Unit 4: Gravitation, Newton's Law

Gravity can be defined as an universal attractive force acting between points of matter.

•  F= -- Gm₁m₂/ r² where G is the gravitational constant (6.67x10-¹¹)

Specifically, the equation describes negative downward motion, but because force is a scalar, it does not have direction, only magnitude, the sign is not necessary.

The force is directly proportional to the product of the masses, while the square of the radius is inversely proportional. 

•  G= Universal Gravitational Constant, 6.67x10-¹¹ Nm²kg-²
•  g= Gravitational Field Strength, on Earth, 9.81 Nkg-¹
•  g= Acceleration due to Gravity, on Earth, 9.81 ms-²

Forces cause acceleration, so both go towards the centre, when centripetal force is acting. This is why the two gs are always the same, even when not on the Earth’s surface.

For a satellite, the centripetal acceleration= acceleration of free-fall at that altitude= g at that point.

Gravitational field strength on the surface of a planet, g₀= GM/r² may appear to suggest that the magnitude of g inside the Earth becomes larger and larger as r gets smaller. However, inside the planet, only the mass in the sphere contributes to g, as up until the surface, the mass has no Resultant force. So inside the Earth, as r gets smaller, g also gets smaller, as the mass that contributes to g gets smaller. Therefore g = 0 at the centre. 

Density is mass per unit volume. 

•  ρ = m/V
•  m…