Topic 1

Question 1

Standard candle

Answer 1

Any type of object whose luminosity is known from its other observable properties, thus allowing its distance to be inferred from the difference between its apparent brightness and its true brightness.

Question 2

Annual parallax / parallax angle

Answer 2

Half the angle that is subtended by its apparent motion against the background stars over the course of a year. One parsec is the distance at which a star would have a parallax of one arcsecond.

Question 3

Annual parallax equation (parallax angle)

Answer 3

d (pc) = 1/(ω/arcsecond)

ω=parallax

Question 4

Parallax uncertainties equation

Answer 4

Δd=Δω/ω^2

ω= parallax

Question 5

Gaia project

Answer 5

This project is mapping the galaxy measuring propper motion and parallaxes of over one billion stars with an accuracy of 10μas.

Question 6

RR Lyrae Stars

Answer 6

These are pulsating stars that are used as standard candles within our galaxy and in galaxy’s nearby for distances of up to around 1Mpc.
They are easily recognised by their folded light curves which have periods of around half a day. They have an absolute magnitude of approx 0.75.

Question 7

Cepheid variables

Answer 7

These are pulsating stars that are used as standard candles for distances of up to tens of Mpc.
They have pulsation periods from a few days to several tens of days, and absolute magnitudes between -1.5 and -6.5.
The relationship between their pulsation and there absolute magnitude can be shown such that

Mv = -2.43 log10(P /day) - 1.62

Question 8

Type la supernovae

Answer 8

This is also used as a standard candle and is believed to form when a white dwarf exceeds a mass of about 1.4 times that of our sun either through accretion, on the combination of two white dwarfs.
The peak brightness of all type la supernovae reach a similar absolute magnitude of Mb = Mv = -19.6 and are useful of measuring distances of up to 1Gpc.

Question 9

Hubble-Lemaître law

Answer 9

A relationship between the apparent speed at which a galaxy is moving away from us and its distance away. It is used to calculate distance of very far objects.

v=Hod

v is the apparent speed of recession, d is the distance and Ho is the Hubble constant around 70 / s / Mpc.

Question 10

Convert arcminutes and arcseconds to degrees

Answer 10

Divide arcminutes by 60 and arcseconds by 3600.

25°21’ 300” = 25 + 21/60 + 300/3600 = 25.4333º

Question 11

Small angle approximation

Answer 11

For any angle smaller than 0.2 rad

sinθ~θ

Question 12

Convert right ascension into degrees

Answer 12

First convert the time measurement into decimal hours by dividing the minutes by 60 and the seconds by 3600.
Then multiply your decimal hours by be appropriate number of degrees.

6 h 34 m 45.67s = 6 + 34/60 + 45.67/3600 = 6.579353 h

at the equator 1 hour is equivalent to 15° so multiply the decimal hours by 15

6.579353 x 15 = 98.69029º

Question 13

Precession definition

Answer 13

The slow movement of the rotation axis of a spinning body the earths axis precesses with a period of around 26000 years.

Question 14

Angular separation with the same right ascension

Answer 14

θ = the difference between the two declination (δ) values.

θ = δ1 - δ2 = Δδ

Question 15

Angular separation with the same declination (equation)

Answer 15

θ = different in right ascension (α) multiplied by the cosine of their common declination (δ)

θ = (α1 - α2)cos(δ)

Question 16

Angular separation with a change in declination and right ascension.

Answer 16

You can use Pythagoras’ theorm to combine both angular separation in both declination (δ) and right ascension (α).

θ^2 = (Δα)^2 (cosδ)^2 + (Δδ)^2

Question 17

Linear separation

Answer 17

Angular separation is how far objects appear to be from eachother, however linear separation is how far apart the actually are. This is calculated using trigonometry.

The sin of the angular separation (θ) = the linear separation (D) / the distance away (d)

Sin(θ) = D/d

Remember to convert to radians and the small angle approximation.

Question 18

Proper motion definition

Answer 18

This term is mostly used to refer to the movement of a star relative to the background coordinate system.

