Weight on Earth, Moon & Space
Weight is not a fixed property of an object — it changes depending on where in the universe that object happens to be. This surprises many students who confuse weight with mass. Mass is the amount of matter in an object, measured in kilograms, and it never changes regardless of location. Weight, by contrast, is the gravitational force acting on that mass. Since gravitational field strength varies from planet to planet, from the surface to orbit, and even slightly across Earth's own surface, so too does weight. On Earth, the gravitational field strength is approximately 9.81 N kg⁻¹, meaning every kilogram of mass experiences roughly 9.81 newtons of gravitational pull downward. On the Moon, the field strength drops to about 1.62 N kg⁻¹ — just one sixth of Earth's value — because the Moon is less massive and smaller. An astronaut who weighs 735 N on Earth would weigh only around 122 N on the lunar surface, yet their mass remains exactly 75 kg throughout. This distinction is fundamental to understanding motion in space. In orbit around Earth, astronauts appear weightless — floating inside the International Space Station as though gravity has vanished. In reality, gravity is still very much present (around 8.7 N kg⁻¹ at orbital altitude). The sensation of weightlessness arises because both the astronaut and the spacecraft are in continuous free fall around Earth. This is called apparent weightlessness, and it is a crucial concept for understanding satellite motion and human spaceflight.
- Mass vs Weight
- Gravitational Field Strength on Different Bodies
- Weight in Orbit and Apparent Weightlessness
- Apparent Weight in Lifts and Acceleration
Mass vs Weight
Mass (m) is a scalar quantity measured in kilograms (kg). It represents the total amount of matter in an object and is invariant — it does not change with location. Weight (W) is a vector force measured in newtons (N), directed toward the centre of the gravitational body. The relationship between the two is W = mg, where g is the local gravitational field strength in N kg⁻¹. Think of mass as 'how much stuff' and weight as 'how hard gravity pulls on that stuff'.
Gravitational Field Strength on Different Bodies
Gravitational field strength g depends on the mass and radius of the astronomical body: g = GM/r². Earth has g ≈ 9.81 N kg⁻¹ at its surface. The Moon, being about 81 times less massive than Earth and having a smaller radius, has g ≈ 1.62 N kg⁻¹. Mars has g ≈ 3.72 N kg⁻¹. Jupiter, being much more massive, has g ≈ 24.8 N kg⁻¹ — nearly 2.5 times Earth's. A 70 kg person would weigh 687 N on Earth, 113 N on the Moon, but a crushing 1736 N on Jupiter.
Weight in Orbit and Apparent Weightlessness
The International Space Station orbits at roughly 400 km above Earth's surface. At that altitude, g ≈ 8.7 N kg⁻¹ — only about 11% less than on the surface. Astronauts are not outside gravity's reach; they are in free fall. Because the station and every object inside it fall together at exactly the same rate, there is no contact force between an astronaut and the floor. A bathroom scale would read zero. This reading — the normal force — is what we call apparent weight. True weight (mg) still acts; apparent weight is zero.
Apparent Weight in Lifts and Acceleration
Apparent weight is the force registered by a scale, equal to the normal contact force. Even on Earth, apparent weight changes with acceleration. In a lift accelerating upward, the scale reads more than your true weight: W_apparent = m(g + a). Accelerating downward, it reads less: W_apparent = m(g − a). In free fall (a = g downward), the apparent weight is zero. This is exactly what happens in orbit — continuous free fall produces zero apparent weight, even though true gravitational weight remains substantial.
The Key Equation
- W — Weight (Newton (N)): The gravitational force acting on the object; a vector pointing toward the centre of the gravitational body.
- m — Mass (Kilogram (kg)): The amount of matter in the object; a scalar that does not change with location.
- g — Gravitational field strength (N kg⁻¹ (equivalent to m s⁻²)): The gravitational force per unit mass at a given location. On Earth g ≈ 9.81 N kg⁻¹; on the Moon g ≈ 1.62 N kg⁻¹.
Worked Example
Problem. An astronaut has a mass of 80 kg. Calculate their weight (a) on Earth's surface where g = 9.81 N kg⁻¹, (b) on the Moon where g = 1.62 N kg⁻¹, and (c) state their mass on the Moon.
Answer. Weight on Earth ≈ 785 N; Weight on Moon ≈ 130 N; Mass on Moon = 80 kg (unchanged).
Origins · 1 minIsaac Newton and how this was discovered
Newton formulated the Law of Universal Gravitation in his 1687 masterwork Principia Mathematica, establishing that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between them (F = GMm/r²). This single law explained planetary orbits, falling apples, and ocean tides. It underpins the modern understanding of weight as a gravitational force: W = mg follows directly from Newton's law when considering objects on or near a planet's surface. Newton reportedly deduced his law of gravitation while sheltering at his family home in Woolsthorpe during the Great Plague of 1665–66. He later recalled that watching a falling apple set him thinking about whether gravity might extend all the way to the Moon — a thought experiment that changed physics forever.
Related Concepts
- Mass and Inertia — Mass is the invariant quantity that weight depends upon; understanding inertia clarifies why mass and weight are fundamentally different properties.
- Newton's Law of Universal Gravitation — The formula W = mg is derived from Newton's universal law, which explains why gravitational field strength g differs between Earth, Moon, and other bodies.
- Gravitational Field Strength — Gravitational field strength g is the key variable that determines weight at any location; this concept explains how g is calculated and why it varies.
- Orbital Motion and Satellites — Orbital motion is the mechanism behind apparent weightlessness in space stations — understanding orbits explains why astronauts float despite gravity being present.