Orbits and the wider universe (Unit 4) Flashcards
Kepler’s first law?
Each planet moves in an ellipse with the Sun at one focus.
Kepler’s second law?
The line joining a planet to the centre of the Sun sweeps out
equal areas in equal times.
Kepler’s third law?
-T^2, the square of the period of the planet’s motion, is proportional to r^3, in which r is the semi-major axis of its
ellipse
(for orbits which are nearly circular, r may be taken
as the mean distance of the planet from the Sun)
What can you use as the semi major axis of a planet’s ellipse when its orbit is circular?
- mean distance of the planet from the sun
If orbit is circular how to work out velocity?
V = 2πr/t
How to derive Kepler’s third law?(when orbit is circular for t)
-Newton’s law of gravitation = centripedal force
-then sub in v=2πr/t
-reaarange for t
What assumption is there for DERIVING Kepler’s third law?
-only valid if the orbit is circular
What is dark matter?
-Matter which we can’t see, or detect by any sort of radiation,
but whose existence we infer from its gravitational effects.
How do orbital speeds of spiral galaxies show the existence of dark matter?
-Within the galactic bulge, the calculated ORBITAL speeds and measure speeds are about the same.
-At larger distances, where the density of the observed matter is low and therefore the galaxy will behave like a point mass, M does not change much (CONSTANT) Theoretically, the orbital speed should decrease with distance.
Should be v ∝ 1/ root r
-What is observed is different orbital speed does not change. —implies that there is more mass present than can be observed. This is dark matter.
How is Higgs Boson linked to dark matter?
- in the same way that Higgs Boson decayed into other particles after a collision, it is hoped that they have another mode of decay, disintegrating into photons and dark matter particles.
What three things must be true for binary systems?
-The centre of mass must be on the line joining the centres of the two objects.
-The centre of mass must be between the objects as the direction of the centripetal acceleration must be towards it.
-The angular velocities (ω) of the objects must be identical.
Binary system equations?
r1= m2x d /m1+m2
(r1 distance to centre of mass, d is the distance between the two planets)
T=2π root d^3 G(m1+m2)
How to work out radial velocity of a star or galaxy?
-doppler relationship
How to work out orbital velocity?
-using w as the two planets/stars have the same angular velocity
Why does t= 1/ho approximate the age of the universe?
-assume that the radial velocity of the galaxies has been constant since the beginning of the universe
-distance they have travelled can be calculated using
distance = speed × time
-sub into Hubble eq
