Gravitational field

The acceleration due to gravity, often written as 'g', is simply how fast an object speeds up when it falls freely under Earth's pull. Every object on Earth experiences this same acceleration of approximately 9.8 m/s² (or 10 m/s² for quick calculations). This means if you drop something from a height, its speed increases by about 10 metres per second every single second it falls.

Think about dropping a mango from a tall tree in your backyard. In the first second, it reaches a speed of 10 m/s. In the second second, it's moving at 20 m/s. The value of g changes slightly depending on your location on Earth—it's about 9.78 m/s² at the equator but slightly higher at the poles because Earth isn't perfectly round.

The formula connecting this to weight is: Weight = mass × g, which is why your mass stays the same everywhere but your weight changes slightly between countries.

Every object with mass attracts every other object with mass. Newton discovered that this gravitational force depends on two things: how massive the objects are and how far apart they are. The bigger the masses, the stronger the pull between them. The farther apart they are, the weaker the attraction becomes.

Think about the Moon orbiting Earth. Earth's huge mass pulls on the Moon constantly, keeping it in orbit around us. Without this invisible gravitational force, the Moon would fly off into space. The same force keeps you standing on the ground—Earth is pulling you downward.

The mathematical relationship is: F = Gm₁m₂/r². This means force equals the gravitational constant times both masses divided by the distance squared. Notice that distance matters most because it's squared.

Gravitational potential measures how much energy an object needs to escape from a planet's gravitational pull. Think of it like this: when you throw a ball upward, Earth's gravity pulls it back down. But if you throw it fast enough, it could escape Earth completely. That minimum speed is called escape velocity.

Escape velocity from Earth is approximately 11.2 km/s. This is why rockets need such powerful engines to reach space. On the Moon, escape velocity is only about 2.4 km/s because the Moon is much smaller and has weaker gravity than Earth.

The faster a planet's escape velocity, the stronger its gravitational field. Jupiter, being massive, has an escape velocity of about 61 km/s, making it incredibly difficult for objects to leave. These concepts explain why some celestial bodies hold onto atmospheres while others cannot.