Stars & EA 3

Question 1

What 2 types of properties do stars have and how are they connected?

Answer 1

Stars have physical and observable properties. We must use the observable properties to find the physical properties.

Question 2

List some physical properties.

Answer 2

Luminosity
Absolute magnitude
Size
Mass
Temperature
Velocity

Question 3

List some observable properties.

Answer 3

Position
Flux
Magnitude
Colour
Spectral type
Lightcurve

Question 4

Describe 3 characteristics of electromagnetic radiation.

Answer 4

All EMR travels at the speed of light (c = 3x10^8 m/s)
It has wave-like properties; described by wavelength (lambda) or frequency (f), e.g interference.
It has particle-like properties; described in photons as ‘packets’ of energy, e.e photoelectric effect

Question 5

Write an equation to describe wave-like properties of EMR.

Answer 5

c = f * (lambda)

Question 6

Write an equation to describe particle-like properties of EMR.

Answer 6

E = hf or E =hc/lambda

h -> Planck’s constant

Question 7

Describe qualitatively the Doppler effect.

Answer 7

The wavelength that we measure is dependent on the relative motion between the source and the detector (us).
If the source doesn’t move, two observers on either side see the same wavelength. But if the source is moving to the right, the observer on the right sees a blue shift as the source is moving towards them and the observer on the left sees a red shift as the source is moving away from them.

Question 8

Describe mathematically blue and red shift.

Answer 8

The source emits wavelength (lambda0)
The observer measures wavelength (lambda)

If (lambda) < (lambda0) = blue-shifted
If (lambda) > (lambda0) = red-shifted

Question 9

Describe quantitatively the Doppler effect.

Answer 9

(Delta)(lambda) / (lambda0) = v/c for v &laquo_space;c

c : speed of light
Delta)(lambda) : differences in wavelength (lambda)-(lambda0
v : radial velocity

Question 10

Define radial velocity

Answer 10

The relative speed along the line of sight of source and observer.

Question 11

Why do stars appear to move on the sky and what is actually happening?

Answer 11

Stars move due to:

• Parallax
• Companion stars
• Motion around galactic centres

In reality there is:

• Radial velocity which is what we observe
• Proper motion which is what movement actually occurs

Question 12

What are binary star systems?

Answer 12

This is 2 stars in a mutual gravitational interaction orbiting their common centre of mass.
Higher multiples are also possible e.g. triples, quadruples

Question 13

Why are binary star systems useful?

Answer 13

Their orbits are determined by gravity or the masses of the stars.
The eclipses are determined by orbits and the radii of the stars.

Question 14

Describe visual binaries.

Answer 14

You can see 2 stars and you can see them move in space together.

Question 15

Describe close binaries.

Answer 15

These stars are too close for you to see separately.

Question 16

Describe eclipsing binaries.

Answer 16

These star regularly show eclipses of each other.

Question 17

Describe spectroscopic binaries.

Answer 17

These are 2 stars with Doppler shifts in opposite directions that vary as they orbit their common centre of mass.

Question 18

What is the equation for the orbital period?

How do you describe the 2 periods?

Answer 18

P = 2 (pi) r / v
P1 = P2

Question 19

Define the centre of mass equation in terms of a binary star system.

Answer 19

m1 r1 = m2 r2

Question 20

Describe the radii and radial velocities of a binary star system

Answer 20

r1 / v1 = r2 / v2

Question 21

Combine the centre of mass equation and the equation describing the radii and radial velocities in terms of a binary star system. What does this equation mean?

Answer 21

v1 / v2 = r1 / r2 = m1 / m2

This means the more massive star is orbiting at a shorter distance from the centre of mass and with a lower velocity.

Question 22

Write Newton’s law of gravity and an equation to describe the force required to keep the star in orbit in terms of a binary star system.

Answer 22

F = G m1 m2 / (r1 + r2)^2
F = m1 v1 ^2 / r1

Question 23

Using Newton’s law of gravity, an equation to describe the force required to keep the star in orbit, v1 = 2(pi)r1/P and R = r1 + r2, write the full verison of Kepler’s 3rd law and the simplified version (due to solar system units)
HINT use the tutorial!

Answer 23

4(pi)^2 * R3 /G = (m1 + m2)P^2

R^3 = (m1 + m2)P^2

Question 24

What is Kepler’s 3rd law used for?

Answer 24

To measure the sum of the masses.

Question 25

What information is neglected when calculating Kepler’s 3rd law?

Answer 25

Elliptical orbits, inclination of orbits against the line of sight or the sky.

Question 26

What information does a spectroscopic binary star system have that can be used in Kepler’s 3rd Law?

Answer 26

The radial velocities v1 and v2 can be measured, together with the period. This immediately gives r1 and r2 and thus R, as well as the ratio m1 and m2.

Question 27

What depends on the properties of stars in eclipsing binary star systems?

Answer 27

Shape, depth and length of eclipse.

Question 28

How can the sizes of stars in an eclipsing/spectroscopic binary star system be determined?

Answer 28

Create a lightcurve during the eclipse to measure 4 t-value (t1, t2, t3, t4). These can be input into 2 different equations to determine diameters of the 2 stars.

(t4 - t1)/ P = (D1 + D2) / 2(pi)R
(t3 - t2)/ P = (D1 - D2) / 2(pi)R