We are independent & ad-supported. We may earn a commission for purchases made through our links.

Advertiser Disclosure

Our website is an independent, advertising-supported platform. We provide our content free of charge to our readers, and to keep it that way, we rely on revenue generated through advertisements and affiliate partnerships. This means that when you click on certain links on our site and make a purchase, we may earn a commission. Learn more.

How We Make Money

We sustain our operations through affiliate commissions and advertising. If you click on an affiliate link and make a purchase, we may receive a commission from the merchant at no additional cost to you. We also display advertisements on our website, which help generate revenue to support our work and keep our content free for readers. Our editorial team operates independently from our advertising and affiliate partnerships to ensure that our content remains unbiased and focused on providing you with the best information and recommendations based on thorough research and honest evaluations. To remain transparent, we’ve provided a list of our current affiliate partners here.

What are Kepler's Laws?

Michael Anissimov
By
Updated Feb 25, 2024
Our promise to you
AllTheScience is dedicated to creating trustworthy, high-quality content that always prioritizes transparency, integrity, and inclusivity above all else. Our ensure that our content creation and review process includes rigorous fact-checking, evidence-based, and continual updates to ensure accuracy and reliability.

Our Promise to you

Founded in 2002, our company has been a trusted resource for readers seeking informative and engaging content. Our dedication to quality remains unwavering—and will never change. We follow a strict editorial policy, ensuring that our content is authored by highly qualified professionals and edited by subject matter experts. This guarantees that everything we publish is objective, accurate, and trustworthy.

Over the years, we've refined our approach to cover a wide range of topics, providing readers with reliable and practical advice to enhance their knowledge and skills. That's why millions of readers turn to us each year. Join us in celebrating the joy of learning, guided by standards you can trust.

Editorial Standards

At AllTheScience, we are committed to creating content that you can trust. Our editorial process is designed to ensure that every piece of content we publish is accurate, reliable, and informative.

Our team of experienced writers and editors follows a strict set of guidelines to ensure the highest quality content. We conduct thorough research, fact-check all information, and rely on credible sources to back up our claims. Our content is reviewed by subject matter experts to ensure accuracy and clarity.

We believe in transparency and maintain editorial independence from our advertisers. Our team does not receive direct compensation from advertisers, allowing us to create unbiased content that prioritizes your interests.

Kepler's laws are three equations which govern the motion of astronomical bodies. Kepler's laws were first discovered by the 17th century astronomer Johannes Kepler while analyzing data collected by Tycho Brahe. Kepler's laws are an extension of Copernicus's earlier heliocentric theory, and eventually paved the way for Isaac Newton's complete theory of how bodies interact. Newton's equations of gravity and motion can be used to derive Kepler's laws, if you assume that there are only two bodies, one of which is fixed, and one of which is orbiting at less than escape velocity. Although Kepler's laws were originally developed to explain planetary motions, they apply to any body which is in orbit around a much more massive body.

The first of Kepler's laws states that a planet, or any other object in orbit around the Sun, follows an elliptical path with the Sun at one focus. The shape of these ellipses depends on the Sun's mass, the planet's position, and the planet's velocity. A set of six numbers, called the Keplerian elements, can be used to specify the exact path that a planet traces out.

The second of Kepler's laws says that a planet in orbit traces out equal areas in equal times. If you draw a line from the planet to the Sun, and add up the area which the line sweeps over during a given time interval, it is always constant. This law is a consequence of the conservation of angular momentum; if the planet is moving faster, it also must be closer to the Sun. The increase in the area covered from the larger angular motion, and the decrease in the area covered from the shorter distance, must exactly cancel each other.

The third law states that the square of the period of the orbit must be directly proportional to the cube of the orbit's semi-major axis. The semi-major axis is half of the total distance between the perihelion, or closest approach to the Sun, and the aphelion, or farthest distance from the Sun. A planet very far from the Sun, such as Neptune, has a much larger orbit; it also moves more slowly, taking more time to cover the same distance than a planet such as Mercury. The exact relationship between orbital period, semi-major axis, mass, and the gravitational constant was later worked out by Isaac Newton.

AllTheScience is dedicated to providing accurate and trustworthy information. We carefully select reputable sources and employ a rigorous fact-checking process to maintain the highest standards. To learn more about our commitment to accuracy, read our editorial process.
Michael Anissimov
By Michael Anissimov

Michael is a longtime AllTheScience contributor who specializes in topics relating to paleontology, physics, biology, astronomy, chemistry, and futurism. In addition to being an avid blogger, Michael is particularly passionate about stem cell research, regenerative medicine, and life extension therapies. He has also worked for the Methuselah Foundation, the Singularity Institute for Artificial Intelligence, and the Lifeboat Foundation.

Discussion Comments

By anon245599 — On Feb 06, 2012

Kepler's area law for time taken can initially be expressed as the area of a triangle t=PXBX1/2. If r replaces both P and B we have t=rXrX1/2, but if the 1/2 becomes a power we have t=rXr^(1/2)which is Kepler's distance law v=r/t=1/r^(1/2) which applies throughout the whole universe.

By anon214263 — On Sep 14, 2011

I would appreciate it if someone could explain how to explain the third law. I'm doing a report and I'm stuck on the third law of planetary motion.

By anon118325 — On Oct 13, 2010

That was actually quite important. Mars is the most eccentric of the planets known at the time and so the elliptical nature of its orbit most visible.

Brahe was a very careful observer and Kepler knew this which meant that he could trust the data and had to move away from his original idea of nested geometrical solids.

By minombre — On Oct 13, 2010

It was while studying the orbit of planet Mars that gave Kepler the insight into two of his laws.

Michael Anissimov

Michael Anissimov

Michael is a longtime AllTheScience contributor who specializes in topics relating to paleontology, physics, biology...

Read more
AllTheScience, in your inbox

Our latest articles, guides, and more, delivered daily.

AllTheScience, in your inbox

Our latest articles, guides, and more, delivered daily.