5.4 Gravitational Fields

Question 1

what is gravity

Answer 1

a universal attractive force

Question 2

what are the properties of gravity

Answer 2

weak force with an infinite range

Question 3

How does the strength of the gravitational field change with distance

Answer 3

As the distance from the centre of mass of an object increases, the gravitational field strength decreases until it becomes negligible.

Question 4

What happens to objects within the gravitational field

Answer 4

Objects placed within the gravitational field will be attracted towards the centre of mass of the object

Question 5

How can objects with mass be modelled in gravity

Answer 5

ll objects with mass can be modelled as a point mass, where the point is the centre of mass of the object

Question 6

what produces a gravitational field

Answer 6

all objects with a mass

Question 7

how is a gravitational field pattern of a radial field drawn

Answer 7

arrows converging to the centre of mass to show that gravity is an attractive force

Question 8

what does it mean when the arrows on a radial gravitational field are closer together

Answer 8

the closer the lines are to each other the stronger the field is at that point

Question 9

when can a gravitational field be modelled as uniform

Answer 9

when looking at the surface of a plane on a small scale

Question 10

when is a gravitational field uniform

Answer 10

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

Question 11

what is the gravitational field strength defined as

Answer 11

the gravitational force experienced per unit mass by an object at that point in a gravitational field

Question 12

is gravitational field strength a vector or scalar quantity

Answer 12

vector

Question 13

what are the units of gravitational field strength

Answer 13

Nkg^-1 or ms^-2

Question 14

what is the equation ofr gravitational field strength

Answer 14

g=F/m
g= gravitational field strength
F= gravitational force
m= mass of the object in the field

Question 15

when is the equation g=F/m for accurate

Answer 15

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

Question 16

what does Newtons law of gravitation state

Answer 16

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

Question 17

what equation can be used to shwo Newtons law of gravitation

Answer 17

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

Question 18

what is the gravitational constant G

Answer 18

G= 6.67x10^-11 Nm^2kg^-2

Question 19

why is there a negative sign in the equation F=-GMm/r^2

Answer 19

to show the attractive nature of the force

Question 20

how is the gravitational field strength for a point mass calculated

Answer 20

by dividing the gravitational force between two point masses by the mass of the other point mass as g=F/m

Question 21

whats the equation for the gravitational field strength for a point mass

Answer 21

g=GM/r^2
g=gravitational field strength of the point mass
G= gravitational constant
M= point mass
r= separation between masses

Question 22

What does the equation g=GM/r^2 show about the gravitational field strength

Answer 22

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

Question 23

How can the gravitational field strength be modelled near Earth’s surface

Answer 23

as uniform and as the same value as the acceleration of free fall

Question 24

what does Keplers first law state

Answer 24

the orbit of a planet is an ellipse with the sun at one focus

Question 25

why can the motion of an orbit in an ellipse be modelled as circular

Answer 25

the eccentricity of the ellipse is very low

Question 26

what does Kepler's second law state

Answer 26

a line segment joining a planet and the sun sweeps out equal area during intervals of equal time

Question 27

why is Kepler's second law true

Answer 27

the speed of the planet is not constant - the planet moves faster when it is closer to the sun

Question 28

what doe Kepler's third law state

Answer 28

the square of the orbital period T is proportional to the cube of the average distance r from the sun

Question 29

how can Kepler's third law be proved

Answer 29

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

Question 30

what formula is used for Keplers third law

Answer 30

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

Question 31

how can T^2=4π^2r^3/GM be used to support Kepler's third law

Answer 31

G and M are constants so T^2 is proportional to r^3

Question 32

how can T^2=4π^2r^3/GM be derived

Answer 32

-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

Question 33

what are satellites

Answer 33

objects that orbit other, larger objects such as the moon or other artificial satellites sent by humans into space

Question 34

what can satellites be used for

Answer 34

communications, scientific research and Global Positioning Systems (GPS)

Question 35

what are geostationary satellites

Answer 35

stellites that have an orbital period of one day

Question 36

what is the motion of a gostationary satellite

Answer 36

same direction as the roation o fthe earth along the equatorial plane- they stay above the same point of the earths surface

Question 37

What are geostationary satellites useful for

Answer 37

Communications and surveying as they provide continuous coverage

Question 38

What is gravitational potential defined as

Answer 38

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

Question 39

What’s the unit for gravitational potential

Answer 39

jkg^-1

Question 40

What is Vg at infinity

Answer 40

Vg at infinity is its maximum value of 0

Question 41

What is Vg at all points other than infinity

Answer 41

Vg is negative which represents how energy is required to move the object out of the field

Question 42

What’s the formula for Vg

Answer 42

Vg=-GM/r G= gravitational constant M= mass the object is moved away from r= separation distance between the object and the mass

Question 43

What is gravitational potential energy

Answer 43

The work done to move an object with a mass m from infinity to a point in that field

Question 44

What’s the equation for gravitational potential energy

Answer 44

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

Question 45

How can the equation for gravitation potential energy be derived

Answer 45

E=mVg Vg= -GM/r E= -GMm/r

Question 46

Escape velocity!