intrigues Newton is — can there be a speed at which cannonball can be fired so that it never touches the ground and makes a full circle around the Earth to come back behind you.

This mathematical genius turns his thought experiment into a numerical problem and calculates such a speed where cannonball will not touch the ground. This becomes Earth’s orbital speed, which comes to about 7,300 m/s, for Earth’s surface. If the projectile’s speed is less than that, it will fall back to Earth. If the speed is greater than 7,300 m/s, but not more than Earth’s escape velocity (10,000 m/s), the projectile’s orbit will form an Ellipse. If the speed is greater than Earth’s escape velocity, the projectile will leave Earth and venture into space.

A Wood engraving of Newton’s famous steps under the apple tree. Credit

The cannons and mountains for us now are the powerful rockets that take satellites into orbit around the Earth. One orbit takes about 90 mins to complete. Our very own International Space Station captures some amazing details of Earth’s surface as it completes multiple orbits during one Earth day.

Newton used the Latin word gravitas (weight) for the effect on objects being pulled towards Earth. Every educated soul on this planet can point to the story of an apple falling and where it all began.

Newton was also a complicated person, with bitter rivalries developed over time with some of the most influential scientists of his era. For example, the development of calculus was also claimed by Leibniz. Though it’s widely accepted now that both of them developed it independently. Then there was strong opposition to his theory of gravity expressed by Christiaan Huygens and Leibniz. Both of whom saw the theory as invoking an occult power of ‘action at a distance’ in the absence of Newton’s having proposed a contact mechanism by means of which forces of gravity could act. This only delayed acceptance of Newton’s law of gravitation. But in the end, these rivalries were just a footnote in his scientific achievements.

Newton was a member of the Parliament of England for Cambridge University in 1689 and 1701. He also took the post of warden, and then master of the Royal Mint in 1696. Knighted by Queen Anne in 1705, Newton became only the second scientist to be knighted.

Newton passed away in 1727 and was given a ceremonial funeral, attended by nobles, scientists, and philosophers. He was buried in Westminster Abbey among kings and queens. The sheer volume of papers he left behind would take many years of research to go through.

A drawing of Sir Isaac Newton dispersing light with a glass prism. Photo: Apic/Getty Images

There’s probably no better tribute to him then what English poet Alexander Pope wrote in his famous epitaph:

Nature, and Nature’s laws lay hid in night.
God said, Let Newton be! and all was light.



Abhinav Yadav

Engineer. Optimist. Top Writer in Space 🚀 🔭🌌