Motion of Celestial Bodies Review PDF

Name: Date: Unit 2 Motion of Celestial Bodies: Kepler’s Laws: HS-ESS1-4 Orbital Motions Use mathematical or computational representations to predict the motion of orbiting o...

Name: Date: Unit 2 Motion of Celestial Bodies: Kepler’s Laws: HS-ESS1-4 Orbital Motions Use mathematical or computational representations to predict the motion of orbiting objects in the solar system. (Scale, Proportion, and Quantity) Checklist Can I use appropriate mathematical models to represent orbital motion (Kepler’s laws) showing work and including appropriate units? Am I able to manipulate variables in your models or calculations (e.g., mass, distance, velocity) to observe how changes affect the motion of orbiting objects? I can use models or calculations to make accurate predictions about future positions of orbiting objects? Can I recognize the vast differences in scale (e.g., distances between planets, sizes of celestial bodies) and how that scale affects the gravitational forces and orbital motions? Am I using proportional reasoning to understand relationships between mass, distance, and gravitational force? Can I explain how changes in one parameter (e.g., mass, velocity) lead to changes in orbital characteristics (like gravitational pull)? Can I interpret information about our solar system using data? Gravitational Forces: Gravitational forces between celestial bodies govern their motion, acting over vast distances. These forces, especially between planets, moons, and the Sun, are responsible for the stable orbits of objects in the solar system. Orbital Motion: Objects in the solar system follow predictable, elliptical orbits due to gravitational forces. Planets, moons, and artificial satellites move in orbits around larger bodies like the Sun or planets. Kepler’s Laws of Planetary Motion: First Law (Law of Ellipses): The orbit of a planet around the Sun is an ellipse, with the Sun at one of the two foci. This explains why planets do not move in perfect circles but in elongated paths. ○ When you increase the distance between the focal points, you increase the eccentricity. ○ Eccentricity is always between 0-1 ○ Closer to 0 is more circular (Slightly eccentric) ○ Closer to 1 more flat or oval (Very eccentric) Eccentricity= Distance between the foci / Length of the major axis  Second Law (Law of Equal Areas): A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This means planets move faster when they are closer to the Sun and slower when farther from the Sun. Third Law (Law of Harmonies): The square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit. This law relates the time it takes a planet to orbit the Sun to its average distance from the Sun, with more distant planets having longer orbital periods. ○ MS x T2 = R3 ○ Newton’s Law of Universal Gravitation: Newton’s law states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force governs the orbital motion of all objects in the solar system. The chart below depicts data about our solar system. Page 2 ESSRT 1. Celestial Object: This lists the objects in the solar system, such as planets, the Sun, and other celestial bodies like Ceres and Eris. 2. Mean Distance from Sun (million km): This indicates the average distance of the celestial object from the Sun in millions of kilometers. 3. Period of Revolution: This shows the time it takes for the celestial object to complete one orbit around the Sun. It is given in Earth days (d) or Earth years (y). 4. Period of Rotation at Equator: This shows the time it takes for the celestial object to complete one rotation on its axis at the equator. It is given in Earth days (d), hours (h), and minutes (min). 5. Eccentricity of Orbit: This indicates how much the orbit deviates from being a perfect circle (0 is a circle, values closer to 1 are more elliptical). 6. Equatorial Diameter (km): This is the diameter of the celestial object at its equator, given in kilometers. 