Frontiers in Physics Flashcards
How do you calculate the moments of inertia of the solar system
MOI of sun –> L = Iw
MOI of planets –> L=mvr
Define flux
Flux is the light received per unit area per second.
Flux = Luminosity / (4 pi r^2)
Define the arcminute
1’ = 1/ 60 degrees
Define the arcsecond
1’’ = 1/3600 degrees
Define the parsec
The parsec is the distance at which 1Astronomical unit subtends 1’’
Define the astronomical unit 1AU
The mean distance between the sun and the earth.
1.5x10^11m
What is one solar mass
1 Solar mass = 2x10^30kg
What order of magnitude is the milkyways diameter
10KPc
What order of magnitude is the universe diameter
GPc
What is Keplers first law
Planets travel in elliptical orbits with the sun at one focus
What is Kepler’s second law
a line connecting a planet to the sun will sweep out equal areas in equal time intervals. Resultant from conservation of angular momentum.
L = mvr = constant
as r increases, v decreases.
What is Kepler’s third law
(orbital Period)^2 ∝ (average distance from the sun)^3
Give the generalised equation of kepler third law
P^2 = 4pi^2 a^3 / G(m+M)
This applies to anything in orbit about a point mass. a is the semi major axis of the elliptical orbit
Derive Keplers laws to derive the universal law of gravitation
Consider a planet in a circular orbit
K3: P^2 = kr^3
k2: v = constant for circular orbit
P = 2pi r / v
sub into K3
rearrange for … = mv^2/r by multiplying both sides by m
by N2 Fplanet = Fsun
solve for newtons law of grav
Describe the virial theorem
GMm/r^2 = mv^2/r (circular orbit)
Therefore, GMm/r = mv^2 = 2KE
GMm/r = PE therefore:
2KE + PE = 0
The virial theorem is true for systems in equilibrium. (Bound orbits)
Give the type of orbits when E<0 , E=0, E>0
E<0: Elliptical orbit, bound orbit
E=0: Parabolic trajectory, unbound orbit
E>0: Hyperbolic trajectory, unbound orbit
Describe how to measure the distances to nearby stars
We can measure the distances to nearby stars using parallax: The apparent positions of nearby stars “wobble” by over ±θ a year relative to distant objects.
Small angle approximation: θ = 1AU/D where D is the distance to star. Hence D (Pc) = 1/θ’’
Define apparent magnitude
apparent magnitude – the brightness of a star as seen from Earth
Define absolute magnitude
a measure of how bright a star would be if it were seen from a standard distance. the absolute mag is the same as the apparent mag if the
source is at 10+ parsec.
Give wein’s law
λ_max = 2.9x10^-3 / T(K)
Hence λ_max emitted by a black body in inversely proportional to its temperature.
Give the conditions for atomic fusion
To overcome strong electromagnetic repulsion between charged ions: HIGH ENERGY, HIGH TEMPERATURE
To collide: HIGH DENSITY
Give the proton-proton reaction chain for fusion of H into He
notes
Describe the formation of a star from a collapsing gas cloud in terms of gravitational and thermal energy
virial theorem where ke is internal thermal energy
Intially, as a cloud of gas collapses, the potential energy (PE)
becomes more negative, so U = -Pe/2 becomes more positive, temp increases, conditions for fusion created
star is born
Why do stars not collapse
The star does not collapse because gravity is balanced by
pressure forces.
Stars have high temperature and density at the centre:
P = ρkT/m
The virial theorem can be applied replacing KE with internal thermal energy, U.
2U + PE = 0
E_tot = U-2U = -U <0
–> star is gravitationally bound