ch17 - gravitational fields Flashcards
gravitational field strength
the gravitational force exerted per unit mass on a small object placed at that point
field lines show:
. arrows show direction for gravitational force on a mass placed in the field
. spacing of the field lines she the strength of the gravitational field (more distance = more surface area = more weak)
point of Earth’s gravitational force
centre
centre of mass
the point at which we can consider the total mass of the object to be concentrated
close to surface, Earth’s gravitational field is
linear
far from surface, Earth’s gravitational field is
radial
Newton’s lae of gravitation
any two point masses attract each other with a force that is:
. directly proportional to Mm
. inversely proportional to r²
F proportional to Mm/r²
F = GMm/r²
G
gravitational constant
G = 6.67 * 10^-11 Nm²kg-²
gravitational field strength due to a point mass derivation
g = F/m
g = GMm/r²m
g = GM/r²
(M = mass of body causing the field)
gravitational field strength formula
g ≈ 9.81 N/kg
gravitational field strength is scalar or vector
vector
gravitational field strength and r
inversely proportional
g
acceleration of free fall - m/s²
gravitational field strength - N/kg
% change in R
<>R/ R * 100%
% change in g
<>R/ R * 2* 100%
why can’t we use gpe = mgh
. assumes gpe = 0 on Earth surface
. if lifted to great height, g will decrease - g not always constant
where is gpe 0
at infinity
gravitational potential/gpe
work done per unit mass in bringing a point mass from infinity
gravitational potential always
negative
orbital period
time taken by object (such as planet) to complete one orbit
gravitational potential formula
o/ = - GM/r
moving closer to body with gravity
less gpe, less potential
difference in gravitational potential
<> o/ = GM (1/r1 - 1/r2)
difference between field strength and potential
field strength = force
potential = potential energy
orbiting, when gravity is Fc
GMm/r² = mv²/r
v² = GM/r
M of planet
orbital period
time taken by an object to complete one orbit
v = 2pi * r / T
T and r relation
T² proportional to r³
(2pi *r/T)² = GM/r
artifical satellite orbit types
. circular - close view, 16orbits in one day
. elliptical - distant view
. geostationary - orbits at same angular speed as Earth
geostationary orbit
an orbit of a satellite such that the satellite remains directly above the same point of the Earth at all times
geostationary orbit uses
. telecommunications
. satellite TV transmissions
geostationary satellite lifespan
10 years (run out of fuel)
