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Heliocentrism and Retrograde motion (1) 1 (1) (1) (1).pptx
- 1. HELIOCENTRISM AND RETROGRADE MOTION Mentor : Mr. Ranit Behera Presented By : Ishan, Maithili, Varada
- 2. THIS PRESENTATION FOCUSES ON : Geocentric and Heliocentric Theory Solar Day and Sidereal Day Retrograde Motion of Planets (wandering stars) Prograde Motion Kepler's Laws Kepler's Orbital Equation Pseudo Forces Lagrange Points (L1,L2,L3,L4,L5) Trojan asteroid belt Energy Conservation Equation(Orbit Shape) Space Missions at Lagrange Points: JWST and Aditya L1 Use of Desmos (a graphing calculator)
- 3. INTRODUCTION In this presentation we will see about the different models of universe proposed by various scientists , their pros and cons. We will also take a look at retrograde motion. We will also look at ellipses as planets revolve in ellipses and various terms related to ellipses.
- 4. HOW DID PEOPLE THINK OF THE UNIVERSE IN THE EARLIER TIMES? • People believed that the earth was in the centre of the universe. It does make some sense in that era as : 1. All the stars and planets were moving in reference to the earth. 2. The earth was a stable/fixed point, hence it felt that earth was at rest. • Astronomers like Aristotle supported this theory
- 5. SOLAR AND SIDEREAL DAY • Solar day: It’s the duration after which sun comes to same location in the Sky. It is defined to be 24 hours. • Sidereal day: It’s the duration after which stars come to same location in the Sky. It is about 4 mins less than Solar day due to orbital motion Earth.
- 6. CELESTIAL SPHERE AND WANDERING STARS • Celestial Sphere: Tracking the position of stars in Sky suggests that the position and distance between stars does not change much in a sidereal day. Early astronomers suggested that all the stars are fixed in an infinitely large sphere called Celestial sphere. And the rotation of stars in a day is due to rotation of this sphere. • Wondering Stars: A handful of stars do seem to change position in the sky in a sidereal day. These are called wondering stars. Astronomers soon realized these are planets like Earth which are close to earth.
- 7. • Geocentric Model: Early astronomers believed all planets including moon and sun revolve around Earth called geocentric model. Few observations were difficult to explain in this model. One such observation is “Retrograde motion”. • Heliocentric model: Today we understand that all planets including Earth orbit around Sun. But this was not always the case. It took mankind around 2000 years to conclude this. GEOCENTRIC AND HELIOCENTRIC MODELS
- 8. RETROGRADE MOTION AND PROGRADE MOTION • A planet such as Mars moves slowly from west to east against the fixed background stars and then mysteriously reverses direction for a period of time before resuming its previous path. The normal motion is called prograde motion while the reversed direction is called retrograde motion.
- 9. Apparent retrograde motion of Mars in 2003 as seen from Earth
- 10. EXPLANATION OF RETROGRADE MOTION IN GEOCENTRIC THEORY • Retrograde motion can be understood using epicyclic motions. Multiple epicycles can be added to improve accuracy Hipparchus Model Ptolemaic Model
- 11. EXPLANATION OF RETROGRADE MOTION IN HELIOCENTRIC THEORY • Explanation in Heliocentric model: Retro grade motion can also be understood using heliocentric model.
- 12. WHY HELIOCENTRIC THEORY • It was observed that a planets become brighter during retrograde motion. Both models can explain this due to less distance of planet from Earth. However, Heliocentric model is easy simpler. • In modern understanding sun is also not at center. It orbits around galactic center. How these orbital motions happen can be understood using Kepler's laws. • https://www.youtube.com/watch?v=ZeS8h1t-uMA
- 13. • After discovery of telescopes, observation like discovery of moons around Jupiter and full range phases of Venus provides more evidence towards Heliocentric model which is current understanding. CONCLUSION
- 14. KEPLER’S LAWS • Kepler’s Laws: Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The three laws state that: 1. The orbit of a planet is an ellipse with the Sun at one of the two foci. 2. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. 3. The square of a planet's orbital period is proportional to the cube of the length of the semi- major axis of its orbit.
