gravitational fields Flashcards
what is newtons law of gravitation
Newtons law of gravitation states that 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 the distance between them
what is the formula for the gravitational force
F= GMm/R^2
explain what it is meant by a gravitational field
A gravitational field is a region of space in which a mass placed in that region experiences a gravitational force
what does the density of the gravitational field lines represent
the strength of the gravitational field
define gravitational field strength
The gravitational field strength at a point in space is defined as a gravitational force experienced per unit mass at that point
what is the formula for gravitational field strength, theres 2
g= F/m
g= GM/R^2
take note:
gravitational field strength points towards the mass that created it, i.e. the mass that it is being attracted towards.
What are some properties from the shell theorem.
For a hollow sphere:
- Any point inside the hollow sphere has a gravitational field strength of 0
- Gravitational field strength outside varies with GM/R^2
For uniform solid sphere
1. Assuming that it has constant density (IMPORTANT)
2. Any point inside the uniform solid sphere of constant density, the gravitational field strength varies linearly with distance from center
PROOF:
M= density x volume = density x 4/3pier^3
g= GM/r^2 = G/R^2 (4/3pieR^3 * density) = 4/3GpieR * density `
what does gravitational potential energy mean
gravitational potential energy of a mass at a point in the gravitational field is defined as the work done by an external force in bringing the mass from infinity to that point
Why is gravitational potential energy negative
As the maximum energy for an object to stay within the gravitational field of the point mass is 0, the total energy has to be less than 0.
what is the formula for gravitational potential energy
-GMm/R
What is the relationship between gravitational force and gravitational potential energy and what are some characteristics about the relationship
F= -du/dr
- the magnitude of the force at point R is the gradient of the potential energy curve at R
define gravitational potential
The gravitational potential at a point in a gravitational field is defined as the work done per unit mass by an external force in bringing a small test mass from infinity to that point
what is the formula of gravitational potential
phi= U/m = -GM/R
what is the relationship between field strength and potential
g= -dphi/dr
what is the criteria for escape velocity
any object will escape from the gravitational pull when it has a total energy of 0
what is the formula for escape velocity
equate ke to gpe and find out what v is
what is keplers third law
the square of the period of revolution of planets is directly proportional to the cubes of their mean distances from the sun
How is kepler’s third law derived
applying N2L:
Fg = Fc
GMm/r^2 = mrw^2
GM/r^2 = r(2pie/T)^2
T^2 = (4pie^2/GM) * r^3
therefore T^2 = k r^3
Derive the KE, GPE and Total Energy of a satellite in a circular orbit
as satellite is in circular orbit, Fg provides for centripetal force
GMm/r^2 = mv^2/r
v^2= GM/r
ke= 1/2 mv^2 = 1/2 * GMm/r
gpe = -GMm/r
Total energy = ke + gpe = 1/2 GMm/r - GMm/r = -1/2 GMm/r
what are 3 characteristics of a geostationary satellite
its orbital period is the same as that of the earth about the axis of rotation
its direction of rotation is same as that of the earth about its axis of rotation
its plane of orbit lies in the same plane as the equator
What are the advantages of the geostationary satellite
constant surveillance of the region under it
easy for ground station to communicate with it as it is permanently within view. ground based antennas can be fixed in one direction
satellite can receive and transmit signals over a large area due to the high altitude
what are the disadvantages of a stationary orbit
significant loss of signal strengths
poorer resolutions in imaging satellites
time lag in telecommunication
