Gravitational Fields

Question 1

What is a Force field ?

Answer 1

is a region in which a body experiences a non-contact force.

-presents in interactions between masses and charges

Question 2

What is newton’s law of gravitation ?

Answer 2

the force of attraction between two point masses is proportional to the ‘product of their masses’ and inversely proportional to the ‘square of their distance apart’
Equation -> F = GMm/r^2
- can’t feel force anymore when infinity distance away

Question 3

What is Gravitational Field strength (g) ?

Answer 3

is the ‘Force per unit mass’ in a gravitational field
g = F/m
- measured in Nkg^-1 (earth =9.81Nkg^-1)
- is a vector

Question 4

How to represent Gravitational Field in either UNIFORM or RADIAL fields ?

Answer 4

UNIFORM (straight line)
-earth surface - parabola effect
RADIAL (circle)
- force stronger when lines closer together
- force parallel to the field lines
- force to surface as point masses isn’t available

Question 5

How to find the value of g in Radial Gravitational Fields ?

And what does the graph look like ?

Answer 5

g = GM/r^2
-is zero between equal masses at the half way point
GRAPH (g/distance)
- decreasing from radius ∝ 1/r^2

Question 6

What is gravitational potential (V) ?

Answer 6

is the work done in moving a unit of mass (1kg) from infinity to a distance r within the gravitational field
Equation -> V = Gm/r
- measured in JKg^-1

Question 7

why is gravitational potential negative ?

Answer 7

at infinity the potential is zero because their is no force so at distance less than infinity, there will be a loss in gpe (zero = max potential)

Question 8

can gravitational potential be positive ?

Answer 8

yes the change of potential energy can be +ve

• only when point is moving away from mass
• Δgpe = gpe2 - gpe2 = -GMm/r2 - -GMm/r2

Question 9

What is the gravitational potential difference ?

Answer 9

is the energy needed to move a unit mass between two points
Equation -> ΔW =mΔV
(work done = mass x change in gravitational potential)
- area under g/distance graph = ΔV
V = -GMm/r

Question 10

How to represent Gravitational Potential in either UNIFORM or RADIAL fields ?

Answer 10

UNIFORM (straight)
- potential perpendicular to field lines
RADIAL - Equipotential
- potential doesn’t change along a equipotential as work done = 0
- e.g. a ball down hill steady but steeper down - closer to centre of mass = less work done

Question 11

what does the graph look like for Gravitational Potential/Distance ?

Answer 11

increasing from radius (-63MV) ∝ 1/r
- the gradient represents the Gravitational field (g)
g = Δv/Δr - potential gradient

Question 12

What is Escape Velocity ?

Answer 12

is the minimum velocity for a body to leave a gravitational field and reach infinity

• kinteric energy lost = gpe gained
• 1/2mv^2 = GMm/r
• Vesc = √2GM/r (r = radius or orbital distance)

Question 13

What is the speed at the surface on mass ? (Uniform field)

Answer 13

ΔEp = mgΔh
- no energy lost =
Ek =ΔEp
1/2mv^2 = mgΔh

Question 14

How to derive the relation T^2 ∝ r^3 ?

Answer 14

Fc = Fg (centripetal = gravitational)
- mv^2/r = GMm/r^2
- v^2 = GM/r
- (2πr/T)^2 = GM/r 
- 4π^2r^2/T^2 = GM/r
- T^2 = (4π^2/GM)r^3
- provided M is constant ( all bodies orbit same object) then 4π^2/GM is a constant 
- T^2 ∝ r^3 
 (T1/T2)^2 = (r1/r2)^3

Question 15

What are Geostationary satellites ?

Answer 15

orbiting object has an orbital period equal to the rotational period of the object it is orbiting.
- period of 24 hours
- equatorial orbit 
- remains in fixed position above earth
Advantages 
- appears stationary 
- don't have to track 
- send tv/telephone signals

Question 16

What are Low orbiting satellites ?

Answer 16

any satellites which orbit between 180-2000km above earth.
Advantages
- cheap
- use less power
- communication
- monitor weather
Satellites - smaller mass which orbit a much larger mass e.g. earth to sun