⇒ The Earth, other planets and stars produce gravitational fields, which exert a force on other massive objects

⇒ A gravitational field exerts a 'non-contact' force, which acts over very long distances

⇒ Gravitational field strength, g, is defined as the force that acts on a mass of 1kg. On Earth, g = 9.81 Nkg^-1

⇒ A planet's or stars gravitational field strength, at its surface, depends on its mass and radius

⇒ The gravitational potential energy, E_p (in J), gained by a mass, m (in kg), lifted through a height, h (in m), in a uniform gravitational field, g (in NKg), is given by E = mgh

⇒ The kinetic energy of an object is given by 1/2 m v²

⇒ Newton's law of gravitation states that the gravitational force of attraction between two point masses, m₁ and m₂ (measured in kg), separated by a distance, r (in metres), is given by:

⇒ This constant can only be accurately measured by careful laboratory experiment

⇒ Although Newton's law only applies to point masses, it can also be used to calculate the force of attraction between two large spherical objects (like planets and stars) because a sphere behaves as if all the mass were concentrated at the centre

⇒ So Newton's law can be correctly used to calculate the force of attraction in each of the cases above:

• In (a), the force between two point masses
• In (b), the force between a planet and a small mass
• In (c), the force between two planets or stars

⇒ Newton's law cannot be used to calculate the force between two irregularly shaped objects, unless a complicated summation of the forces is made

⇒ When Newton formulated his law of gravity, he imagined that the law of gravity spreads out in the same way as light spreads out from a candle

⇒ This image shows his idea

⇒ When you hold a card at a distance of 1m from the candle, you see a particular intensity of light, l

⇒ When you move a distance of 2m from the candle, the same amount of light now spreads out over four cards of the same area

• So the light intensity is now a quarter of its original value, 1/4 l

⇒ Light intensity obeys an inverse square law:

⇒ Here I is the intensity of light in W m^-2, L is the luminosity of the light source (the amount of energy emitted per second) in W, and r is the distance away from the light source in m

⇒ The factor 4π comes into the equation because the light spreads out into a sphere, and the surface area of a sphere of radius r is 4πr²

⇒ Also see our notes on:

• Gravitational Fields
• Gravitational Potential
• Escape Velocity
• Orbits