7. Axial Tilt (°): This is the angle between the object's rotational axis and its orbital axis. It is given in degrees. Lunar and Celestial Cycles: HS- ESS1-7 Construct an explanation using evidence to support the claim that the phases of the moon, eclipses, tides and seasons change cyclically. Checklist: Can I describe how the tilt of the Earth’s axis leads to seasonal changes and demonstrate this using a model? Can I explain, using evidence, how we know Earth rotates on its axis and revolves around the sun? Can I observe and describe the patterns in the moon phases and model them to predict future phases? Can I explain how the patterns of solar and lunar eclipses demonstrate the cyclical nature of the Earth-moon-sun system? Can I explain how the gravitational pull of the moon affects ocean tides and provide evidence to support this? Can I create a model to represent the Earth-moon-sun system and explain phenomena such as eclipses and tides? Can I identify the interactions within this system that lead to changes in tidal patterns and visualize these interactions? Earth’s Motions Earth Rotates on its axis DAILY. Natural Phenomena: ○ All celestial objects appear to rise in the east and move west (apparent motion) ○ Star Trails (Stars appear to rotate 15 ̊/hour with Polaris at center). Evidence: ○ Coriolis Effect (deflects winds to right in the Northern Hemisphere) ○ Foucault Pendulum (appearance of change in swing direction) Earth Revolves around the Sun YEARLY. Natural Phenomena: ○ Constellations are change throughout the year ○ Seasons Seasonal changes Seasonal changes are caused by: ○ Earth’s revolution around the Sun ○ Earth’s axis is tilted at 23.5 ̊ with North Pole aligned with Polaris (parallelism). Seasons in the Southern Hemisphere are opposite. Duration of Insolation: length of daylight period ○ Length of daylight depends on your latitude and time of year. ○ The Equator always has 12 hours of daylight. Angle of Insolation: how high the sun is in the sky (between 0 and 90 degrees) ○ The greater the angle of insolation, the greater the intensity of insolation and the warmer the temperature. ○ Vertical rays: locations that receive sunlight directly overhead (90 degrees above the observer) NEW YORK STATE NEVER RECEIVES VERTICAL RAYS! Season starts in Date Location of Direction of sun Length of day in the N. Vertical Rays rise and sun set N. Hemisphere Hemisphere Winter Solstice 12/21 23.5S Tropic of SE & SW Shortest day (9 Capricorn hours in NY) Equinoxes 3/21 & 9/23 0 E&W 12 hours of day and night Summer Solstice 6/21 23.5N Tropic of NE & NW Longest day (15 Cancer hours in NY)  Sun’s apparent path in New York State: Solar Time: the time of day can be estimated using the Sun’s location on its path through the sky. a. Solar noon: halfway through the daylight period. Represented by the location where the Sun’s path intersects the arc of the diagram. b. Sunrise: where the sun intersects the eastern horizon c. Sunset: where the sun intersects the western horizon Shadows always point in the opposite direction from the light. a. The lower the altitude of the Sun, the longer the shadow. (winter, sunrise, sunset) b. The higher the altitude of the Sun, the shorter the shadow. (summer & solar noon) The Moon Phases & Motions of the Moon ○ Moon phases are cyclic and predictable. ○ We only see the same side of the moon because the Moon’s period of rotation (27.3 days) equals the Moon’s period of revolution around Earth (27.3 days). (ESRT p. 15) ○ Moon phases are caused by the Moon’s revolution of Earth. We see a full cycle of Moon phases every 29.5 days. ○ Know how to determine Moon phase as seen from Earth using a diagram of the Moon’s orbit:  Ocean Tides ○ Tides are the cyclic & predictable rise and fall of ocean waters. i. Tides are caused by the gravitational pull of the Sun and the Moon. ii. The Moon has more influence over the tides because it is closer to Earth. ○ Time from high tide to high tide (or low tide to low tide) = 12 hours 26 minutes ○ Spring tides: Extreme tidal change (highest high tides/lowest low tides) = Full or New Moon ○ Neap tides: Minimal tidal change (lowest high tides/highest low tides) = 1st or 3rd Quarter Moon Eclipses ○ Solar eclipse: Sun is blocked by the Moon. Only occurs during the New Moon. ○ Lunar eclipse: Moon moves into Earth’s shadow. Only occurs during Full Moon. ○ Eclipses are rare because the Moon orbits Earth on a 5 ̊ incline.