Orbits And The Wider Universe Flashcards
What is Kepler’s First Law of planetary motion?
Each planet moves in an ellipse with the sun, at one focus
What is Kepler’s Second Law of planetary motion?
The line joining a planet to the centre of the sun, sweeps out equal areas in equal time
What is Kepler’s Third Law of Planetary motion?
T^2, The square of the period of a planet’s motion, is proportional to the r^3, where r is the semi-major axis of the ellipse
What do you find the semi-major axis?
r = r(max) + r(min)/2
What is the equation for Kepler’s Third Law?
T^2 = 4(π^2)(r^3)/GM
How do you derive Kepler’s Third law?
By using the Force between 2 masses as the planets are assumed to be circular, while also equating it to the centripetal force as their orbit is assumed to be circular
What do we assume when using Kepler’s Third Law?
A much smaller mass is orbiting a much greater mass, for example a planet and satellite.
What is true for most orbits?
Most orbits are not circular, both objects within an orbit, orbit a centre of mass between the 2 objects
How do you calculate the centre of mass?
r1 = d * M1/M1+M2
Where d is the centre of mass
What is the equation used to calculate the period of a binary system?
T^2 = 4π^2 * d^3/G(M1+M2)
How can we predict the rotational speed of a planet in circular motion?
By equating both centripetal force equation and newtons law of gravitation and rearranging for v
What is the equation for rotational speed?
v = √(GM/r)
What is the assumption of when M1»_space;> M2?
M1 + M2 = M1
For binary systems how do you find r1 or r2?
r1 = d(M2/M1+M2)
or
r2 = d(M1/M2+M1)
What is the equation for periodic time for both bodies in a binary system
T = 2π√(d^3/G(M1+M2))
How do you calculate the radial velocity?
c(Δλ/λ) = V
What is Hubble’s Law?
Each object has a superimposed radial velocity given by the equation:
v = H₀D
How can we use Hubble’s law to calculate the age of the universe?
By rearranging the equation to obtain
t = 1/H₀
And that gives us the age of the universe
Explain dark matter
The detected mass from the electromagnetic radiation provides us with a calculated speed that doesn’t match with what is observed. What is observed hints at there being more mass than expected and this proposes the idea of dark matter, a form of matter which cannot be detected using any form of E-M Radiation.
What is the suggestion from the higgs boson?
Dark matter is speculated to arise from a certain decay mode from the higgs boson