Question 19

Proper motion definition

Answer 19

This term is mostly used to refer to the movement of a star relative to the background coordinate system.

Question 20

Proper motion in right ascension

Answer 20

This is defined as the difference in a RA measurements divided by the time interval that separates them.

μα = (α2 - α1) / Δt = Δα / Δt

Question 21

Proper motion in declination

Answer 21

This is defined as the difference between two dec measures divided by the time between them.

μδ = (δ2 - δ1) / Δt = Δδ / Δt

Question 22

Magnitude of proper motion (equation)

Answer 22

The two components of the magnitude of proper motion (μα and μδ) are at right angles to each other so pythagores’ theorem can be used to calculate their magnitude.

μ^2 = (Δα)^2 (cosδ)^2 + (Δδ)^2

If the cosine factor is already included in the proper motion of RA then it will by written as

μα* = (μα)(cosδ)

So the equation becomes

μ^2 = (μα*)^2 + (μδ)^2

Question 23

Transverse velocity (equation)

Answer 23

The component of a stars velocity in the plane of the sky i.e. In a direction perpendicular to the line of sight of an observer. Typically measured in km/s.

The sine of the magnitude of proper motion (μ) = the transverse velocity (νt) / the objects distance (d)

Sin(μ) = νt / d

Question 24

Apparent magnitude (m)

Answer 24

A numerical measure of the apparent brightness of a body. For a star it is a measure of the flux received.

Question 25

Absolute magnitude (M) (equation)

Answer 25

A numerical measure of the intrinsic brightness of a star equal to the apparent magnitude (m) the star would have if observed from a standard distance of 10 pc. The absolute magnitude (M) provides a measure of a stars luminosity. M = m - 5log10(d /pc) + 5

Question 26

Extinction and absolute magnitude

Answer 26

The combined effect of the scattering of electromagnetic radiation by a medium and absorption of such radiation by the medium. Due to extinction the equation for absolute magnitude can be rewritten: M = m - 5log10(d /pc) + 5 - A A represents an equivalent number of magnitudes by which a stars brightness is diminished.

Question 27

Reddening definition

Answer 27

An effect of extinction to cause the observed colour of an astrological object to appear redder than its intrinsic colour.

Question 28

Astronomical colour

Answer 28

The difference measured in magnitudes, of the brightness of an object in two specified wavebands ( eg in the blue 'B' and the red 'R’ wavebands, in which case the difference is denoted mB-mR or simply B-R). Sometimes referred to as colour index. A larger B - R value would indicate a redder star, where's a smaller one would indicate a bluer one.

Question 29

Apparent colour

Answer 29

The difference between two apparent magnitudes.

Question 30

Intrinsic colour

Answer 30

The difference between two absolute magnitudes. This is indicated by a subscript 0 on the magnitude difference for example: MB-MR = (B-R)0

Question 31

Relationship between apparent magnitude and flux

Answer 31

This can be expressed as m1 - m2 = 2.5log10(F2 / F1) Where m1 and m2 are the apparent magnitudes of two objects, while F1 and F2 are their respective fluxes. This can be rearranged to find the ratio of fluxes given a known difference in magnitude F2 / F1 = 10^((m1 - m2) / 2.5)

Question 32

Absolute magnitude and luminosities

Answer 32

This are connected using the equation M1 - M2 = 2.5log10(L2 / L1) Where M1 and M2 are absolute magnitudes of 2 objects, and L1 and L2 are their respective luminosities. The equation can be rearranged to find the ratio of luminosities from known absolute magnitudes. L2 / L1 = 10^((M1 - M2) / 2.5)

Question 33

Working an objects maximum size from light time travel

Answer 33

The time interval in which an object changes in brightness can be used to calculate its maximum size. This is because information cannot propagate faster than the speed of light. So if X-ray emissions double in brightness in a few hours, the size of the x-ray emitting region cannot be larger than the distance traveled by the electro magnetic radiation in that time interval. This interval is known as light travel time.