What is gravity?
Gravity is a pull that every object with mass has on every other object. Big objects like the Earth, the Moon and the Sun pull strongly, so we notice it. The Earth pulls everything towards its centre, so "down" for a person in India and "down" for a person in Brazil point in opposite directions in space.
The Sun's gravity keeps the planets going round it. The Earth's gravity keeps the Moon going round us and keeps our air from drifting away.
Free fall and g
When gravity is the only force acting, an object is in free fall. Its speed grows by the same amount every second. Near Earth this is g ≈ 9.8 m/s²: after 1 s the speed is 9.8 m/s, after 2 s it is 19.6 m/s.
Heavy and light objects fall together because a heavier object is pulled harder, but it also needs a bigger push to speed up. The two effects cancel. A feather falls slowly only because air pushes up on it; on the Moon, where there is no air, a feather and a hammer land together.
Mass, weight and standard gravity
Mass is how much matter an object has (kg). It never changes. Weight is the pull of gravity on that mass (newton, N): W = m × g. A 50 kg student weighs 490 N on Earth but only about 80 N on the Moon, where g is about 1.6 m/s².
Scientists agreed on a standard gravity of 9.80665 m/s² for weighing and calibration. Real g changes a little from place to place: about 9.83 at the poles and 9.78 at the equator. Rocks that are denser underground, such as a big ore body, pull a little more. Tiny differences like these are called gravity anomalies, and geologists measure them to look for what is hidden underground.
Orbits and escape speed
Throw a ball sideways. It curves down and lands. Throw faster and it lands farther away. The Earth's surface curves too, so at about 7.9 km/s the ball falls but the ground curves away just as fast: the ball keeps falling round the Earth. That is an orbit. A satellite is such a ball, launched high above the air.
At about 11.2 km/s (escape speed) a body can leave Earth for good. Each world has its own escape speed: the Moon's is only 2.4 km/s, so it cannot hold an atmosphere, while Jupiter's is 59.5 km/s. A planet keeps an atmosphere when its gravity is strong enough for the air to stay.
Try it
Drop a sheet of paper and a book together: the paper floats. Now put the paper flat on top of the book and drop both. They fall together, because the book pushes the air out of the way. Predict first, then check. Then use the sliders in the 3D above.
Key formulas and definitions
- W = m × g (weight in N, mass in kg, g in m/s²)
- g (Earth) ≈ 9.8 m/s²; standard gravity = 9.80665 m/s²
- v = g × t (speed of a body dropped from rest)
- s = ½ × g × t² (distance fallen from rest)
- Orbit speed near Earth ≈ 7.9 km/s; escape speed ≈ 11.2 km/s (≈ √2 × orbit speed)
- Moon g ≈ 1.6 m/s²; Jupiter g ≈ 24.8 m/s²
Worked examples
1. A stone is dropped from rest. Find its speed and the distance fallen after 3 s (g = 9.8 m/s²).
v = g t = 9.8 × 3 = 29.4 m/s. s = ½ g t² = ½ × 9.8 × 9 = 44.1 m.
2. A girl has mass 60 kg. Find her weight on Earth (g = 9.8) and on the Moon (g = 1.6).
Earth: W = 60 × 9.8 = 588 N. Moon: W = 60 × 1.6 = 96 N. Her mass is 60 kg in both places.
3. A bag weighs 49 N on Earth. What is its mass, and what does it weigh on the Moon?
m = W / g = 49 / 9.8 = 5 kg. On the Moon W = 5 × 1.6 = 8 N.
4. A 10 kg box is taken to Jupiter (g = 24.8 m/s²). What is its weight there?
W = 10 × 24.8 = 248 N. (On Earth it is 98 N, so it weighs about 2.5 times more.)
Common mistakes
- Saying mass and weight are the same thing. Mass is in kg and never changes; weight is in N and depends on g.
- Thinking heavy objects fall faster. In free fall all objects have the same g; only air resistance makes a feather slow.
- Thinking there is no gravity in space. Gravity is still strong at a satellite height; the astronauts are in free fall.
- Mixing units in a formula. Keep metres, seconds and kilograms together.