12-The gravitational field Flashcards
When an object is moving in a circular path, where is its acceleration directed towards?
The centre
What is the acceleration of an object moving in a circular path?
v squared / radius
What is the centripetal force?
The force producing the centripetal acceleration
What is the equation of the centripetal force?
Force = m v squared / radius
What is the equation of the speed of an object moving in a circle?
Circumference / time taken
What is the angular velocity?
The number of radians per second an object travels past when moving in a cricle?
What does the centripetal acceleration equal in terms of angular veclocity?
a = w^2 r , as v=wr
What direction does the force always act in relation to the motion of the body?
At right angles to the motion of the body
Before his experiments, what did Newton already know?
- How rapidly an apple accelerated to the ground
- He could calculate the acceleration of the moon towards the earth using v^2 / r
How did Newton calculate the acceleration of the moon from motion?
Using the equation a = v^2 / raDIUS
How did Newton calculate the acceleration of the moon from the inverse square law?
He found ratio of moon’s orbit to earth’s radius = 60, and did 9.8 X 1/60^2, and found that the acceleration was equal to the one found from motion(0.0027ms^-2)
What is the core principle of Newton’s theory of gravity?
All particles in the universe attract all other particles
What is the force of gravity between 2 mass bodies of M and m?
F = -GMm / r^2
What law does the force of gravity obey?
The inverse square law
What does the gravitational field strength describe?
The effect of a gravitating body M, regardless of the mass placed near it
What is the equation of the gravitational field strength?
g = -Gm /r^2
What does mg therefore equal?
mg = -GMm / r^2
What law does the gravitational field strength obey?
The inverse-square law
How is the gravitational field direction shown on a diagram?
By the direction of the lines
How is the gravitational field strength shown on a diagram?
By the closeness of the lines
What is the gravitational field strength inside earth proportional to?
The distance from the centre
What is the gravitational field strength at the centre of the earth?
0
What happens to the gravitational field strength beyond the radius?
Is decreases (not linearly)
What would happen if a geostationary staellite was positioned too close to the earth??
It will orbit the earth too quickly
What will happen if a geostationary satellite was positioned too far from the earth?
It will orbit earth too slowly
What 2 equations do you make equal each other to find the correct orbital radius?
The force producing the acceleration towards the centre mv^2 / R and the gravitational force on satellite GMm / R^2
When calculating orbital radius, what do we find R^3 is proportional to?
T^2 (time of orbit)
Near the surface of the earth, what is the change in gravitational potential energy with height?
mgh
What is the gravitational potential?
The gravitational energy per kilogram of material, gh
For calculations near the surface of the earth, what does the gravitational potential increase by?
9.8J/Kg for every metre raised
What are equipotential surfaces?
Surfaces of constant potential, where the increase in gravitational potential is constant
What is the distinguishing characteristic of a uniform field?
The separation between the 0 and 10J/Kg equipotential (potential difference of 10) is the same as the separation between the 10J/Kg and 20J/Kg equipotential
What is the change in energy when moving a distance s along an equipotential?
Force X Distance
What does the change in gravitational potential energy equal?
The change in kinetic energy
What is the potential difference equal to?
gh = 1/2v^2
What happens to the value of the gravitational potential as you go away from earth?
It increases
How do you get a spacecraft away from earth?
You escape the gravitational potential well
What is the relationship between the size of the planet and the value of the gravitational potential?
The larger the planet, the more negative the value of the gravitational potential
Why is the gravitational potential negative?
Gravitational potential at an infinite distance from a planet is zero, as there is no gravitational force on an object at this location. Work must be done to move the object from the planet to infinity, increasing its gravitational potential energy. Hence gravitational potential and gravitational potential energy must be negative as it is increasing towards zero.
Why does a spacecraft with its engine switched off increase in speed when approaching earth?
Its kinetic energy increased and its potential energy decreased
What does the total energy of a spacecraft equal?
The kinetic energy + The gravitational potential energy
What happens to the value of the gravitational potential with distance?
It gradually becomes more positive
What is the gravitational potential proportional to?
1/r
What is the equation of the gravitational potential energy?
-GMm / r
What is the equation of the gravitation potential?
-GM / r
When we calculate the potential on the surface of the planet, what do we assume?
All the mass of the planet is concentrated at a point at its centre
What is the escape velocity?
The speed an object in a gravitational potential well must reach if it is then to coast to infinity out of the gravitational potential well.
What is the depth of the gravitational potential well?
The energy per kilogram needed to move a mass from the earth’s surface to a very long distance away
In order to escape a potential well, what must the total energy be?
Greater than 0
In order to escape a potential well, what must the sum of the gravitational potential energy and kinetic energy be?
Greater than 0
What is the minimum kinetic energy needed to escape given by?
1/2mv^2 = GMm / r
What is the equation of the escape velocity?
Vescape = root (2GM / r)
Mathematically, what is the required escape velocity to leave Earth’s surface?
11 km/s
What are the 2 main reasons the actual escape velocity of the earth is lower than expected?
Clever methods are adopted to find extra energy
- Rotation of earth means that rocket has kinetic energy before it is launched
- Spacecraft can gain kinetic energy through encounter with another planet
What is the area under a gravitational field g - distance graph?
The chnage in energy per unit mass between point A and point B
What is the area under a Gravitational force-distance graph?
The change in energy between point A and B
When you plot a curve of gravitational potential against radius, what does the gradient of the curve equal?
The gravitational field strength
When you plot a curve of gravitational potential energy against radius, what does the gradient equal?
The force
