astronomy test

Scientific Measurement Fundamentals

• Parts of a Scientific Measurement:

  • Best Guess or Estimate: The first part of a measurement, e.g., 12.34 cm.

  • Tolerance or Instrument Limiting Error (ILE): Measurement uncertainty, e.g., +0.02 cm.

  • Unit: The physical unit of measurement, e.g., cm.

Confidence Intervals

1. Determining a Confidence Interval:

   • Example: For a measurement of 12.34 cm with a ±0.02 cm error, the confidence interval is (12.32 cm, 12.36 cm).

   • This interval is a range of values representing where the true measurement likely falls.

2. Significance of Confidence Intervals:

   • They indicate that no measurement can be absolute; instead, we estimate a range where the true value exists.

   • A specific probability (e.g., 67% or 100%) conveys the confidence that the interval contains the true measurement.

3. Probability for a Single Measurement:

   • Determined by finding the smallest ILE which results in a 100% confidence interval around the measurement.

Significant Figures and Measurement Reliability

• Significant Figures in Measurement:

  • For 23.76 ± 0.01 m:

    • Significant figures: 4.

    • Least significant digit: 2, due to the precision of ±0.01.

    • Least count: 0.005 m, derived from halving the smallest division (0.01 m).

    • Potential values for the least significant digit: 0, 5, or possibly 1.

• Importance of Ratchet in Micrometer Measurements:

  • Ensures consistent application of pressure, preventing distortion and inaccuracies.

  • The mechanism provides reliable and repeatable measurements by controlling the force applied.

Number Significance and Measurement Metrics

7. Significance of Leading Zeros:

   • Example: 0.0078 has 2 significant figures; can be rewritten as 7.8 x 10^-3 in scientific notation.

8. Understanding Accuracy and Precision:

   • Accuracy: Closeness of a measurement to the true value.

   • Precision: The number of significant figures represented in a measurement.

   • Precision alone does not ensure accuracy; both are necessary for trustworthy results.

9. Multiplication of Measured Quantities:

   • Example Calculation: 13.675 x 19.43 = 265.70525.

     • Rounded result based on significant figures: 2.657 x 10^2 (4 significant figures determined by the lesser of the two measurements).

Systematic Errors and Distance Measurements

10. Types of Errors:

    • Non-Trivial Systematic Error: Inherent issues in equipment or procedures affecting measurements.

    • Trivial Systematic Error: Minor issues like parallax or zero error.

11. Astronomical Definitions:

    • Astronomical Unit (AU): Average distance from the Earth to the Sun (approximately 93 million miles).

    • Light-Year: Distance light travels in one year.

12. Stellar Distance Measurement:

    • Stellar Parallax: A technique to measure distances to stars based on apparent shifts in position relative to distant stars.

    • Accurate up to distances around 10,000 light-years, facilitated by instruments like the Hubble Space Telescope.

Notable Astronomers and Variables

• Henrietta Swan Leavitt: Discovered the relationship between the period of cepheid stars and their intrinsic brightness.

• Cepheid Variable Stars: Stars that change brightness in a periodic manner; crucial for distance measurement.

• Type Ia Supernovae: Result from white dwarf explosions, also used for cosmic distance scaling.

Cosmic Distance Ladder

13. Three Rungs of the Cosmic Distance Ladder:

    • Parallax: Previously discussed.

    • Variable Stars: Utilize the inverse square law for distance calculations.

    • Type Ia Supernovae: Also rely on the inverse square law for distance.

Free Fall and Motion Laws

1. Free Fall:

   • Objects falling under gravity experience uniform acceleration.

2. Acceleration: Definition as rate of change of velocity.

3. Acceleration Due to Gravity:

   • Varies by location; poles measure approximately 9.870 m/s², while equator measures about 9.803 m/s².

4. Newton’s Laws of Motion:

   • Second Law: F_net = m*a describes how a net external force causes acceleration.

   • Weight and Mass Relationship: Weight (W) is determined by W = m*g, where m is mass and g is gravitational acceleration.

5. Newton’s Law of Gravity: Universal attraction between masses; proportional to their product and inversely related to distance squared.

Tidal Effects and Planetary Orbits

6. Spring and Neap Tides:

   • Spring Tides: Occur during New and Full Moons.

   • Neap Tides: Happen during First and Third Quartiles of the Moon.

Planetary Science

7. Order of Solar System Planets from the Sun:

   • Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.

8. Pluto’s Classification: Now a dwarf planet rather than the traditional planet classification.

9. Constellations: There are 88 recognized constellations in the celestial sphere. The Zodiac consists of 13 constellations.

Kepler’s Planetary Motion Laws

10. Kepler’s Laws:

    • First Law: Planetary orbits are elliptical with the Sun at one focus.

    • Second Law: Equal areas are swept out in equal times.

    • Third Law: Orbital period squared is proportional to the semi-major axis cubed.

Atmospheric Science

1. Earth’s Atmospheric Composition:

   • 78% Nitrogen (N₂), 21% Oxygen (O₂), 0.93% Argon (Ar), and 0.04% Carbon Dioxide (CO₂).

2. Layers of the Atmosphere:

   • Troposphere, Stratosphere, Mesosphere, Thermosphere.

   • Weather occurs largely in the Troposphere.

3. Cumulonimbus Clouds: Terminate at the tropopause due to temperature changes.

4. UV Protection: Ozone and oxygen in the stratosphere protect against harmful UV radiation.

5. Ionospheric Reflection: Reflects radio waves up to 30 MHz.

Weather Principles

6. Ingredients for Weather:

   • Atmosphere, water, the Sun, Earth's rotation, volcanic, and biological activities.

7. Forms of Precipitation: Rain, snow, sleet, and hail.

8. Cloud Composition: Clouds contain tiny water droplets or ice crystals.

9. Dew Point Temperature: Temperature when air reaches 100% humidity.

10. Evaporation: Process of water molecules transitioning from liquid to vapor.

11. Greenhouse Gases: Include CO₂, CH₄, H₂O, N₂O, and O₃ which contribute to global warming.

12. Jet Stream Movement: Influenced by the Coriolis Effect, causing high altitude winds to shift eastward in the Northern Hemisphere.

Space Weather

13. Definition of Space Weather: Solar storm impacts on Earth, affecting telecommunications.

14. Solar Wind Speed: Travels at about a million miles per hour.