# 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 *F*= −_{g}*Gm*_{1}*m*_{2}*r*^{2}*F*=_{g}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 m^{2}/kg^{2})*m*_{1},*m*_{2}=mass of the two objects *r*=separation between the centers of the two objects vector notation **F**= −_{g}*Gm*_{1}*m*_{2}**r̂***r*^{2}**F**=_{g}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 × 10
^{−24}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*F*= 0 in Newton's law of universal gravitation._{g} - Gravity can be reduced (by moving far away from massive objects), but it can never be eliminated.

- There is no value of the separation,
- 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**=**F**_{g}*m***g**=gravitational field (gravitational field strength) **F**=_{g}gravitational force on test mass *m*=mass of test mass - Units
⎡

⎢

⎣N = m ⎤

⎥

⎦kg s ^{2} - 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