Gravitational Fields Flashcards
(23 cards)
What is a field?
A field is a space wherein each point is assigned a value.
A basic example of a field is a matrix, a two-dimensional grid of numbers.
How can a field be visualized?
A useful way to picture a field is as a thin rubber sheet, where height differences correspond to potentials.
Rolling a ball up a hill in this model illustrates how a positive potential is indicative of a repulsive field.
What are force fields?
Electric, magnetic, and gravitational fields are examples of force fields that can produce a force only in the presence of a second force field.
What is gravitational potential?
Gravitational potential is work done per unit mass when moving from infinity to a point in the field, measured in J kg⁻¹.
What is the value of gravitational potential at infinity?
Gravitational potentials are always negative (attractive), with the potential at infinity taken to be zero.
What does negative potential indicate?
In an attractive field, negative potential indicates that no work is needed to move from infinity to that point; instead the field does work on the mass.
What is given by the gradient of a potential-radius graph?
Field strength
What is gravitational field strength?
Gravitational field strength is force per unit mass, with units equivalent to acceleration, often referred to as acceleration due to gravity.
What do field lines represent?
Field lines represent the strength and direction of a field, and indicate the direction that a unit mass/positive test charge/north pole would move, if it were placed into the field at that point
What do equipotential lines indicate?
Equipotential lines indicate locations of equal potential in a field and are always perpendicular to field lines.
They’re a bit like contour lines on a map
What is the equation for work done in a gravitational field?
Work done (W) is calculated as W = m * V, where m is mass and V is gravitational potential.
State Newton’s law of gravitation
The attractive force between two masses is directly proportional to the product of the masses and inversely proportional to their separation squared.
What is escape velocity?
Escape velocity is the speed at which an object can escape the gravitational pull of a planet without further propulsion.
True or False: Gravitational fields are always attractive.
True.
Geometrically, what are the two types of fields that we need to know about?
- Radial
- Uniform
What is the reason objects stay in orbit?
Objects in orbit are a constant state of freefall, with their weight being equal to their centripetal force
What happens if an object in orbit starts going faster?
It will start spiraling outwards.
How do you calculate orbital velocity?
By putting centripetal force equal to gravitational force
This balance allows the derivation of the formula for orbital velocity.
What is a geostationary orbit?
An orbit where a satellite remains in a fixed position relative to the Earth’s surface by orbiting at the same rotational speed as the Earth.
Geostationary satellites are typically positioned at approximately 35,000 km above the equator.
What are the requirements for a geostationary orbit?
Orbit must be equatorial, have a period of 24 hours (which corresponds to an orbital radius of about 35000 km) and orbit anti-clockwise as viewed from celestial North
What type of orbit do most monitoring satellites follow?
Polar orbits.
Polar orbits allow satellites to pass over the entire surface of the Earth as it rotates.
State Kepler’s Third Law
The squares of the orbital periods of objects in orbit are directly proportional to the cubes of their mean distances from the bodies they’re orbitting.
How is Kepler’s Third Law mathematically expressed?
T² ∝ r³
