5.4 Gravitational Fields Flashcards
what is gravity
a universal attractive force
what are the properties of gravity
weak force with an infinite range
How does the strength of the gravitational field change with distance
As the distance from the centre of mass of an object increases, the gravitational field strength decreases until it becomes negligible.
What happens to objects within the gravitational field
Objects placed within the gravitational field will be attracted towards the centre of mass of the object
How can objects with mass be modelled in gravity
ll objects with mass can be modelled as a point mass, where the point is the centre of mass of the object
what produces a gravitational field
all objects with a mass
how is a gravitational field pattern of a radial field drawn
arrows converging to the centre of mass to show that gravity is an attractive force
what does it mean when the arrows on a radial gravitational field are closer together
the closer the lines are to each other the stronger the field is at that point
when can a gravitational field be modelled as uniform
when looking at the surface of a plane on a small scale
when is a gravitational field uniform
when the strength is equal at all position so the field is drawn as parallel lines towards the surface at equal intervals from each other
what is the gravitational field strength defined as
the gravitational force experienced per unit mass by an object at that point in a gravitational field
is gravitational field strength a vector or scalar quantity
vector
what are the units of gravitational field strength
Nkg^-1 or ms^-2
what is the equation ofr gravitational field strength
g=F/m
g= gravitational field strength
F= gravitational force
m= mass of the object in the field
when is the equation g=F/m for accurate
when the mass of the object in the field is small enough that the object’s gravitational field is negligible compared to the external gravitational field the object
is in
what does Newtons law of gravitation state
two point masses attract each other with a force that is directly proportional to the product of their asses and inversely proportional to the square of their separation
what equation can be used to shwo Newtons law of gravitation
F=-GMm/r^2
F= gravitational force
G=gravitational constant
M and m= masses of the two objects
r= the distance between the centres of the objects
what is the gravitational constant G
G= 6.67x10^-11 Nm^2kg^-2
why is there a negative sign in the equation F=-GMm/r^2
to show the attractive nature of the force
how is the gravitational field strength for a point mass calculated
by dividing the gravitational force between two point masses by the mass of the other point mass as g=F/m
whats the equation for the gravitational field strength for a point mass
g=GM/r^2
g=gravitational field strength of the point mass
G= gravitational constant
M= point mass
r= separation between masses
What does the equation g=GM/r^2 show about the gravitational field strength
the field strength for an object (like a planet) does not depend on the mass of the object in orbit, only on the mass of the planet and the distance between them
How can the gravitational field strength be modelled near Earth’s surface
as uniform and as the same value as the acceleration of free fall
what does Keplers first law state
the orbit of a planet is an ellipse with the sun at one focus
why can the motion of an orbit in an ellipse be modelled as circular
the eccentricity of the ellipse is very low
what does Kepler’s second law state
a line segment joining a planet and the sun sweeps out equal area during intervals of equal time
why is Kepler’s second law true
the speed of the planet is not constant - the planet moves faster when it is closer to the sun
what doe Kepler’s third law state
the square of the orbital period T is proportional to the cube of the average distance r from the sun
how can Kepler’s third law be proved
by considering the forces acting on the planet- centripetal force is required to keep the planet in orbit and this force is provided by the gravitational field of the sun
what formula is used for Keplers third law
T^2=4π^2r^3/GM
T= period of orbit
r= average distance between the planet and the sun (centre to centre)
G= gravitational constant
M= solar mass
how can T^2=4π^2r^3/GM be used to support Kepler’s third law
G and M are constants so T^2 is proportional to r^3
how can T^2=4π^2r^3/GM be derived
-F=mv^2/r=GMm/r^2
-GM/r=v^2
-v=2πr/T -> GM/r=4πr^2/T^2
-T^2=4π^2r^3/GM
what are satellites
objects that orbit other, larger objects such as the moon or other artificial satellites sent by humans into space
what can satellites be used for
communications, scientific research and Global Positioning Systems (GPS)
what are geostationary satellites
stellites that have an orbital period of one day
what is the motion of a gostationary satellite
same direction as the roation o fthe earth along the equatorial plane- they stay above the same point of the earths surface
What are geostationary satellites useful for
Communications and surveying as they provide continuous coverage
What is gravitational potential defined as
The work done per unit mass to move an object to that point from infinity
What’s the unit for gravitational potential
jkg^-1
What is Vg at infinity
Vg at infinity is its maximum value of 0
What is Vg at all points other than infinity
Vg is negative which represents how energy is required to move the object out of the field
What’s the formula for Vg
Vg=-GM/r
G= gravitational constant
M= mass the object is moved away from
r= separation distance between the object and the mass
What is gravitational potential energy
The work done to move an object with a mass m from infinity to a point in that field
What’s the equation for gravitational potential energy
E=-GMm/r
G= gravitational constant
M= mass object is being moved away from
m= mass of the object
r= separation between the mass and the object
How can the equation for gravitation potential energy be derived
E=mVg
Vg= -GM/r
E= -GMm/r
Escape velocity!
