## How Far Is It?

One of the three or four most commonly asked questions at Frosty Drew Observatory is "How far is it?" where "it" might be something in the solar system, an interstellar or intergalactic object. The high school trigonometric techniques for measuring distant objects can only be used for the nearest objects unless we know something "special" about what we are looking at. All the angles used in measuring very distant objects are extremely small. Every measurement introduces some probable error. When the error approaches and eventually becomes larger than the measured angle, the technique fails.

Everything within the solar system is close enough for us to determine its distance to a few parts per billion using simple trigonometry. However simple trigonometry only works for a very few of the closest extra solar stars. Even the closest star's angle is 0.0002145°. Space probes and radar which are feasible for the planets are impossible outside the solar system. Probes would take tens of thousands of years to reach the nearest stars. Radar echoes would be so impossibly faint that we couldn't detect them.

When we know how long it takes for light to reach us from an object with some degree of accuracy, we also know the distance to the object to the same degree of accuracy. In those rare lucky cases where light travels to us directly and indirectly by reflecting off another surface or volume of gas, we can establish the ratio between the direct and reflected path times. If we can measure the angle between the direct and reflected events, we can determine the sides of a triangle, establishing the distance.

V838 Monocerotis, a bright star in a huge gaseous envelope, went nova, increasing its brightness 3000 fold. As we watched the event unfold through the Hubble Space Telescope, the light not only reached us directly but was reflected from the surrounding gas. As time progressed, light from the original flare illuminated ever great volumes of gas. Since the speed of light is constant, the expanding wave front of light illuminated a ever increasing spherical volume of gas. For example after six months, the sphere had a radius of one half lightyear and so on. Measuring this enlarging sphere has allowed us to determine that V838 Monocerotis is 20,000 light years away. You can view these remarkable successive light echoes in a movie or in still images.

Another method for determining the distances depends on stellar systems with two or more stars. By watching the system over a long period (usually decades) it is possible to determine the longest axis of the orbital ellipse. If we know the mass of the system and each of its stars, it is possible to apply a combination of algebra and trigonometry to determine the true shape of the ellipse and ultimately how far away the pair of stars are. Since half the stars in the sky come in multiple star groups this method sounds like it should be ideal for determining distances. There is a problem however. We need to know the mass of the system - and guess what we usually need to know to determine the mass - yes indeed - the very geometry which we need the mass to know. This is a classic "chicken and the egg" type problem. It isn't totally hopeless. We can determine the upper limit of the masses simply knowing the orbital period and observing the stars.

It may seem odd that we know the distances to galaxies on a relative basis with more accuracy than we know the distances within most of our galaxy but this indeed happens to be the case. Galaxies rotate. One side spin toward us as the other side spins away. This difference appears as a blue tinge on one side and a red tinge on the other. The faster the galaxy spins, the more pronounced this red/blue shifting. Galaxies must not spin too fast or too slowly or gravity will either not be enough to hold the galaxy together or it will be too much to keep the galaxy from collapsing in on itself. Knowing the gravity force implies the mass of the galaxy. Combined with the image of the galaxy, we have enough information to determine the distance to the galaxy to several significant digits. Once again there is a problem with this technique. We can only determine red/blue shifting for relatively nearby galaxies. The distant galaxies create such tiny images that we can't separate the colors well. For the smallest of these distant galaxies we can't even determine its image size well.

Author:
Leslie Coleman
Entry Date:
May 1, 2003
Published Under:
Leslie Coleman's Columns