Module 5 Gravitational Fields Flashcards
Define Newton’s law of gravitation?
the force of attraction between two masses is directly proportional to the product of masses and inversely proportional to the square of their separation
In the formula for newtons law of gravitation, why is the value given a negative?
attractive force
What value do you substitute in for r in newtons law of gravitation for a satellite orbiting a planet?
r is separation between centres
so take radius of planet plus height/distance from surface
What is m and M in equations of gravity?
M is central mass and m is the orbiting mass
How do you test if a gravitational field is present?
place a small mass m within the suspected field, it will accelerate towards M
How are gravitational fields shown in diagrams?
gravitational field lines are arrows in the direction of the field (usually towards centre)
For a radial field - check all field lines meet at the centre of M
What does the density of arrows in a gravitational field diagram represent?
strength of the field
How do you draw Earth’s local gravitational field?
arrows pointing down evenly spaced and at 90 degrees to surface
This represents a uniform field (equal magnitude and direction)
What can be said about earth’s local field in terms of variation?
virtually uniform with constant strength (magnitude) and direction
Define g?
gravitational force per unit mass
(g is gravitational field strength)
How can the inverse square law be applied to the relationship between g and R?
g=GM/R^2
G is a constant and M is constant for individual planets
What is Kepler’s first law?
the orbit of a planet is an ellipse with the sun at one of the foci
What is Kepler’s second law?
a line joining a planet and the sun sweeps out equal areas in equal time intervals
What does Kepler’s second law imply in terms of the speed of planets orbiting the sun in an elipse?
travel faster when it is closer to the sun.
Greater loss in PE=gain in KE
What is Kepler’s third law?
For planets orbiting the same star, time period squared is directly proportional to the orbital radius cubed
What is an approximate value for the mass of the earth?
6x10^24kg
What is an approximate value for the radius of the earth?
6.4x10^6m
When using Kepler’s third law in ratio form, what can be done concerning the use of radius or time period?
When using the ratio T^2 proportional to r^3
can use different units (days for example) if used consistently
What is a geostationary orbit?
A satellite that remains in a fixed position above the earth’s surface
What are the three properties of geostationary orbits?
Time period of 24 hours for the earth
Must orbit above the equator
Must rotate from west to east like the earths (same direction as planet)
Explain how you find the height of a geostationary orbit for earth
Plug T=8.64x10^4s (24 hours) into Kepler’s third law equation
Find r
then subtract the radius of the earth to find the height
What are polar satellites?
satellites passing over north and south poles in a short time period
Give a use for polar satellites
weather monitoring
Military surveillance
Climate analysis
If given a height of a satellite, what is the value of r?
height plus radius of planet
Why for large values of h, can the formula for PE=mgh not be used?
g decreases with height so formula becomes inaccurate
What is the area under a force against radius graph?
work done to move the mass to orbital radius r
Why is PE defined as zero at a distance of infinity?
no gravitational field is present to cause a force so no associated energy
Why is GPE considered negative?
GPE is defined as zero at infinity
Gravity is an attractive force
A mass must gain energy in order to escape gravitational field
Define is gravitational potential Vg (simple summary)?
gravitational potential energy per unit mass
Define gravitational potential?
Vg at a point is the work done per unit mass from infinity to that point, with the potential defined as zero at infinity
How to convert from Vg to GPE?
multiply by m (SMALL MASS)
How to calculate change in GPE from change in Vg
Change in GPE = mΔVg
What is Vg (as words)
gravitational potential
What is the unit for gravitational potential?
J kg^-1
Define escape velocity?
minimum velocity needed to escape the gravitational force of a mass
be able to derive formula for escape velocity
Explain why the earth has lost most of it’s hydrogen and helium from it’s atmosphere
All atoms/molecules have the same average KE in a gas at one temperature
Lighter atoms travel faster (larger root mean square velocity)
More likely to have a V>escape velocity
Remember - Spread of velocities in a gas even if one type of atom/molecule (Maxwell Boltzmann distribution)
Explain why lighter planets lose their atmospheres?
Smaller mass, smaller escape velocities, particles in atmosphere escape more easier
If asked to calculate the sum of energies for an object orbiting a planet, what must be done?
Find KE
Find PE
Add them (KE-PE as PE is negative)
How can you use find KE from change in Vg?
mΔVg = ΔPE= ΔKE
m in both equations cancel out as you don’t need it
(remember Vg is energy per unit mass so to get energy multiply by mass)
