PHYS 1411 Introduction to Astronomy Basic Physics Chapter 5 What We Covered Last Class Recap of Newton s Laws Mass and Weight Work, Energy and Conservation of Energy Rotation, Angular velocity and acceleration Centripetal Force Angular Momentum Universal Law of Gravity Remaining Topics Center of Mass Center of Mass and Newton s Laws Orbits Circular Velocity Gravitational Potential Energy Escape Velocity Artificial Gravity Gravity Assist An Alternate Theory of Gravity Center of Gravity and Mass Sun Earth System Earth- Sun System Balance point of any System Atvconnection.com Wikipedia.com karatechoach.com https://www.youtube.com/watch?v=1isr3yw6fxo Wikipedia.com 1
Center of Mass and Newton's Laws Why Earth has to Move around Sun? a sun = F/M sun a earth = F / M earth M sun is 300,000 times larger than M earth Therefore a sun is much small than a earth The sun also moves slowly just as you would move if you swing a child in a circle. The center of mass is inside the Sun, therefore we see only a wobble motion. Understanding Orbital Motion The universal law of gravity allows us to understand orbital motion of planets and moons: Example: Earth and moon attract each other through gravitation. Since Earth is much more massive than the moon, the moon s effect on Earth is small. Earth s gravitational force constantly accelerates the moon towards Earth. This acceleration is constantly changing the moon s direction of motion, holding it on its almost circular orbit. v v Moon F Earth v Types of Orbits In order to stay on a closed orbit, an object has to be within a certain range of velocities: Too slow => Object falls back down to Earth Circular Velocity A speed a planet or a satellite must have to remain in a circular orbit 2 / / Too fast => Object escapes Earth s gravity How to calculate velocity of escape? Moons circular velocity is 1.02 km/s Orbital Velocities of Planets A geosynchronous satellite orbits eastward with the rotation of Earth and remains above a fixed spot on the equator, which is ideal for communications and weather satellites Geosynchronous Orbits 2
Gravitational Potential Energy It is the gravitational energy the object would have above the earth surface. GPE = Gravitational Force x Distance GPE Satellite (m) Earth (M) Distance (r) KE PE 1 GMm mv 2 2 r 2 GM v r Escape Velocity Escape velocity is the velocity required to escape an astronomical body For the case of Rocket on Earth If mass of the spaceship << the mass of Earth, then the escape velocity is M = mass of the central body in kg G = gravitational constant (6.67ˣ10-11 m3/s2/kg) r = radius of the central body For Earth it is 11.2 km/s or 24,600 miles/hour Can We Create Artificial Gravity? Concept https://www.youtube.com/watch?v=jkgrvl69mma cv.nrao.edu Image source: NASA, STSI What is Gravity Assist? How to increase velocity of a spacecraft without using fuel? https://www.youtube.com/watch?v=2r9smrho-oc Source: wikipedia Source: wikipedia https://www.youtube.com/watch?v=0iagrditiie Gravity Assist 3
What is Gravity? Newton's View Gravity A force called gravity keeps the planets in motion around the Sun. The motion of planets can be described by Newton s laws of motion and law of gravity Space is static i.e. not expanding or contracting Space is flat Euclid s law of geometry applies The acceleration due to a force on a body depends on the mass (we call this mass inertial mass ). a = F / m i i = inertial An Alternative viewpoint of Gravity Einstein and Relativity Einstein (1879 1955) Noticed that Newton s laws of motion are only correct in the limit of low velocities (<<speed of light) leading to his theory of special relativity Also revised the understanding of gravity leading to his theory of general relativity The First Postulate of Relativity The principle of relativity says that observers can never detect their uniform motion, except relative to other objects. Neither of these travelers can decide who is moving and who is not. The Second Postulate of Relativity The speed of light in a vacuum is constant and will have the same value for all observers independent of their motion relative to the light source The Theory of Special Relativity The first two postulates describe the theory of special relativity Observed mass of a moving particle depends on its velocity The energy of a body at rest 0 Instead, we find E = m 0 c 2 4
Effects of Special Relativity The observed mass of moving electrons depends on their velocity. As the ratio of their velocity to the velocity of light, v/c, increases, the mass of the electrons relative to their mass at rest, m/m 0, increases. Such relativistic effects are quite evident in particle accelerators, which accelerate atomic particles to very high velocities. The Third Postulate of Relativity The general theory of relativity The equivalence principle: new description of gravity Observers cannot distinguish locally between inertial forces due to acceleration and uniform gravitational forces due to the presence of a massive body Inertia and Acceleration in a Spaceship (a) An observer in a closed spaceship on the surface of a planet feels gravity. (b) In space, with the rockets smoothly firing and accelerating the spaceship, the observer feels inertial forces that are equivalent to gravitational forces. Einstein view on Gravity Einstein Uses principle of equivalence to put forth his theory of General Relativity Mass and energy are related E = mc 2 Gravity is a property of space-time not matter Gravity affects light even though it has no mass Confirmation of the Curvature of Space- Time: Mercury s Perihelion (a) Mercury s orbit precesses 42.98 0.04 arc seconds per century faster than predicted by Newton s laws. (b) Even when you ignore the influences of the other planets, Mercury s orbit is not a perfect ellipse. Curved space-time near the Sun distorts the orbit from an ellipse into a rosette. The advance of Mercury s perihelion is exaggerated by a factor of about one million in this figure. Confirmation of the Curvature of Space- Time: Deflection of Sunlight Like a depression in a putting green, the curved space-time near the Sun deflects light from distant stars and makes them appear to lie slightly farther from the Sun than their true positions. 5
Quora.com Einstein Theory of Gravity Comparing Newton and Einstein's View Newton Mass and energy are very different Space and time are very different Light takes the shortest distance between two points Shortest distance is a straight line in flat space Mass tells gravity how much force to exert; force tells mass how to move Einstein Mass and energy are interchangeable Space and time are interchangeable, time is the 4 th dimension In presence of gravity space is curved not flat or mass curves space-time Mass-energy tells spacetime how to curve; curved space-time tells massenergy how to move Worm Holes Sci Fi How to Make a Worm Hole? Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 6