chapter 18 - gravitational fields

Question 1

field lines

Answer 1

• density of lines is prop to field strength
• always perp to surface
• never cross
• always attractive (gravitational)

Question 2

gravitational fields

Answer 2

a region in space where any mass experiences a force of attraction
- act anything with a mass
- are infinite
- always attractive
- at surface are considered uniform

Question 3

gravitational field strength

Answer 3

force per unit mass
generally g = F/m
for a point mass g = -GM/r²

Question 4

radial fields equation

Answer 4

F = GMm/r²
F ∝1/r²
G = 6.67*10^-11 Nm^2kg^-2

Question 5

uniform fields equation

Answer 5

F = mg

Question 6

newtons law of gravitation

Answer 6

F ∝ Mm - prop to product of masses
F ∝ 1/r² - inversely prop to seperation squared
F = -GMm/r²

Question 7

gravitational field strength graph

Answer 7

g against 1/r²
- always in neg quadrant
- straight line
g against r
- always in neg quadrant
- staight line down then curve back up
- straight line section until rE (assume uniform density)

Question 8

satellites

Answer 8

• geostationary
• polar

Question 9

geostationary

Answer 9

• orbital period 24h
• stay above same country + therefore are all at a specific height - equatorial orbit
• same direction as Earth
• uses: communications, weather prediction, GPS
• 35,768 km above Earths surface

Question 10

polar

Answer 10

• pole to pole orbit
• low orbit - 200-1000km
• faster speeds
• cover a number of countries
• uses: spying, weather prediction

Question 11

equipotentials

Answer 11

lines of equal gravitational energy

Question 12

keplers 1st law

Answer 12

the orbit of a planet is an ellipse with the sun at one of the two foci
- but most orbits have low eccentricity and can be modelled as circles

Question 13

keplers 2nd law

Answer 13

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

(planets travel faster nearer the sun)

Question 14

keplers 3rd law

Answer 14

the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun
T² ∝R³

Question 15

gravitational potential

Answer 15

Vg at any point in a gravitational field is defined as the work done per unit mass to move an object to that point from infinity

infinity is a distance so far away from the object producing the field that g = 0

= -GM/r

Question 16

gravitational potential graph

Answer 16

Vg against r
inversely proportional in the negative quadrant
and asymptotes are where the surface is

Question 17

gravitational potential energy

Answer 17

E = mVg = -GMm/r

Question 18

g varies due to

Answer 18

• non uniformities in the Earths shape and composition
• the effect of the Earths spin which reduces g by an amount
• varying from zero at the poles to a maximum at the equator

Question 19

deriving keplers 3rd

Answer 19

F(g) = F(c)
m⍵²r = GMm/r²
⍵ = 2𝞹/T
m4𝞹²r/T² = GMm/r²
T²/R³ = 4𝞹²/GM

Question 20

escape velocity

Answer 20

the minimum speed required by an object to escape a gravitational field
KE = GPE
v = root (2GM/r)

Question 21

gravitational potential at infinity

Answer 21

there is none = 0
as you move away from a planet you gain Vg( tends to zero)