3.7.2 Gravitational fields Flashcards
Properties of Gravity/Gravitational force
- Acts on objects with mass
- Always attractive
Newtons’s Laws of gravitation
- Directly proportional to the product masses
- Inversely proportional to the square of the distance between them
Gravitational Force Equation
F = (G * m1 * m2) / r²
Relationship between Mass and gravitational force
Larger masses exert greater gravitational force
Relationship between distance and gravitational force
Greater distance results in weaker gravitational force
Uniform Field
- Same gravitational force everywhere
- Represented by parallel, equally spaced field lines
Radial Field
- Force varies with position
- Field lines spread out as distance increases
Field Lines
- Direction of force on mass
- Closer lines indicate stronger force
Earth’s Gravitational Field
- Radial in nature
- Nearly uniform close to the surface
Gravitational Field Strength (g) (definition and variability)
Definition
* Force per unit mass exerted by a gravitational field
Variability
* Constant in uniform fields
Varies in radial fields
Formulas for Gravitational Field Strength
General Formula
* g = F / m
Radial Field Formula
* g = (G * M) / r²
Gravitational Potential
- Work done per unit mass
- Moving an object from infinity to a point
Gravitational potential at infinity
Zero
Is the Gravitational Potential positive or negative
Always negative due to energy release
Gravitational potential formula
Gravitational Potential Difference (ΔV)
Energy needed to move a unit mass between two points
Gravitational Potential Difference (ΔV) equation
Equipotential Surfaces
- Surfaces of equal gravitational potential
- Constant potential across the surface
- No work done when moving along these surfaces
* since gravitational potential difference = 0
V vs r relationship
gravitational potential(V) Inversely proportional to the distance between the centres of the two objects (r)
1.
area under g vs r graph
- gravitational potential difference
- Typically shows a decrease as distance increases.
Kepler’s Third Law
Square of orbital period (T) is directly proportional to the cube of radius (r)
How would you derive the equation
- Centripetal Force = Gravitational Force
- Rearrangement to find velocity (v)
- Substitute v² into gravitational equation
- (4π² / GM) is a constant
What is the total energy of a satellite
- Kinetic Energy + Potential Energy
- Constant total energy in orbit
Escape velocity
Minimum velocity to escape gravitational field
Synchronous Orbit
Orbital period equals rotational period of the planet
Equation for escape velocity
Geostationary Satellites
- Specific type of synchronous orbit
- Always above the same point on Earth
- Useful for communication (TV, telephone)
Calculating Geostationary Orbit
