Gravitational Fields Flashcards
What is Newton’s Universal Law of Gravitation?
The force of attraction between two point masses is
Proportional to the product of their masses
Inversely proportional to the square of their distance apart
Where must radial distances be measured from?
The centre of mass
What is meant by “Point Masses”?
It is assumed that the masses are infinitesimally small
What is the equation for Newton’s Law of Gravitation?
F=GMm/r²
What is the Universal Gravitational constant?
6.67x10^-11
When a question refers to the height of a satellite, what is meant?
The height of the satellite from Earth’s surface.
Therefore r=radius of earth + height above Earth’s surface
What is the definition of Gravitational Field Strength?
The Force acting on a unit mass
What is the equation of the definition of Gravitational Field Strength?
g=F/m
What equation is used to calculate Gravitational Field Strength?
g=GM/r²
Is a g field a scalar or vector?
Vector
What is the direction of a g field?
Always towards the centre of mass
What does the magnitude of the g field depend on?
The mass of the body creating the field
Where is the g field greatest?
At the surface of the body creating it
What happens to the g field within the body creating it?
It reduces to zero as you approach its centre
What is Kepler’s Third Law of Planetary Motion
T²=4π²r³/GM
What provides the centripetal force required for Earth to orbit the Sun?
The gravitational force of attraction.
For an orbit to be Geostationary, what must it do?
Have a period of 24 hours
Lie on Earth’s equatorial plane
Rotate the same direction of Earth
What is an advantage of a Geostationary orbit?
The satellite appears stationary to the observer, therefore doesnt require tracking
The satellite will not set beneath the observers horizon.
How many Geostationary satelittes are required of full global coverage?
3
What is the equation for Gravitational Potential Energy?
GPE=-GMm/r
not on equation sheet
What is the definition of Gravitational Potential Energy?
The work done in moving a mass form infinity to a distance r within a gravitational field.
Why are all GPE’s negative?
Energy is required to move a mass to infinity.
At infinity the field is zero, therefore the force is zero, therefore the GPE is zero.
At a distance less than infinity energy is lost therefore GPE is zero.
What equation is used to calculate the change in GPE?
ΔGPE= - Gmm (1/r(2) - 1/r(1) )
What is the equation for escape velocity?
v²=2GM/r
What equations are used in deriving the equation for escape velocity?
W=0.5mv²
and
GPE=GMm/r
What is escape velocity?
The minimum velocity required to leave a body and travel infinetly far away.
Rockets to orbit do not achive escape velocity, why is this?
Escape velocity is to get infinetly far away.
Orbits are not infinetly far away.
A rockets initial launch velocity is not escape velocity, why is this?
Rockets accelerate over a longer period. As escape velocity decreases with altitude as the field strength decreases.
Define Gravitational Potential
The work done in moving a unit mass from infinity to a distance r within the gravitaional field
what is the unit of Graviational Potential?
Joules per Kilogram
JKg^-1
What is the equation to calculate Gravitational Potential?
Vg=-GM/r
Vg is subscrpt g
(As Gravitational Potentials is the same as Gravitational potential energys but for a unit mass, imagine
GMm/r with m=1 as it is a unit mass)
Is Gravitational Potential scalar or vector?
Scalar
Are Gravitataional Potentials positive or negative?
Negative
The magnitude of Gravitational Potentails relies on what?
Mass of the body creating the field
What is Gravitational Potential proportional to?
1/r
Where is Gravitational Potential greatest?
At the surface of body creating the field
What equation is used to calculate a change in Gravitational Potential?
ΔV=-Gm(1/r(2) - 1/r(1))
What equation links Work done, Mass and Gravitational Potential?
ΔW=mΔV
What is a Gravitational Equipotential?
A graphical means to display Gravitaional Potential
They are perpendicular to field lines
Are Equipotentials equally spaced in radial and uniform fields?
In uniform fields equipotentials are equally spaced as the field strength doesn’t change.
In radial fields equipotentials are not equally spaced as the field strength weakens, V is proportional to 1/r.
What is the equation related to Potential Gradients?
g= - ΔV/Δr
What is the Potential Gradient equal to?
The field strength at that point in space
What is the gradient of a distance-gravitational potential graph equal to?
Field strength at that point in space
