Gravity Calculator

What is Gravity? Unveiling the Universal Force

Gravity is one of the four fundamental forces of nature, and it is the force that governs the motion of planets, stars, and galaxies. On a more familiar scale, it’s what keeps us anchored to the Earth, causes apples to fall from trees, and gives objects their weight. This Gravity Calculator is a versatile tool designed to explore this force through the lens of classical mechanics, as described by Sir Isaac Newton.

At its core, gravity is a natural phenomenon by which all things with mass or energy are brought toward (or gravitate toward) one another. Unlike the other fundamental forces—electromagnetism and the strong and weak nuclear forces—gravity has an infinite range, although its strength decreases with distance. It is also the weakest of the four forces, which is why you can easily overcome the Earth’s entire gravitational pull with your muscles by simply jumping. However, on a cosmic scale, gravity is the dominant force, shaping the structure and evolution of the entire universe.

The calculations in this tool are based on Newton’s Law of Universal Gravitation, a revolutionary idea from the 17th century that provides an incredibly accurate description of gravity for most practical purposes, from calculating satellite orbits to understanding the weight of an object on different planets.

Newton’s Law of Universal Gravitation Explained

Sir Isaac Newton’s law of universal gravitation, published in his Principia in 1687, was a monumental achievement. It states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The formula is one of the most famous in all of science:

F = G × (m₁ × m₂) / r²

Let’s break down the components:

• F is the gravitational force between the two objects, measured in Newtons (N).
• G is the Universal Gravitational Constant, an empirical physical constant with a value of approximately 6.67430 × 10⁻¹¹ N·m²/kg². Its incredibly small value is why gravity is the weakest of the fundamental forces.
• m₁ and m₂ are the masses of the two objects, measured in kilograms (kg). The formula shows that the more massive the objects, the stronger the gravitational pull between them.
• r is the distance between the centers of the two masses, measured in meters (m). This is the most impactful term.

The Inverse-Square Law

The “r²” in the denominator is critically important. This is known as an inverse-square law, and it means that as the distance between two objects doubles, the gravitational force between them decreases by a factor of four (2²). If the distance triples, the force decreases by a factor of nine (3²). This rapid drop-off in strength with distance is a key feature of gravity.

Mass vs. Weight: A Critical Distinction

One of the most common points of confusion in physics is the difference between mass and weight. While often used interchangeably in everyday language, they are distinct concepts. This Gravity Calculator can compute weight using the formula W = m × g.

Mass (m)

Mass is an intrinsic property of matter. It is a measure of an object’s inertia, or its resistance to being accelerated when a force is applied. An object’s mass is the same everywhere in the universe, whether it’s on Earth, on the Moon, or in deep space. It is measured in kilograms (kg).

Weight (W)

Weight is a force. Specifically, it is the gravitational force exerted on an object by a large body, like a planet. Since weight is a force, its value depends on both the object’s mass and the strength of the gravitational field it is in. It is measured in Newtons (N).

Your mass (the amount of “stuff” you are made of) is constant, but your weight changes depending on where you are. You would weigh about one-sixth as much on the Moon as you do on Earth because the Moon’s gravitational pull is weaker, even though your mass remains the same.

Calculating “g”: The Acceleration Due to Gravity

The term ‘g’ represents the acceleration that an object experiences due to the force of gravity when in free fall. On the surface of the Earth, this value is approximately 9.81 m/s². But where does this number come from? We can derive it by combining Newton’s two most famous laws.

1. Newton’s Second Law of Motion: F = m × a (Force equals mass times acceleration)
2. Newton’s Law of Universal Gravitation: F = G × (M × m) / r²

If we consider an object of mass ‘m’ near the surface of a large body like Earth (with mass ‘M’), both formulas describe the same force acting on the object. Therefore, we can set them equal to each other:

m × a = G × (M × m) / r²

Notice that the mass of the smaller object, ‘m’, appears on both sides and can be canceled out. This is a profound result: it means the acceleration an object experiences due to gravity is independent of its own mass (in a vacuum, a feather and a bowling ball fall at the same rate). The acceleration ‘a’ is what we call ‘g’.

g = G × M / r²

• G is the Universal Gravitational Constant.
• M is the mass of the large body (e.g., a planet).
• r is the radius of that body.

The “Acceleration (g)” mode of our Gravity Calculator uses this formula to find the surface gravity of any celestial body if you know its mass and radius.

Beyond Newton: Einstein and the Curvature of Spacetime

While Newton’s Law of Universal Gravitation is incredibly accurate for most applications, Albert Einstein’s Theory of General Relativity, published in 1915, provided a more complete and profound understanding of gravity. It is the model used by modern physics to describe the universe on a large scale.

General relativity describes gravity not as a force, but as a consequence of the curvature of spacetime. Einstein proposed that massive objects do not “pull” on other objects; instead, they warp or bend the very fabric of spacetime around them. Other objects then move along the straightest possible paths (called geodesics) through this curved spacetime. We perceive this motion along a curved path as the effect of gravity.

An Analogy: Imagine a stretched-out rubber sheet. If you place a heavy bowling ball in the center, it will create a dip or a curve in the sheet. If you then roll a small marble nearby, it won’t be “pulled” by the bowling ball directly; instead, it will follow the curve in the sheet created by the bowling ball’s mass, causing it to spiral inward. This is analogous to how planets orbit the Sun.

For everyday calculations like those performed by this Gravity Calculator, the difference between Newton’s and Einstein’s predictions is infinitesimally small. However, general relativity is essential for explaining extreme gravitational phenomena like black holes, the bending of light by gravity (gravitational lensing), and the precise orbits of planets like Mercury.