Gravitational fields Flashcards
Newton’s universal law of gravitation
All masses attract each other.
The strength of Fg of attraction between any 2 masses is proportional to the magnitude of each of the masses.
Inverse square law
Fg between 2 masses gets weaker as distance between them increases.
It’s inversely proportional to the square of the distance between the centres of the 2 masses.
Value of gravitational force
The value of the gravitational constant is very small, and over short distances, g-forces are generally weaker than electrical and magnetic forces.
Radially inward net force on a satellite.
Gravitational field
A vector field describing the property of space that causes an object with mass to experience a force in a particular direction.
The larger the primary mass, the greater the magnitude of g-field.
Fg of a body on Earth
“F on body by Earth”
Field
A physical quantity that has a value at each point in space.
Gravitational field strength
g in Nkg^-1
g-Field arrows
Show the direction of F that a mass at a point would experience.
Spacing of field lines
Indicate field strength - closer lines indicate a stronger field.
Why do field lines never touch/intersect?
As the force on an object cannot have multiple magnitudes or directions at the same time.
Why are g-fields non-uniform?
The field lines become further apart as the distance from a primary increases, showing that the field is weakening.
Primary
The body orbited by a smaller satellite or companion.
Earth’s g-field
Is static, it doesn’t change with time.
g-fields from 2 masses
The vector (direction) sum of the 2 fields
Acceleration from g-fields
When Fg is the only force acting on a mass, the mass is in ‘free fall’.
In free fall, acceleration experienced by the mass is equal to the g-field at that point in space.
Satellite
An object that’s orbiting a larger central mass. Satellites can be natural or man-made.
Circle a primary at constant speeds.
Centripetal acceleration
The acceleration towards the centre of a circle experienced by an object moving in a circular motion.
Causes velocity to constantly change direction.
Velocity
= 2 pi r / T
Orbital period
The time taken for a satellite to complete one orbit around a central object.
Newton’s gravitational relationship
G M / 4 pi ^2 = r ^3 / T ^2
Kepler’s 3rd Law
Applies to all satellites going around the same central mass.
(r1 / r2)^3 = (T1 / T2)^2
You must be consistent with units used.
Geostationary
Stationary relative to a point directly below it on Earth’s surface. A geostationary orbit has the same period as the rotation of Earth.
Geostationary satellites
Required to stay constantly above one place on Earth’s surface.
So, they must have an orbital period that’s the same as the time for the primary to complete one rotation about its axis.
Astronaut in a spacecraft
The astronaut’s acceleration is independent of the spacecraft.
There’s no normal force unless the astronaut is strapped to a surface.
Weightlessness
When there is no forces acting on a mass, no gravitational field, and therefore, the mass experience’s freefall.
Apparent weightlessness
When there is no normal force acting on a mass. As gravity is a non-contact force, it cannot be felt without any opposing force.
Kinetic energy
The energy associated with the movement of an object. A scalar quantity.
Gravitational potential energy
Energy stored in an object as a result of its position relative to another object (primary) to which it’s attracted by Fg.
Force-distance graph
The change in GPE = area under graph
Field-distance graph
The change in GPE = area under graph x mass as area = (newtons per kilogram) x metre, so we must multiply by mass to calculate energy.
G-field close to Earth’s surface
Is relatively constant as the distance from the primary doesn’t significantly vary.
