Orbits And The Wider Universe

Question 1

What is Kepler’s First Law of planetary motion?

Answer 1

Each planet moves in an ellipse with the sun, at one focus

Question 2

What is Kepler’s Second Law of planetary motion?

Answer 2

The line joining a planet to the centre of the sun, sweeps out equal areas in equal time

Question 3

What is Kepler’s Third Law of Planetary motion?

Answer 3

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

Question 4

What do you find the semi-major axis?

Answer 4

r = r(max) + r(min)/2

Question 5

What is the equation for Kepler’s Third Law?

Answer 5

T^2 = 4(π^2)(r^3)/GM

Question 6

How do you derive Kepler’s Third law?

Answer 6

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

Question 7

What do we assume when using Kepler’s Third Law?

Answer 7

A much smaller mass is orbiting a much greater mass, for example a planet and satellite.

Question 8

What is true for most orbits?

Answer 8

Most orbits are not circular, both objects within an orbit, orbit a centre of mass between the 2 objects

Question 9

How do you calculate the centre of mass?

Answer 9

r1 = d * M1/M1+M2

Where d is the centre of mass

Question 10

What is the equation used to calculate the period of a binary system?

Answer 10

T^2 = 4π^2 * d^3/G(M1+M2)

Question 11

How can we predict the rotational speed of a planet in circular motion?

Answer 11

By equating both centripetal force equation and newtons law of gravitation and rearranging for v

Question 12

What is the equation for rotational speed?

Answer 12

v = √(GM/r)

Question 13

What is the assumption of when M1&raquo_space;> M2?

Answer 13

M1 + M2 = M1

Question 14

For binary systems how do you find r1 or r2?

Answer 14

r1 = d(M2/M1+M2)
or
r2 = d(M1/M2+M1)

Question 15

What is the equation for periodic time for both bodies in a binary system

Answer 15

T = 2π√(d^3/G(M1+M2))

Question 16

How do you calculate the radial velocity?

Answer 16

c(Δλ/λ) = V

Question 17

What is Hubble’s Law?

Answer 17

Each object has a superimposed radial velocity given by the equation:

v = H₀D

Question 18

How can we use Hubble’s law to calculate the age of the universe?

Answer 18

By rearranging the equation to obtain

t = 1/H₀

And that gives us the age of the universe

Question 19

Explain dark matter

Answer 19

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.

Question 20

What is the suggestion from the higgs boson?

Answer 20

Dark matter is speculated to arise from a certain decay mode from the higgs boson