Phys - Orbits & The Wider Universe

Question 1

Kepler’s Laws

Answer 1

1st Law - Orbits are elliptical
2nd Law - Equal areas are sweeped by orbits during equal time periods
3rd Law - T^2 = kr^3

Question 2

How Does The Difference Between Theoretical and Observed Speeds Of Bodies At Large Distances From Center Of Galaxies Imply The Existence of Dark Matter?

Answer 2

Theoretical speed of bodies is much smaller than observed speed.

Since v = ksqrt(m), there must be some hidden mass that isn’t taken into account when calculating theoretical speed.

This extra mass is attributed to dark matter.

Question 3

How Does The Higgs Boson Relate To Dark Matter?

Question 4

Potential Assumptions

Answer 4

Mass is concentrated at one point rather than being distributed

For two-body systems, planet mass may be ignored for approximations if it is small enough.

Question 5

How Is A Spectrum Used To Determine An Orbital Period And Velocity?

Answer 5

Find difference between wavelengths of spectral lines observed on Earth and emission spectrum observed from the celestial body due to Doppler Shift.

Use the relationship deltah / h = v / c to determine orbital velocity.

Emission spectrum wavelengths will vary with maximum achieved when the body is moving away from and minimum when moving towards the Earth. Determine orbital period by finding time taken between first maximum to second consecutive maximum emission spectrum wavelengths.

Question 6

Hubble Constant

Answer 6

Rate of universe expansion, 1/H0 gives the age of the universe, the time taken for a given body to travel distance D at a constant velocity v in the relationship v = H0D

Question 7

Universe Critical Mass Density

Answer 7

For p < pc, the universe will continue to accelerate in its expansion as there isn’t enough mass per unit volume to decelerate the expansion with gravity. Heat death.

For p = pc, the universe will asymptotically approach an equillibrium point with its expansion and gravity resisting it.

For p > pc, the universe will decelerate in its expansion, until gravity overcomes the expansion, leading the universe to contract. Big crunch

Question 8

Find The Critical Mass Density of The Universe

Answer 8

Define the mass inside a spherical universe

Equate kinetic energy and gravitational potential energy with respect to the center of the sphere

Substitute