Chapter 18 - Gravitational Fields Flashcards
What is Gravity?
A universal attractive force. Considered a weak force but has infinite range. Objects placed within a gravitational field are always attracted towards the centre of mass.
Radial Fields
Radial fields, like planets, has a gravitational field pattern consisting of straight lines which converge at the centre of mass.
For planets, due to their size, the field is model as uniform and the field is classed as parallel.
Define Gravitational Field Strength?
The gravitational force experience per unit mass.
g = F / m
F is the Gravitational Force and m is the Mass of the Object.
Only valid is mass of object in field produces a negligible gravitation field of its own.
What is Newton’s Law of Gravitation?
Two point masses attract each other with a force that is directly proportional to the product of their masses, and inversely proportional to the square of their separation.
F = -GMm / r^2
What is G?
G is the gravitational constant. 6.67 x 10^-11
How can you calculate the gravitational field strength for a point mass?
g = GM/r²
G is the Gravitational Constant
M is the mass of the Planet
r is the distance between the object and the planet
What is Kepler’s First Law?
The orbit of a planet is an ellipse, with the sun at one focus.
What is Kepler’s Second Law?
A line segment joining a planet and the sun sweeps out equal areas during equal time periods.
What is Kepler’s Third Law?
The square of the orbital period T is proportional to the cube of the average distance r from the sun.
t² = 4π²r³ / GM
Derive Kepler’s Third Law
F = mv²/r = GMm/r²
v² = GM/r
We know v = 2πr/T
4π²r²/T² = GM/r
T² = 4π²r³/GM
What is a Satellite?
Satellites are objects that orbit larger objects.
Uses of Satellites
Satellites can be uses for communication, scientific research and Global Positioning Systems (GPS).
What is a Geostationary Satellite?
Has an orbital period of 1 day, therefore maintaining a constant position in relation to the earth. Used for communication.
Define Gravitational Potential
Gravitational potential, Vg, is defined as the work done per unit mass to move an object from that point from infinity.
Infinity is when Vg = 0
Vg = - GM / r
What is Gravitational Potential Energy?
Gravitational potential energy is the work done to move an object with mass, m, from infinity to a point in that field.
E = - GMm / r
What is escape velocity?
Escape velocity is the minimum velocity required to escape a gravitational field.
The kinetic energy of the object at the start must be equal to or greater than the gravitational potential energy required to lift it to infinity.
½mv² = GMm/r
v = √(2GM/r)
