Astronomical Distance

Methods of measurement

Radar The classic method of measuring distance by sending waves and recording the time delay taken for the waves to return, and thus calculating the distance travelled by the waves in knowing their speed and the time taken using basic SUVAT equations. However, it is not very useful in the field of astronomy, as the distances to be measured are so large, the reflected waves become too weak to be measured accurately, or at all, in most cases. In the case of Venus, which was successfully detected with radar, at 100 million km, the reflected signal even then was very weak. Radar is obviously not the tool for choice when distances of several million light years are common. However, it is useful in scenarios when smaller distances need to be measured, for instance, when an asteroid is passing near Earth, you can use radar to ascertain how far away it is, and also whether it is getting closer or further away depending on whether the time delay increases or decreases.

Parallax Parallax is the apparent change in position of an object due to change in position of the viewer and thus the angle at which the object is being observed. It is usually observed every 6 months, when the Earth is on the opposite side of the sun, to calculate the maximum parallax possible, which is itself half of the angle measured between the two different positions. When the parallax has been measured, the distance between the Earth and the object can be calculated using trigonometry, however, this method is not useful beyond distances of 100 parsecs, since the measurements beyond these are not accurate enough.

Standard Candles A standard candle is a class of astrophysical objects, such as supernovae or variable stars, which have known luminosity due to some characteristic quality possessed by the entire class of objects. If a distant object can be identified as a standard candle, then its absolute magnitude, M, can be known (derived from the logarithm of its luminosity as seen from a distance of 10 parsecs). Using the inverse square law, the distance of the object can be calculated using the absolute magnitude, the apparent magnitude, m, (the luminosity as observed by the viewer) using the equation:

Cepheid Variables A Cepheid variable is a star that pulsates radially, varying in both temperature and diameter to produce brightness changes with a well-defined stable period and amplitude. A strong direct relationship between a Cepheid variable's luminosity and pulsation period means that their distance can be easily calculated, and they can be used as distance indicators. By measuring the period of a Cepheid from its light curve (a graph of light intensity if an astronomical object against time), the distance can be calculated.

Red Shift Red and blue shift is a change in the colour of an astronomical body due to the Doppler Effect changing the wavelengths of the waves emitted by the object. Red shift occurs when the object is moving away, increasing wavelength, and blue shift occurs when the object is moving towards you, decreasing wavelength. It is quantified using for example the standard atomic emission spectrum of Hydrogen, which is easily identifiable and known. By comparison of such spectra, one can see the movement of the emission line, here redshifted below: Units of Distance Astronomical Unit The distance between the Earth of the Sun, now defined as exactly 149597870700m, since the actual distance varies. Light Year The distance travelled by light, or a photon, in a year: 9.4 x 1015m to 2 s.f Parsec An abbreviation for the parallax or one arcsecond: the distance from the sun to an astronomical object that has a parallax angle of one arcsecond, an arcsecond being 1/3600 of a degree, or approximately 4.848 micro radians.

Equations for DistancesSHIFT = cT (From Distance = Speed x Time)Due to Doppler shift, the change in wavelength depends on the speed of the object emiiting waves: = T Therefore describing the fractional change in wavelength:/ = c/This equation is more accurate for lower values for , and even though relativity hasnt been taken into account, at lower values of , for example 10-4c, the correction for relativity is only 1/106.RADARThe distance travelled by the wave must be the universal constant multiplied by time taken:s = ctHowever, this is twice the distance between the object and the viewer, and the wave travels there and back, thus:s = ct/2PARALLAXUsing the angle , the parallax measured, tan() equals the radius of the orbit of the Earth around the sun (an astronomical unit) divided by the distance between the sun and the object. tan() = r/dRearrangement gives us:d = r/tan() in degrees, d in mA simple formula connects it to the distance d between a star and our Sun:tan() = radius of earths orbit (1AU)/distanceThe parallax angle is always extremely small, we can say that tan(), thus:=> = 1/d=>d = 1/ 1 is 1AU, d in pc, in asec