# Measuring the Universe

Contents

How have we applied science and mathematics to understand our solar system?

## Modeling the solar system

Astronomy begins when we look up and start asking questions. Where are we? How big is the earth? This lesson is for all ages, start here!

Article

The geocentric universe

Article

Planets & epicycles

Article

The heliocentric model

Creation

INTERACT: Models of the solar system

Change your model of the universe by selecting from menu.

3:06

Conjunctions

The three brightest planets in the night sky on May 26th, 2013 lined up for a beautiful sunset conjunction.

1:47

Lunar eclipse

When the moon passes through the Earth's shadow, it causes the moon to look very unusual for a short period of time. This event is called a lunar eclipse, and it occurs roughly twice a year.

Creation

ANIMATE: Phases of the moon

The red dot represents your position on the earth.It's on the equator and assumes the earth's axis is perpendicular to its orbit with the sun and moon. The top of the screen shows what you see as you look into the sky.

Article

Typs of lunar eclipses

Creation

INTERACT: Lunar eclipse

Challenge: Use sliders to simulate a lunar eclipse.

Exercise

Modelling the solar system

## Measuring the solar system

How can we apply geometry and trigonometry in order to measure the size of the earth, moon and sun?

Article

A flat earth

Exercise

Arc length

Relate the length of an arc to the circumference of a whole circle and the central angle subtended by the arc.

7:29

Circumference of Earth

Article

Occultations

Exercise

Occultation vs. transit vs. eclipse

Article

Size of the moon

Article

Angular measure 1

Exercise

Angular measure 1

warm up questions on angular measure

Exercise

Trigonometric ratios in right triangles

Given the side lengths of a right triangle, find the sine, cosine, or tangent of one of the acute angles.

Article

Angular Measure 2

Exercise

Angular Measure 2

Article

Intro to parallax

Article

Parallax: distance

Exercise

Parallax method

Article

Solar distance

Exercise

Solve similar triangles (advanced)

Given two similar triangles and some of their side lengths, find a missing side length.

Article

Size of the sun

12:31

Scale of solar system

Sal Khan describes the scale of our Solar System.

## Orbital mechanics 1

How do planets move? An introduction to orbital mechanics and the work of Johannes Kepler.

Article

Discovering pi

Article

Applying pi

Exercise

Area and circumference of circles challenge

Practice interesting area and circumference problems.

Article

Circular orbits

Creation

Coding a circular orbit

Article

Kepler's first law

14:14

Intro to ellipses

Sal introduces ellipses and shows how their standard equation relates to their center and radii (ellipses have two radii: major and minor).

Exercise

Center & radii of ellipses from equation

Find the center and major and minor radius of an ellipse given its equation.

Creation

INTERACT: Elliptical orbits

Click and drag either foci to change orbit. You can also mouseover the terms below for definitions.

## Spectroscopy

There is much more to light than meets the eye. Introduction to the electromagnetic spectrum and the science of spectroscopy.

Article

Origins of spectroscopy

4:50

Visible light (1672)

5:23

Infrared waves (1800)

3:40

Ultraviolet waves (1801)

Article

Absorption/emission lines

Exercise

Absorption lines

5:56

Spectroscopy

3:39

Radio waves (1888)

2:50

X-rays (1895)

3:42

Gamma waves (1900)

3:04

Microwaves (1930)

6:23

Spitzer telescope

400 years of Astronomy using Telescopes. To commemorate this International Year of Astronomy, three of NASA's flagship observatories have put a new spin on how we see the Pinwheel Galaxy!