Parallax

How do astronomers measure distances to stars? One way is to measure what is called the parallax angle of the star which compares the position of the star to more distant, background stars. Parallax is a part of astronomy called astrometry which is the measure of stellar distances and motions.

• p is the parallax angle measured in arcseconds (1 arcsecond is 1/3600 of a degree)
• r is the distance from the Earth to the Sun (astronomical unit)
• d is the distance from the Sun to the star (in essence from the Earth to the star since r<<

In trigonometry, p is actually the arctan of r/d, but for small angles, tan(p) is approximately p. Astronomers then define a unit of measure called a parsec to make calculations easier.

• One parsec is the distance a star would have to be from the Sun to create a parallax angle of 1 arcsecond (1") as seen from Earth (r = 1 AU)

Notice that the parallax angle is only one-half of the total angle created for the star's position in January and June.

What's nice about this equation, is it works for any distance r as long as r is measured in AU. There was talk about placing a space probe near Jupiter's orbit to create a much larger baseline. Remember, that r for Jupiter is approximately 5.2 AU which means the angle p would be 5.2 times larger than at Earth. Larger angle are obviously easier to measure than small angles.

The closest star to the Sun (Earth) is Proxima Centauri. Its parallax angle is approximately 0.75" which means it is about 1.3 parsecs from Earth. All other stars have a larger distance, so they have much smaller parallax angles, which is why it would be better to measure parallax farther out in the Solar System.

New Horizons

On December 6, New Horizons "woke up" for the last time. It is on its last 162 million mile journey to an object in our solar system that has never been visited by Earth spacecraft until now.


Pluto will be visited for the first time and we will have the best resolution images of Pluto ever by mid-May. By July of 2015, New Horizons will finally arrive at the Pluto system and we will also have close-up images of five of its major moons (or co-orbital bodies): Charon, Nix, Styx, Hydra, and Cerebus.

New Horizons Instrumentation

Image Credit:

NASA/Johns Hopkins University Applied Physics Laboratory/Southwest Research Institute

Read more about the mission at NASA.gov

If Our Sun was a Black Hole

Back in 1994, Soundgarden released a song off their album Superunknown called "Black Hole Sun". Since I want to talk about what would happen if our Sun became a black hole, it gives me an excuse to post this video.

from Soundgarden's Official YouTube Channel

 

Remember, the Sun will never become a black hole as it is too small, but for fun, let's find out what would happen if it did.

First, we should determine what the Schwarzschild radius of the Sun would theoretically be. When a black hole evolves, not all the mass of the main sequence star is in the black hole, but for our purposes, we will assume that somehow the Sun we see shining right now will have all its mass converted into the black hole. We will need to know two things: the Sun's mass in kilograms and the Sun's radius in meters (we do everything in metric).

• Sun's Mass (M₈) = 1.99x10³⁰ kg (we will say 2x10³⁰ kg for simplicity)
• Sun’s Radius (R₈) = 696,342 km = 6.96x10⁸m

Note: the symbol 8 refers to the Sun. When that subscript follows M or R, it just means the unit is in solar masses or solar radii.

Recall that the Schwarzschild radius is this:

Plugging in the values for the Sun's mass, G (6.67x10^-11 m³kg^-1s^-2), and c (3x10⁸ m/s), we find that if all the mass of the Sun became a black hole, the Schwarzschild radius would be 2,960 meters or about 3 km.  Compare that to the actual radius of the Sun and you can see how much smaller it would be.

So what would it mean for the Earth if the Sun became a black hole? In a couple of words, not much. The Earth would still be orbiting the same mass, so our orbital radius and speed would not change. However, life on Earth would die out because we would not be receiving the same radiation from the Sun to which we have been accustomed. No visible light from the Sun warming us, heck, no radiation of any kind. Black holes do not give off radiation in that manner. Due to Hawking radiation, particles near the event horizon of the black hole (the theoretical distance where light could escape from the black hole) would evaporate off. Some might hit Earth, but there wouldn't be anything to keep our planet warm.

Observation of a Black Hole

As mentioned in the last post, black holes are black because light cannot escape them. In fact, black holes do not emit any radiation at all because of their extreme density. So exactly how can we observe a black hole?




There are a couple of ways. The first way is too look at the gas and dust that surround a black hole. This gas and dust are in what is called an accretion disk and as the accretion disk orbits the black hole (just outside the Schwarzschild radius), it does two things.

1. It falls into the black hole, in turn making the black hole slightly bigger. This is where the term accretion comes from as the material accretes onto the black hole.
2. The inner edge of the disk is very hot because it's moving very fast. The gas and dust gets so hot that the material begins to radiate energy and give off energy in the form of jets. We see these coming from the "poles" of the black hole and know that there is a black hole there.

Accretion Disk around a Black Hole with jets

Image Credit:

Christopher Wanjek/NASA

Also, if you observe the gas and dust, you can measure the orbital velocity of the gas. You can also determine the radial distance of the gas and dust from the central body. By using these two values, the mass of the central body can be measured. For any radius, a mass above a certain value for that radius will tell you that the body is a black hole using the Schwarzschild radius equation.




Another strange thing about black holes is that black holes are not permanent. Hawking radiation predicts that due to quantum effects, particles of the black hole near the Schwarzschild radius can escape. Over time, as more and more particles escape, the black hole can shrink in size. See more about Hawking radiation here.

Black Holes

Black holes may be one of the most strange features in the universe. These objects are so dense, light cannot even escape from them!





Amazingly enough, almost all black holes started out as a hot, bright, large star. These stars go through the same evolution that leads to a neutron star, but unlike a neutron star, these objects are so massive, even neutron degeneracy is not enough to overcome gravity. Gravity compresses the star so much that instead of having a small core remnant after the supernova explosion, all that's left is what is called a singularity. Singularities are thought to be an object so small but so massive that it has an infinite density. In reality, this isn't true, but a naked black hole has never been observed, so the assumption is accurate for now.





There are a couple of things that define a black hole. One is its Schwarschild (pronounced Schwartz-Shield), which is the theoretical distance from the center of the black hole where the escape velocity from the black hole equals the speed of light. The speed of light is approximately 300,000 kilometers per second, or fast enough that a beam of light can circle the Earth 12 times at the equator. The escape velocity is given by the square root of 2 times G (the gravitational constant ~ 6.67*10^-11 m³/kg*s²) times the mass of the star or planet divided by the radius of the planet squared.





Or in equation form:

If you change V_esc to the speed of light, c, you can solve for R, and solve for the Schwarschild radius, R_s.

where M_Star is the mass of the Star, or in this case a black hole.

Next time, we will learn more about black holes, like how they are observed and what else we know about them.

Pulsars

As mentioned in the last post, pulsars are a specific type of neutron stars. Neutron stars have very strong magnetic fields, that are not necessarily lined up with their axes of rotation. Pulsars give off radiation as energy is directed along the axis of the magnetic poles and "beamed" towards Earth. These beams or jets are very energetic and can be seen for thousand of light years. When the jet of energy is pointed in the direction of Earth, we see them as a pulsar.

A very badly drawn schematic of a pulsar

A pulsar acts kind of a like a lighthouse in that the beam sweeps around as the light source rotates. Unlike a lighthouse, however, a pulsar's period can be extremely short, on the scale of milliseconds. The faster pulsar discovered has a period of about 3 milliseconds, and for something as large as a neutron star (about 10 km in diameter), the pulsar has to be rotating very fast.

We are unsure whether or not all neutron stars are pulsars, though we do know that most pulsars are neutron stars. Since pulsars can only be detected if the jet of energy is pointed directly towards Earth, we don't know if all neutron stars do this.