Distances to the Stars Flashcards
what is a light year and its value
- it is the distance light can travel in one year
- which is 9.46x10^15 m
what is the definition of an astronomical unit (AU)
the radius of the earths orbit around the sun
what is the value of 1 AU
1.5x10^11 m
how does the trigonometric parallax illusion work with earth, the sun and other stars
- as the earth moves around the sun
- a relatively close star will appear to move across the background of more distant stars
- but the star doesnt actually move significantly during the course of observation
how do you determine the the trigonometric parallax
- measure the angle to a star
- observe how that angle changes as the position of the earth changes
what change in the position of the earth are we looking for and why
- we are looking for the earth to be on the opposite side of its orbit relative to the sun
- which would take 6 months
- this means the distance the earth travelled (distance in a straight line) was 2 AU
what is the large triangle that has been set up from the movement of earth around its orbit when observing another star
- the two positions of the earth make one side of the triangle (2r)
- while the distance between earth 6 months prior and the star makes one side
- and the distance between earth now and the star makes the final side
- the angle formed at the star is 2 theta
what would distance d be in this case
the (horizontal) distance between the sun and the star
using the distance d, what new triangle could be made
- a right angled triangle
- the angle at the star is now just theta
- the distance between the sun and star is d
- the distance between the sun and earth is r
- and the distance between the earth and star makes the hypotenuse
given that you usually only know r and d, what equation wold you use to calculate the parallax angle
- r and d are the opposite and adjacent angles
- so tan0 = r / d
at small angles. what simplified equation could we use to calculate d and why
- rearrange to d = r / tan0
- giving d = r / 0
- because tan0 approximates to just 0 at small angles
what is the definition of a parsec (pc)
- the distance a star must be from the sun
- in order for the right angle earth-star-sun to be 1 arcsecond
what is the full name of a parsec
a parallax second
how do you convert arcseconds to angles
by dividing the arcseconds by 60x60 (3600)
how do you convert angles to arcminutes
by multiplying the angle by 60
what is the symbol for 1 arcsecond and 1 arcminute
- 1 arcsecond = 1”
- 1 arcminute = 1’
if a parsec requires the angle at the star to be 1 arcsecond and it is defined to be the distance between the sun and the star, how would you work out the length of a parsec
- earth to sun = 1AU (opposite)
- angle at star = 1 arcsecond
- sun to star = 1 parsec (adjacent)
- therefore tan(1 arcsecond) = 1AU / 1 parsec
- 1 parsec = 1AU / tan(1 arcsecond)
- 1AU = 1.5x10^11 and 1 arcsecond = 1 / 3600
- therefore 1 parsec = (1.5x10^11) / tan(1/3600)
using that calculation, what is the value of 1 parsec
3.09x10^16 m
what is the length of 1 parsec in light years
(3.09x10^16) / (9.46x10^15) = 3.27 light years
if the angle measurement is in arcseconds (0), what equation could you use to calculate the distance d
d = 1 / theta (0)
what is the equation for radiation flux
F = L / 4 pi d^2
what are the variables in that equation
- F = radiation flux / radiant energy intensity (Wm-2)
- L = luminosity (W)
- d = distance between star and observer (m)
what is the difference between radiation flux and luminosity
- luminosity is the total power output of a star from its surface
- whereas radiation flux is the power from a star that reaches earth
what are standard candles
Stars with properties which means their luminosity can be determined from measurements other than brightness
how would you work out the distance these types of stars are away from us
- work out their luminosity from earth (or just have it)
- measure the radiation flux from earth
- compare it with a standard candle with the same luminosity to work out how far away it is
what did henrietta leavitt discover by observing many stars in the nearby magellanic clouds
- that the brightness of some of the stars changed
- varying in a repeating cycle
although the brightness of the stars varied, what was constant in her time-luminosity graph
- the time period of the oscillations in brightness
- basically the time between the highest peaks were constant
what is the brightness of the stars proportional to
the luminosity of the star
why does this alternation in brightness even occur in the first place
- these stars have left the main sequence stage
- but hey havent exhausted all of their fuel
- the unbalancing between its gravity and thermal expansion cause the star to repeatedly expand and contract
- causing their surface areas as therefore luminosity (and therefore brightness) to vary
what did a star having a longer period for oscillation imply about it
it was brighter than others
after you have found a cepheid star, how do you use it to work out the distance between earth and it
- measure the time period for that star (between times of peak brightness)
- find the stars luminosity using leavitts time-luminosity data
- measure the radiation flux from the star on earth
- calculate d using F = L / 4 pi d^2
- its literally the same thing with the standard candles but this is more accurate
what is the simplest way of determining the luminosity of a star
by looking at its spectrum
how does looking at its spectrum work
- the peak wavelength gives the temp from weins law
- the width of the spectral lines can determine whether its a M.S. star
- if it is you find its place on the M.S. section on the luminosity-temp graph
- thereby giving you luminosity
what is the definition of a parallax angle
- the difference in angular observation of a given star
- for use in the trigonometric parallax method of measuring the distance to a star
what is the definition of the trigonometric parallax
a method for measuring the distance to relatively close stars
