18 - Gravitational Fields

Question 1

effect of us on the earth

Answer 1

we pull up the earth with the same amount of force we put on the earth - forces equal due to N3L but accelerations are different

earth is attracted to us but does not experience it as is mass is so big, a=F/m

Question 2

newtons square law of gravitation

Answer 2

grav. force between two bodies, m and M, is proportional to mM and inversely proportional to the square of the distance between their centres

Fgrav ∝ mM/r^2

Question 3

full mathematical expression of Newton’s law of universal gravitation

Answer 3

Fgrav = -GmM/r^2
Universal gravitational constant: G = 6.67 × 10–11 Nm2kg–2

Question 4

why is gravitational force only significant when at least one of the masses involved is very large

Answer 4

G is a very small number

Question 5

why is force have a negative sign

Answer 5

to indicate that the force is attractive

Question 6

The Earth’s gravitational field appears to act from…

Answer 6

it’s centre of mass.

Question 7

how does grav field strength change as distance increases from surface of earth

Answer 7

The Earth’s gravitational field gets weaker with distance from the Earth, this is shown by the greater separation of field lines.

Question 8

new equation for grav. field strength

Answer 8

g=F/m and F=-GmM/r^2

> g=-GM/r^2
M > massive object causing grav. field

Question 9

Define gravitational field strength at a point in space.

Answer 9

the force per unit mass an object feels whilst in orbit of a large mass (causing grav. field) at that point.

Question 10

relationship between velocity and radius of a stable
geostationary orbit

Answer 10

Fcentriptal = Fgrav
mv^2/r = GMm/r^2
v=root(GM/r)

Question 11

name for being closest anf furthest away from sun in an eliptical orbit

Answer 11

closest to sun - perihelion (perigee for moon)
furthest from son - aphelion (apogee for moon)

Question 12

first law of planetary motion

Answer 12

the orbit of a planet is an ellipse with the sun at one focus
(eccentricity (how long and narrow) is low so motion can be modelled as circular)

Question 13

second law of planetary motion

Answer 13

a line joining a planet and the sun sweeps out equal areas during equal intervals of time
(due to moving faster when closer to sun)

Question 14

orbital period

Answer 14

t=d/v
T=2πr/v (time for one complete circuit)

Question 15

keplers 3rd law equation

Answer 15

v^2=GM/r and T=2πr/v
T^2 = (4π^2/GM)r^3
T^2∝r^3

Question 16

keplers third law

Answer 16

T^2∝r^3
The square of a planet’s orbital period is proportional to the cube of the radius of its orbit

Question 17

what is a satellite

Answer 17

an object that orbits a larger object

Question 18

examples of satellites

Answer 18

natural - moons, comets, asteroids
artificial - ISS, HST

Question 19

what does a stable orbit depend on

Answer 19

distance and velocity

Question 20

satellite that orbit the earth lower..

Answer 20

require to be faster in order to stay in orbit
v= rootGM/r

Question 21

define gravitational potential

Answer 21

the work done per unit mass to move an object to that point from infinity

Vg=Ep/m
so units Jkg-1

Question 22

GPE and height

Answer 22

GPE increasess as height increases as energy is required to reach the higher, doing work

Question 23

GPE is defined as

Answer 23

being 0 at infinity as distance is too large and force of attraction is small

Question 24

potential gradient

Answer 24

=ΔV/Δr
Vg = -GM/r
so potential gradient = -GM/r^2
potential gradient = Vg/r = g = grav field strength

g acts in opposite direction to potential gradient hence the negative sign

Question 25

gravitational equipotentials

Answer 25

no word done by grav force when mass moved along equipotential surface
perpendicular to field lines
e.g. contour lines
potential changes more rapidly when closer to earth

Question 26

how are orbits modelled as circular

Answer 26

the centripetal force on the satellite or planet is provided by the gravitational force of the mass

Question 27

general uses of satellites

Answer 27

communications - satellite phones, satellite TV…
military uses - reconnaissance
scientific research - earth + universe
weather, climate - predicting + monitoring
global positioning

Question 28

polar orbits

Answer 28

circles the poles so offers a complete view of Earth as earth rotates beneath path of orbit (new orbital path each time)
useful for global mapping and reconnaissance

Question 29

low Earth orbits

Answer 29

short time to orbit Earth (less than 2 hours) due to short orbital radius, keplers law equation
uses include communications

Question 30

geostationary orbit

Answer 30

remains above same point on earth while earth rotates
continuous coverage of a certain area
orbits above equator
rotates in same direction as earths rotation
has orbital period of 24 hours
uses - communications, GPS, satellite TV, weather forecasting

Question 31

gravitational potential and infinity

Answer 31

infinity is so far that grav field strength at that point is 0, Vg is 0 at infinity (maximum) and so all values of Vg are negative as it takes external energy to move the object out of the field as all masses attract each other

Question 32

if it takes 20MJ to move a unit mass to infinity, how much energy is needed to move a 2kg object to infinity?

Answer 32

40MJ
Vp=E/m

Question 33

equation for Vg and derivation

Answer 33

Vg=-GM/r
using newtons square law of gravitation
and W=Fd

Question 34

Vg proportionality

Answer 34

Vg=-GM/r
Vg is proportional to M and inversely proportional to r
where M is mass of point mass (e.g. Earth)
and r is the distance from point mass causing grav field

Question 35

r is the distance…

Answer 35

from the centre of the planet

Question 36

Vg graph

Answer 36

V against r:
Vg is proportional to 1/r
Vg tends to 0 as r approaches infinity
smallest value of r is equal to radius of earth and gives maximum magnitude of Vg
Vg against 1/r:
produces straight line through origin
gradient equal to -GM

Question 37

change in Vg

Answer 37

moving towards point mass - decrease in Vg
moving away from point mass - increase in Vg

Question 38

what type of quantity is gravitational potential

Answer 38

scalar quantity
… so total gravitational potential at any point is equal to the algebraic sum of the gravitational potentials from each mass at that point.

Question 39

Vg graph (including moon)

Answer 39

Vg rises as you move away from earth surface, reaching a max (not 0) and falls again as distance to moon reduces

Question 40

grav potential energy eqaution

Answer 40

E=mVg
energy = mass x grav potential
ΔE=mΔVg (m is constant)

Question 41

grav potential and grav potential energy relationship

Answer 41

change in Vg results in change in E
so no change in Vg results in no change in E
as Vg decreases, E decreases (this energy is usually transferred into kinetic energy as object accelerates)

Question 42

grav potential energy equation and derivation

Answer 42

Vg=-GM/r and E=mVg
so E=-GMm/r
> change in r results in change in Vg so change in E

Question 43

energy needed for orbit

Answer 43

GPE is not the energy required to lift the satellite into orbit as it already had GPE on surface of earth. it will also need some kinetic energy in orbit

Question 44

graph of gravitational force against r

Answer 44

F=-GMm/r^2
so graph of F against r is inverse square relationship
F ∝ 1/r^2

Question 45

area under force-radius graph

Answer 45

work done to move mass

Question 46

escape velocity

Answer 46

the MINIMUM velocity required for a mass to escape the gravitational field of another mass
energy required must equal the gain in gravitational potential energy
KE transferred into GPE (loss of KE = gain in GPE)
equating both prior results in v=root2GM/r
(escape velocity is same for all objects regardless of their individual masses)