Weight Near a Celestial Body’s Surface

Multiply mass m by the local gravitational acceleration g: F_G=mg. For 12 kg on Earth with g≈9.81 m/s², the result is 117.72 N. The unit follows from kg·m/s²=N. Use mass in kilograms and g in metres per second squared; convert grams first. Near Earth’s surface g is approximately constant, but not exactly the same everywhere. For another celestial body, insert its local gravitational acceleration. The force points toward the body producing the gravitational field. The formula gives magnitude; add direction as a vector toward the attracting body in a force diagram.

No. Mass m describes the body and is measured in kilograms; it stays nearly the same when moving from Earth to the Moon. Weight F_G is a force measured in newtons and also depends on local g. The same mass weighs less on the Moon than on Earth. A scale may measure force and display a kilogram value because it is calibrated for a particular gravitational acceleration. In physics problems, keep kg for mass distinct from N for force. Units provide a useful error check: one newton is exactly one kg·m/s².

Weight depends on g, and gravitational field strength varies with the celestial body and distance. Near sea level on Earth, g is about 9.81 m/s²; on the Moon it is roughly 1.62 m/s². At greater altitude above Earth, gravity also becomes slightly weaker. For everyday heights, g can usually be treated as constant. For satellite orbits or large distances, that approximation becomes inaccurate, so use the general law of gravitation. The mass m does not change in either case. Mass and weight have different units and must not be identified even when using an everyday scale.

First choose the body as your system, then draw F_G at the body pointing downward, toward Earth’s centre. Arrow length represents the force magnitude; choose it proportionally to mg and label it with the symbol or value. Do not assume weight is the only force: a support usually exerts a normal force, and a hanging object has tension. An object at rest still has weight; other forces may balance it. A free-body diagram shows each external force separately. The normal force from a surface is a separate force, not another name for weight.

The shortcut assumes an approximately uniform field, so g stays nearly constant over the region considered. This is a good approximation near a surface for small height changes. At large altitude, long distances, or in orbital calculations, g changes noticeably; use the gravitational law F=GmM/r² with distance from the centre. On another celestial body, use its value of g as well. Check whether the problem concerns a near-surface situation. For an ordinary school experiment with falling bodies, mg is usually the appropriate local formula. If the problem gives g, use that local value instead of automatically inserting 9.81 m/s².