Today’s lecture

• Scientific method• Night sky• Celestial coordinate systems• Parallax• Angular size

To understand the universe, scientists use the “Scientific Method”

1. Observe - Observe something. Write down the observations and make sure that other people can repeat them on their own.

2. Guess - Make a guess about how that something happens. The guess has to be in the form of an explanation that can be used in other contexts. The guess must help to make predictions about other observations.

3. Test and Criticize - Observe similar things to see if the guess (the explanation) is correct or needs to be modified.

4. Repeat - until you get it right.

Types of Guesses

Hypothesis• One or more ideas to explain an observation or set of

observations. Must be useful in making predictions about other observations, be testable, and be falsifiable.

Model• Hypotheses that have withstood observational and

experimental tests.Theory• A well-founded body of related hypotheses and models

that form a self-consistent description of nature.Law• A theory that has been very well tested and is applicable

over a wide range of different situations.

Which are legitimate scientific hypotheses?

1. Any two objects dropped from the same height above the surface of the moon will hit the lunar surface at the same time.

2. Our universe is surrounded by another, larger universe, with which we can have absolutely no contact or interaction.

3. All horses are brown.

Science, religion, and pseudo-science

• Scientific theories are experimentally verifiable (or falsifiable) and predictive. They address how questions (e.g. How do stars form? How is a lunar eclipse caused? How did the Universe evolve?)

• Religious and ethical statements are (generally) not verifiable. They address why questions (e.g. Why does the Universe exist? What kind of life is worth living?). These are not intrinsically less worthwhile than scientific inquiries, they are simply addressing different questions. Religion and science come into conflict when religion supplies answers for questions that can now be addressed by science, i.e. evolution of humans, age of the Universe.

• Pseudo-science theories pretend to be scientific but are either not falsifiable (e.g. séances, ) or supporters or use anecdotal evidence to support claims (e.g. astrology, ‘creation’ science).

Skepticism and Truth• Role of skepticism. An essential part of the scientific

method. Scientists always question the basis for an scientific assertion. This is often considered ‘impolite’ behavior in social settings, but is not impolite in scientific discussion.

• ‘What is truth?’ - Scientific theories are not statements of truth. They are the best available explanation for observed facts, but are subject to revision or falsification.

• Scientists must be able to admit that they are wrong.

Occam's Razor• What if two or more competing hypotheses both pass some

initial tests - how do you choose between them?

• If the hypotheses generate different predictions it will be a simple matter to pick the best one - as long as it is feasible to carry out the experimental tests. What if the competing hypotheses don't give distinguishable, feasible predictions? Enter "Occam's Razor".

• William of Occam was a medieval scholar and logician, and, in modern form, the principle that has come to be known as Occam's Razor says:

If two hypotheses can't be distinguished experimentally, choose the simpler one.

How does one locate an object on the night sky?

1. By drawing imaginary patterns on the sky (the constellations) and then locating the object relative to the stars in the constellations.

2. By drawing an imaginary coordinate system on the sky, then specifying the objects coordinates.

Eighty-eight constellations cover the entire sky.

• 6000 stars visible to unaided eye (only half are above the horizon).

• 88 semi-rectangular groups of stars called constellations.

• Some stars in the constellations are quite close while others are very far away.

Finding M51

Finding M51

Finding M51

We use angles to denote the positions and apparent sizes of objects in the sky.

Your hand at arm’s length is about 10 degrees wide

Your thumb at arm’s length is about 2 degrees wide

Coordinate system

Coordinates are

Latitude = degrees North or South of the equator

Longitude = degrees East or West of the “Prime meridian”

Prime meridian is historically defined as longitude of the Royal Observatory in Greenwich, England

Sky coordinate system

Introduce the ‘celestial sphere’

This is an imaginary sphere drawn in space with the earth at its center.

We align the sphere with the Earth.

Coordinates are:

Declination = degrees North or South of the equator.

Right ascension = degrees East of the “Vernal equinox”.

Vernal equinox is defined as the position of the Sun on the first day of spring. Note it is a point on the sky, not the earth.

Motion of stars on the

sky

The rotation of the Earth causes the stars to appear to move on the sky.

Precession

• If you spin a top, its very hard to get it to spin exactly straight – usually it wobbles around in a circle

• The spinning Earth wobbles in exactly the same way – this is called precession

Precession of the Earth

Precession causes celestial coordinates to change slowly with time. When observing, one must have coordinates for the correct epoch.

Angular Measure for Small Angles

1º = 60 arcminutes = 60′

1′ = 60 arcseconds = 60″

e.g., On January 1, 2004, the planet Saturn had an angular diameter of 19.7″ as viewed

from Earth.

How can you measure the distance to an object you can’t reach?

• Use triangles…

Triangles

The small triangle has the same shape as the large one.

By measuring the two sides of the small triangle and the short side of the big triangle, we can calculate the length of the long side of the big triangle.

Measuring distance

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So, how can we measure the distance to stars?

Take two telescopes some distance apart and observe the same star.Measure the tilt between the two telescopes – this sets all the angles for the triangles.Then we can find the distance to the star from the distance between the telescopes and the angle of the tilt.

p

p

So, how can we measure the distance to stars?

• We want to use the largest distance we can for the short side of the big triangle

• What is the largest distance we can get between the two telescopes (if both of them have to be on Earth – no spacecraft).

So, how can we measure the distance to stars?

• The largest distance is not by placing the two telescopes at opposite ends of the Earth.

• Instead, we can use one telescope and just let the earth move.

A.U. = Astronomical Unit = distance from Earth to Sun

Stellar Parallax

As Earth moves from one side of the Sun to the other, a nearby star will seem to change its position relative to the distant background stars.

d = 1 / pd = distance to nearby star in parsecs

p = parallax angle of that star in arcseconds

Closer star – larger parallax

Example: Using parallax to determine distance

The bright star Vega has a measured parallax of 0.1 arcsec (p = 0.1″)

This means that Vega appears to move from +0.1″ to -0.1″ with respect to distant stars over a year’s observation

D(pc) = 1/p(″) = 1/0.1 = 10 pc

Vega is 10 pc (parsec) from Earth(remember: 1 pc = 3.26 light years)

Sizes of Astronomical Objects

• How can we measure the sizes of astronomical objects?

• The same way that we measure distances – using triangles

The Small-Angle Formula D = linear size of object

θ = angular size of object (in arcseconds)

d = distance to the object206265dD

Example: On November 28, 2000, the planet Jupiter was 609 million kilometers from Earth

and had an angular diameter of 48.6″. Using the small-angle formula, determine Jupiter’s actual

diameter.

D = 48.6″ x 609,000,000 km / 206265 = 143,000 km

The Small-Angle Formula D = linear size of object

θ = angular size of object (in arcsec)

d = distance to the object206265

dD

Review questions• What do we mean by a model in science?• Determine the distance to Alpha Centauri

which has a parallax of 0.75 arcseconds.• If one can measure stellar positions to an

accuracy of 0.01”, what is the farthest distance that can be measured to an accuracy of 10% or better?

• If the distance to the Sun is known, describe how one could determine its physical size.