Gravitational and Electric Fields Flashcards
What is a gravitational field?
A force field where any object with mass will experience an attractive force
What is a point mass?
A mass with negligible volume, or a uniform sphere whose mass acts as if it’s concentrated at the centre
What is the law of gravitation?
- An inverse square law
- Force is proportional to the inverse of distance between two point masses squared
Define gravitational field strength
The force per unit mass, in N/Kg
What is the approximate value of g on Earth?
9.81N/kg
Describe the graph of g against r for Earth
- Exponential when x = Re, where Re is the surface of the Earth
- Exponential where g = 9.81N/kg
- L shaped
Define gravitational potential
The gravitational potential energy that a unit mass would have at a specific point
Why is gravitational potential negative?
As work is being done against the gravitational field to move an object out of it
Describe the graph of V against r
- x axis(r) at the top, y axis(V) negative to zero
- Exponential when x = The radius of the sphere
- r shaped curve
What is gravitational potential difference?
The energy needed to move a unit mass
Derive the equation for gravitational potential energy
- ∆W = m ∆V
- ∆Potential energy = m ∆V
- Potential energy = m(-GM/r) = -GMm/r
What are equipotentials?
Lines(in 2D) or surface(in 3D) that join all the points with the same gravitational potential
- This means ΔV = 0 and as ΔW = mΔV, work done is also 0
What is a satellite?
Any smaller mass which orbits a much larger mass
How are satellites kept in orbit?
By the gravitational pull of the mass they’re orbiting
Derive the equation for the orbital speed of a satellite
- F = mv²/r and F = GMm/r
- mv²/r = GMm/r
- v² = GM/r
- v = √GM/r
What is the relationship between orbital speed and orbital radius of a satellite?
- Orbital speed is inversely proportional to the square root of orbital radius
- v = √GM/r
- v = √1/r
What is the orbital period?
The time taken for a satellite to complete one orbit
Derive the equation for the orbital period of a satellite
- s = d/t , so v = 2πr/T
- T = 2πr/v = 2πr/√GM/r
- T = 2πr√r/√GM
- T² = 4π²r³/GM
What is the relationship between orbital period and orbital radius of a satellite?
Orbital period squared is proportional to the orbital radius cubed
What is the on the y-axis and x-axis of a graph on orbital period?
- y axis: Period, in years
- x axis: orbital radius, in
x10⁶ m
How would kinetic and potential energies change for a satellite in an elliptical orbit?
- As the radius decreases, satellite speeds up, increasing kinetic energy and decreasing potential energy
- Total of kinetic and potential energy is always constant
Define escape velocity
The minimum speed an unpowered object to leave the gravitational field of a planet and not be pulled back due to gravitational attraction