- 15. KEPLER’S LAWS 1. The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. 2. The second law helps to establish that when a planet is closer to the Sun, it travels faster. 3. The third law expresses that the farther a planet is from the Sun, the slower its orbital speed, and vice versa.
- 17. BASIC SHAPE OF ELLIPSE Centre Focus 1 Focus 2 Semi-Minor Axis Semi-Major Axis 𝑎 𝑎𝑒 • Eccentricity is ratio between distance from centre to focus and semi-major axis. • 0 ≤ 𝑒 < 1 • Eccentricity is zero for circle (Special case of ellipse).
- 18. • Ellipse equation in polar coordinate: Using Pythagoras theorem and basic trigonometry we derived the following ellipse equation. 𝑟 𝜃 = 𝑎 1 − 𝑒2 1 − 𝑒 cos 𝜃 • This equation tells us how the distance of any planet from the sun changes with angle. There are two parameters semi- major axis (𝑎) and eccentricity (𝑒) which depends on energy and angular BASIC SHAPE OF ELLIPSE
- 19. • Applied conservation of energy to find the shape of ellipse. 𝐸 Total Energy = 1 2 𝑚𝑣𝑟 2 + 𝓁2 2𝑚𝑟2 Kinetic Energy − 𝐺𝑀𝑚 𝑟 Potential Energy • Radial kinetic energy becomes zero when 𝐸 = 𝓁2 2𝑚𝑟2 − 𝐺𝑀𝑚 𝑟 Effective potential Energy • Giving us the perihelion and aphelion distance. https://www.desmos.com/calculator/x9w9zwwddg SHAPE OF ORBIT
- 20. • The shape of orbit is an ellipse whose shape depends upon total energy of planet and its angular momentum. • If total energy is negative : Bound orbit • If total energy is positive : Unbound orbit • For a given angular momentum circular orbit has minimum energy. CONCLUSION
- 21. • Lagrange points are positions in space where the gravitational forces of two large bodies, such as Earth and the moon or Earth and the sun, balance the centrifugal force felt by a much smaller third body. LAGRANGE POINT
- 22. • The virtual force appearing in non-inertial frames so that Newton’s Laws can be applied. • Lagrange points are easily explained in corotating frame which is an non inertial frame. • So we have to account for pseudo forces appearing in rotating frame (a) Centrifugal force – Radially outward (b) Coriolis force – Present if a body moves in rotating frame PSEUDO FORCES
- 23. • In corotating frame following forces are present (i) Centrifugal force (ii) Gravitational Force from Earth (iii) Gravitational Force from Sun • The points at which the resultant force is zero are equilibrium points (Lagrange Point). It turns out that there are 5 such Lagrange points. • In inertial frame Centrifugal force is not present and the residual resultant force plays the role of centripetal force. BALANCING THE FORCES
- 24. 1. L1, L2, L3 : Semi-stable 2. L4,L5 : Stable due to Coriolis force TYPES OF STABILITY
- 25. • James Webb at 𝑳𝟐: It is a space telescope currently conducting infrared astronomy. • Its high resolution and high sensitive instruments allow us to observe faint distant universe and hence to look back in time. JAMES WEBB SPACE TELESCOPE
- 26. JAMES WEBB SPACE TELESCOPE
- 27. TRAJECTORY
- 29. • A large group of asteroids that share the planet Jupiter's orbit around the Sun. JUPITER TROJAN ASTEROIDS AT 𝑳𝟒 & 𝑳𝟓
- 30. • Aditya L1 is a planned spacecraft to study solar atmosphere, currently being designed and developed by the ISRO and various other Indian research institutes. • The SUIT (Solar Ultraviolet Imaging Telescope) instrument payload is developed at IUCAA, Pune n collaboration with ISRO and other institutes. • The spacecraft will be places at L1 point between Earth and Sun. ADITYA L1