###### By Joshua N. Winn, Princeton University

## Astrophysics and astronomy: The two words are basically interchangeable these days, but there is a subtle intellectual distinction. Astrophysics is the application of the laws of physics to understand celestial phenomena. Occasionally, we even discover a new law of physics by studying what’s out there. In contrast, astronomy can be defined as the careful observation of heavenly bodies which only gradually has become scientific.

### Astrophysics Vs Astronomy

Astrophysics began in the 17th century with Isaac Newton, who explained the motion of the planets with his new equations relating force, mass, acceleration, and gravity. The actual word ‘astrophysics’ is more recent. It’s from the mid-19th century, after the invention of photography and spectroscopy. Those two techniques were crucial because they allowed us to go beyond looking through telescopes with our eyes. Now, we could make more objective records, detect fainter sources, and connect our observations to laboratory experiments with light, heat, and atoms.

On the other hand, astronomy is a cultural activity dating back thousands of years, which only gradually became scientific. The ancient Babylonians, the Chinese, and the Mayans were all accomplished astronomers, but they weren’t astrophysicists.

### Spanning Vast Range of Scales

There are many reasons to love astrophysics, one of which is that no other science spans such a vast range of scales, from nanometers to billions of light years, from the radiation of a single electron to the output of trillions of suns.

If we make a scale model of the solar system, with everything shrunk down by a factor of almost a billion, the Sun would be a sphere as tall as a man, and the Earth would be like a grape, located 2.5 blocks away. This works well to put the solar system into perspective

But this approach fails when we try to put the whole universe into perspective. Even if we scale everything down by a factor of a billion, the very nearest star to the Sun would be 25 thousand miles away and our next-door neighboring galaxy would be 20 billion miles away.

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### Space between Stars

No matter how much we try to scale things down to a manageable size, we would still get mind-boggling numbers. The problem is there’s no one scale factor that can put all the different phenomena into a mentally comprehensible map.

All the natural scales are separated by factors of order a hundred, or a thousand, except for the parsec, the scale in between the stars, which is 206,265 times bigger than the AU (Astronomical Unit), the scale of planetary systems.

What this means is that stars and their planets are unusually isolated—the spacing between them, relative to their size, is larger than for other types of astronomical objects. This has the fascinating implication that collisions between galaxies are common, but collisions between stars are vanishingly rare. Even when 2 entire galaxies are colliding, there’s not much chance that any 2 stars inside those galaxies will hit each other.

### Logarithmic Maps

There is a tactic astrophysicists use to cope with all these orders of magnitude. They make logarithmic maps. Taking the logarithm of a number means expressing the number as a power of 10, and then plucking out the exponent. For example, 1000 is 10^{3} power. So, the logarithm of 1000 is 3. The log of a million is 6. And this works for numbers smaller than 10, too. The number one is equal to 10 to the zeroth power, so the log of one is zero. One-tenth is 10^{–1} power, so the log of a 10th is negative one. And so on.

So, what’s a logarithmic map? An ordinary map is based on a single scale factor. One inch on the map might be one kilometer in real-life. But on a logarithmic map, the scale factor changes as we move from one end to the other. The first inch might correspond to one meter in real-life, but then the second inch is 10 meters, then 100 meters, a 1000, 10^{4}, 10^{5}, and so on. Mathematically, with every inch, we increase the logarithm of the scale factor by one unit.

### Logarithmic Charts

There are logarithmic charts, besides maps. Astrophysicists use logarithmic time lines, and they make more abstract logarithmic charts to help understand things that range over many orders of magnitude.

For example, our galaxy is full of objects ranging widely in mass, and in size. Among other things, there are asteroids, moons, planets, and stars. Let’s say we go around the galaxy and measure the mass and radius of everything smaller than the Sun. To compare all these things, there is made a chart of mass versus radius.

On a regular chart, the horizontal axis is mass, in units of Earth masses, and the vertical axis is radius, in units of Earth radii. Each data point shows the mass and radius of a single object. There’s clearly a relationship between radius and mass; the more massive the object, the bigger the radius, which makes sense. But there’s a problem with this chart. Because we need to make the axes range high enough to encompass the very largest objects—millions of Earth masses—the more numerous smaller objects end up crammed in close to the origin, and we can’t make out the details.

If we remake this chart with logarithmic axes, then the horizontal axis still tells us the mass, but now each tick mark represents a factor of 10. So, the Earth is at one Earth mass, 10 to the zero. And the Sun is a few hundred thousand Earth masses, which is 10^{5.5} power, so the data point for the Sun is 5.5 ticks to the right. Likewise, the vertical axis still tells us the radius, but on a logarithmic scale.

### Common Questions about Astrophysics

**Q: What is the difference between astrophysics and astronomy?**

Astrophysics is the application of the laws of physics to understand celestial phenomena. Meanwhile, astronomy is the careful observation of heavenly bodies which only gradually has become scientific.

**Q: What is the implication of parsec being much bigger than AU?**

Parsec, the scale in between the stars, is 206,265 times bigger than the AU (Astronomical Unit), the scale of planetary systems.

**Q: How is logarithmic map different from ordinary map?**

Unlike an ordinary map, which is based on a single scale factor, on a logarithmic map, the scale factor changes as we move from one end to the other. The first inch might correspond to one meter in real-life, but then the second inch is 10 meters, then 100 meters, a 1000, 10^{4}, 10^{5}, and so on.