what is newtons law of gravitation and what is the value of G
What is a Gravitational field and what do gravitational field lines show and what do the density of them indicate
A Gravitational field is a region of space where a mass will experience a force.
Gravitational field lines show the direction of the force that would be exerted on a (positive) test mass at that point in the gravitational field
The density (i.e no. per unit area) of gravitational field lines is proportional to the magnitude of the gravitational field strength
what is the Gravitational Field Strength
The gravitational field strength is the force per unit mass that would act on a test mass placed in the field.
𝑔=𝐹/𝑚
It is measured in N kg^(−1) or m s^(−2) and is a vector quantity.
Adding Gravitational Field Strengths
The resultant gravitational force on an object due to several masses is calculated as the vector sum of the gravitational forces exerted on it by each individual mass.
Therefore, the gravitational field strength at a point due to several masses can be calculated as the vector sum of the gravitational field strengths due to each individual mass.
Adding Gravitational Field Strengths - example - find the distance from the 9kg mass of the position of zero field strength
Sketch of the magnitude of the gravitiational field strength between 2 masses
What is the Gravitational Potential Difference
Gravitational Potential definition
The gravitational potential at a point is the work done (against gravity) per unit mass to move a test mass from infinity to that point
By definition, the gravitational potential is zero at infinity (and nowhere else)
Since gravity is always attractive, positive work must be done to move a test mass to infinity, so the potential is always negative
Positive or Negative?
Work done against gravity when moving a mass from infinity to a point
Negative
Positive or Negative?
Work done by gravity when moving a mass from infinity to a point
Positive
Positive or Negative?
Work done by gravity when climbing the stairs
Negative
Positive or Negative?
Work done against gravity when falling down the stairs
Negative
calculating Gravitational Potential
The gravitational potential from a point mass (or outside a spherical mass) can be calculated using the equation - (J/Kg)
𝑉=−𝐺𝑀/𝑟
If there are multiple masses together, the potentials simply add together
Relationship between Field Strength and Potential
gravitational field strength is the derivative of gravitational potential with respect to r.
What is the radius & gravitational field strength at the surface of this star
what is the gravitational potential at the centre of the star
radius at surface = 0.5x10^9 Meters
gravitiational field strength at surface= option D
gravitational potential at the centre of the star = value of total area under graph * -1
Maximum point
derivation of equation for gravitational potential
what are Equipotential Surfaces & their relation with field lines & what does the closeness of their lines indicate
Equipotential surfaces have constant potential
Field lines are perpendicular to equipotentials, because no work is done moving along an equipotential
More closely spaced equipotentials show a larger field strength
Sketch equipotential lines for a planet (mass 8m) and its moon (mass m)
C,A,D,B
Radius 2 Mm,
GM=20e12 m3s-2 M=3e23 kg
surface V=-10^7 Jkg-1, core V=-1.5e7 Jkg-1,
Gravitational Potential Energy
The gravitational potential energy of a system is equal to the work done (against gravity) when that system is formed from infinitely separated masses
If non-gravitational forces are negligible, then the change in a system’s gravitational potential energy will equal the change in its kinetic energy
Escape Velocity & its derivation
Escape velocity is the minimum velocity required for a test mass to escape a body’s gravitational field and reach infinite separation, without any additional energy input.
escape velocity means total energy (KE+GPE) is +ve
Kepler’s Laws of Planetary Motion
Law1:
Planets follow elliptical orbits with the Sun located at one focus
Law2:
The line between the planet and the Sun sweeps out equal areas in equal times
Law3:
The orbital period squared is directly proportional to the length of the major axis cubed.
