A field is a region of space where a force is experienced:
- Gravitational fields - objects with mass
- Electrostatic fields - objects with charge
- Magnetic fields - moving charges or permanent magnets
Key Concepts
Gravity is the phenomenon by which objects with mass are attracted to one another.
To describe a region of space where a body experiences a force we use the term field. A gravitational field is a region where a mass experiences a force due to its mass. The force is also dependent on the mass of the body \(F=mg\).
Instead of using the term gravity:
- Weight refers to the force acting downwards on objects close to the surface of the Earth
- Gravitational force refers to the force acting between objects in radial fields
NB: Take time to consider the Earth's gravitational field in each question, as our model varies depending on distance away. Is it uniform and parallel or radial from the centre?
Gravitational field strength is the gravitational force per unit mass experienced by a small test mass* placed in the field:
\(g={F_G\over m}\)
Gravitational field strength has units Nkg-1. While dimensionally equivalent to ms-2, avoid making this reference to acceleration here.
*The reference to a small test mass means that the shape and magnitude of the field is not influenced by the introduction of another mass.
Field lines are drawn to show the direction and strength of the field. There are some features to note:
- The proximity of lines gives the strength of the field
- The direction of the arrows is the direction in which a test mass would move
- Field lines must not cross; they always show a resultant direction
- Field lines are perpendicular to equipotentials, lines of constant gravitational potential energy (literally like contours on a map)
Field strength is a vector quantity so must be added vectorially. Using this simulation you can observe how the resultant field changes as you move around the field.
Newton wasn't able to go into space to measure the gravitational force but realised that the origin of the force causing an apple to fall to the earth was the same as the force holding the planets in orbit around the Sun. He was also convinced that this could be explained with a single mathematical equation.
Every particle of mass attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation squared.
\(F=G{Mm \over r^2}\)
In this equation, \(G\) is the universal gravitational constant, 6.67 × 10-11 m3kg-1s-2.
The gravitational force can provide the centripetal force required to cause a body to move in a circle.
In the absence of other forces (a very reasonable assumption in space), we can equate the gravitational force to the centripetal force to derive Kepler's Third Law:
\(F_G={GMm\over r^2}={mv^2 \over r}\)
\({GM\over r}=v^2={(2\pi r)^2\over T^2}\)
\(\Rightarrow {T^2 \over r^3}={4\pi ^2\over GM}\)
Kepler's Third Law tells us that the ratio of T2 to r3 is constant for any body orbitting a common centre. This means that, for example, we could work out the distance from any planet to the Sun if we knew its length of year.
Since everything on the right hand side is constant, we can also say that:
\(({T_1\over T_2})^2=({r_1\over r_2})^3\)
Why don´t satellites fall down?
Is it possible to have a satellite above the same point on the Earth at all times?
How much of Gravitation have you understood?
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