Gravitational fields Flashcards
force field
a force field is a region in which a body experiences a non-contact force
point mass
a mass with negligable volume or a uniform sphere whose mass acts as if its concerntrated at the centre
force equation
F = Gmm / r^2
gravitational constant
6.67 x 10^-11 Nm^2kg^-2
force on masses
the force on m1 due to m2 is equal and opposite to the force on m2 due to m1
the law of gravitation
inverse square law
F directly proportional to 1/r^2
gravitational field strength
force per unit mass
vector
force always pointing towards the centre of mass
gravitational field strength equation
g = F / m
equation for g using G
g = GM / r^2
g-r graph
1/x^2
area under = change in gravitational potential
gravitational potential energy
energy stored by an object due to its position in a gravitational field
equals work done moving an object from infinity to that position
gravitational potential
the gravitational potential energy that a unit mass would have at a specific point
equation for gravitation potential
V = -GM / r
value of gravitational potential at the surface of the mass and at infinity
surface = negative
infinity = 0
V-r graph
-1/x^2
gradient = field strength
gravitational field strength gradient
g = -V/r
gravitational potential difference
energy needed to move a unit mass from two points at different distances from a mass have different potentials
means there is a difference in potential
work done
when you move an object you do work against gravity
W = mV
Ep equationS
Change in Ep = m change in V
Ep = - GMm / r
equipotentials
lines (2D) and surfaces (3D) that join together a;ll points with the same gravitational potential
means if you travel along the equipotential your potential doesnt change and you dont lose or gain any energy
therefore gravitational potential difference and change in work done is both zero
satellites
any smaller mass that orbits a much larger mass and kept in orbit by gravitational forces
kept in orbit by centripetal forces
orbital speed
v = root(GM / r)
v directly proportional to 1 / root( r )
equation for time period
T^2 = 4pi^2 / GM X r^3
Ke and Ep of satellites
circular orbit
total energy is constant
in circular orbit orbital speed and distance above mass is constant
means Ke and Ep is constant
Ke and Ep of satellites
elliptical orbit
the satellite will speed up as its orbital radius deacreases meaning Ke increases and Ep decreases
escape velocity
minimum speed an unpowered object needs in order to leave the gravitational fields and not fall back towards the planet due to gravitational attraction
deriving escape velocity equation
Ke lost = Ep gained
0.5mv^2 = GMm / r
v = root (2GM / r )
synmchronus orbit
when an orbiting onject has an orbital period equal to the rotational period of the object its orbiting
e.g. geostationary satellite
geostationary satellites
always above same point on earth
must in the plane of the equator
travels at same angular speedas the earth turns in the same direction ( west to east)
orbit take roughly 24h and orbital radius is 42000km, 36000km above earth
geostationary satellites uses
useful for sending TV and telephone signals
low orbiting satellites
satellites that orbit 180 to 2000km above earth
proximity to earth means they have high orbital speeds in comparison to earth meaning you need multiple satellites working together for constant coverage
benefits of low orbiting satellites
cheaper to launch and require less powerful transmitters as they’re closer
useful for communications
low orbiting satellite uses
imaging and monitoring weather
