Motions in the Sky, Seasons, and Parallax

Motions in Sky, Seasons, and Parallax

Seasons

• Earth's distance from the sun has a minor influence on seasonal temperature variations.

• The seasons are not related to Earth's distance from the sun. Earth is slightly closer to the sun in the Northern Hemisphere's winter than in summer.

Earth's Axis

• The angle of sunlight is closer to perpendicular in summer, concentrating energy.

• The Southern Hemisphere's seasons are opposite to the Northern Hemisphere.

• Earth's axis is not perpendicular to the ecliptic plane but is at an angle of 23.5 degrees, which is why there are seasons.

• Seasons are caused by the varying angle of incidence of the sun’s rays.

• More energy is received when the sun shines onto Earth's surface at a steeper angle of incidence.

Special Days of the Year

• Summer solstice: Sun farthest north.

• Autumnal equinox: Sun on the equator, moving southward.

• Winter solstice: Sun farthest south.

• Vernal equinox: Sun on the equator, moving northward.

Measuring Distances

• Use geometry to find the distance of something beyond the reach of measuring instruments.

Measurement of Distance

• Triangulation: measure baseline and angles, calculate distance.

Angular Measurements

• Astronomers use angles to measure apparent sizes of objects in the sky.

• The basic unit of angular measure is a degree (°).

• The angular size of the Moon is ½°.

• The angle between lines from your eyes to two stars is the angular distance between them.

• The adult human hand held at arm’s length provides a means of estimating angles.

Trigonometric Parallax

• Demonstration: Notice how your finger appears to move relative to a lamppost when viewed with alternating eyes.

Stellar Parallax

• The ½ of the angle between the now location and the 6-month location is called the stellar parallax.

• Nearby stars appear to move with respect to more distant background stars due to the Earth's motion around the Sun.

Angular Measurements

• Full circle = 360°

• 1° = 60' (arcminutes)

• 1' = 60'' (arcseconds)

Parallax Distance: Parsec

• A star with a parallax of 1 arcsecond has a distance of 1 Parsec.

• Distance to a star: d (parsec) = \frac{1}{p (\text{arcseconds})}

• Example 1: p of 0.01” => 100 pc

• Example 2: p of 0.05” => 20 pc

• d = \frac{3 \times 10^{13} \text{ km}}{p}

• 1' = \frac{1}{60}°

• 1'' = \frac{1}{3600}° = \frac{1}{60}'

Lecture Tutorials

• Work quickly 10-15 minutes for each activity.

• Questions go from easier to harder.

• Exam questions are like those in the Lecture Tutorials.

• Write clear explanations for answers.

• It is okay to change groups to find people to work with.

Lecture Tutorial: Parallax pp. 41-43

• Work with partners, not alone.

• Work quickly - you have 10 minutes.

• Read the instructions and questions carefully.

• Discuss concepts and answers with one another. Understand the concepts now.

• Come to a consensus answer you all agree on.

• Write clear explanations for your answers.

• Ask another group if you get stuck.

• Ask for help if you get really stuck or don’t understand the Lecture Tutorial.

Parallax and Distance

• Parallax decreases with distance.