Universal Gravitation
Summary
- Gravitational Force
- Newton's law of universal gravitation states that any two objects with mass will experience a gravitational force that is…
- universal (acts on all objects)
- attractive (there is no such thing as antigravity)
- directly proportional to the mass of each object (mass makes gravity)
- inversely proportional to the square of the separation between their centers (inverse square rule)
- Equations
magnitude notation Fg = − Gm1m2 r2 Fg = magnitude of the gravitational force between two objects (Note: A minus sign is often added to the equation to show that the force is attractive. It is frequently ignored in practical calculations.) G = universal gravitational constant, often shortened to gravitational constant, or referred to informally as Big G (6.67 × 10−11 N m2/kg2) m1, m2 = mass of the two objects r = separation between the centers of the two objects vector notation Fg = − Gm1m2 r̂ r2 Fg = gravitational force vector between two objects r̂ = unit vector along the line separating the centers of the two objects (Note: The use of the minus sign here shows that the force vector points in the opposite direction of the separation vector. The force and separation have opposite sense.) - Since the universal gravitational constant is a "small" number, gravity is a "weak" force.
- The only object that exerts an appreciable gravitational force on other objects in daily life is the Earth.
- We perceive the gravitational force of the Earth because it is massive (5.97 × 1024 kg) and we are not normally far from it (usually less than 6,400 km from its center).
- A typical human can easily push up on a small patch of ground with a normal force that is equal to or greater than the gravitational force of the entire Earth pulling them down.
- The gravitational force between objects has infinite range.
- There is no value of the separation, r, that can make Fg = 0 in Newton's law of universal gravitation.
- Gravity can be reduced (by moving far away from massive objects), but it can never be eliminated.
- Gravity is the dominant force in the universe when energies are low and volumes are large (solar systems, galaxies, clusters, superclusters, and larger structures).
- Newton's law of universal gravitation states that any two objects with mass will experience a gravitational force that is…
- Field
- A field is…
- a physical quantity that has a value (or set of values) at every point in space and time
- a mathematical function that returns a value (or set of values) for every point in space and time
- a way to deal with philosophical arguments against action at a distance
- Fields can be…
- scalar fields associated with quantities such as…
- temperature
- pressure
- density
- electric charge
- vector fields associated with…
- the flow of fluids (the velocity field) such as…
- wind
- ocean currents
- solar wind
- non-contact forces (force fields) such as…
- gravitational field
- electric field
- magnetic field
- the flow of fluids (the velocity field) such as…
- tensor fields associated with…
- continuum mechanics quantities, namely the…
- stress tensor
- general relativity quantities such as the…
- metric tensor
- stress-energy tensor
- Ricci curvature tensor
- continuum mechanics quantities, namely the…
- scalar fields associated with quantities such as…
- A field is…
- Gravitational Field
- Magnitude
g = Fg m g = gravitational field (gravitational field strength) Fg = gravitational force on test mass m = mass of test mass - Units
⎡
⎢
⎣N = m ⎤
⎥
⎦kg s2 - Direction
- Gravity is described by a vector field.
- The direction of the gravitational field at any point in space is the direction of the net gravitational force on a "small" test mass.
- The gravitational field around a spherically symmetric mass is radial and points inward.
- Use vector addition to find the net gravitational field when more than one massive object is present.
- Magnitude