The question of where a person would weigh the most is fundamentally about the strength of gravity, which varies significantly depending on location. Weight is a measure of the force of gravity acting on an object’s mass, meaning it changes with the local gravitational pull. While the amount of matter in an object, known as its mass, remains constant everywhere, weight depends entirely on the local gravitational field strength. This distinction is key to understanding how measurements on a scale differ across the Earth and the solar system.
Understanding Weight Versus Mass
In physics, mass is an intrinsic property of an object, representing the amount of matter it contains. A person with a mass of 70 kilograms on Earth will maintain that same mass if they travel to the Moon or float in deep space. Unlike mass, weight is a force exerted on an object by gravity and is properly measured in units like Newtons.
This force is governed by Newton’s Law of Universal Gravitation. The law states that gravitational force is directly proportional to the product of the objects’ masses and inversely proportional to the square of the distance between their centers. This inverse square relationship means that even a small increase in distance from a massive body results in a rapid decrease in gravitational force, and consequently, a person’s weight.
Weight is mathematically expressed as the product of an object’s mass (\(m\)) and the local acceleration due to gravity (\(g\)). The standard value of \(g\) on Earth is approximated as \(9.8\) meters per second squared. However, the actual force of gravity, and thus the weight, changes based on location because the local \(g\) value is not uniform. Any factor that alters the planet’s mass or the distance to its center will cause a person’s weight to vary.
Factors Causing Weight Variation on Earth
Even on Earth’s surface, a person’s weight is not perfectly constant, with measurable differences between various locations. The primary factors causing these variations are the Earth’s rotation and its non-spherical shape. The force of gravity is greatest at the poles and weakest at the equator.
The Earth’s rotation creates a slight outward centrifugal force that acts against gravity. This force is greatest at the equator, where rotational speed is highest, and non-existent at the poles, contributing to a lower apparent weight near the equator. This rotation has also caused the planet to bulge slightly, making the equatorial radius approximately 21 kilometers greater than the polar radius.
Since gravity weakens with the square of the distance, being farther from the Earth’s center at the equator results in a weaker gravitational pull. The combined effect of the equatorial bulge and the centrifugal force means an object will weigh approximately 0.5% more at the poles compared to the equator.
Weight also slightly decreases with altitude because higher elevation means a greater distance from the Earth’s center of mass. Moving from sea level to the top of a mountain decreases weight by a small amount, though this effect is minor compared to the pole-to-equator difference. Local geological density variations, such as underground mineral deposits, also cause minor, localized gravitational anomalies.
Where Maximum and Minimum Weight Occur in the Solar System
Moving beyond Earth, the location where a person would weigh the most is determined by the most massive celestial body. While the Sun is the most massive, standing on it is not practically possible. Therefore, the planet that offers the highest surface gravity is Jupiter, whose immense mass gives it a surface gravity almost two and a half times that of Earth.
On Jupiter, the acceleration due to gravity is approximately 24.79 meters per second squared, meaning a person who weighs 154 pounds (70 kg) on Earth would weigh about 370 pounds (168 kg) on Jupiter. While other massive bodies like Saturn also have high gravity, Jupiter’s combination of mass and radius gives it the highest practical surface gravity among the planets. The absolute theoretical maximum would be a compact object like a neutron star, but this is not a location where a human could exist.
The minimum weight occurs in environments with the weakest gravitational fields. The Moon has a significantly lower surface gravity, only about one-sixth of Earth’s, where a person would weigh substantially less. Similarly, Mars’s gravity is about 38% of Earth’s, where one would weigh less than half their Earth weight. The theoretical minimum weight would be experienced in deep space, far from any significant source of gravity, or while in orbit, which is a state of continuous freefall, resulting in apparent weightlessness.