Basic Physics. Remaining Topics. Gravitational Potential Energy. PHYS 1403 Introduction to Astronomy. Can We Create Artificial Gravity?

Transcription

1 PHYS 1403 Introduction to Astronomy Basic Physics Chapter 5 Remaining Topics Gravitational Potential Energy Escape Velocity Artificial Gravity Gravity Assist An Alternate Theory of Gravity Gravitational Potential Energy It is the gravitational energy the object would have above the earth surface. GPE = Gravitational Force x Distance GPE Satellite (m) Distance (r) Earth (M) 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 Can We Create Artificial Gravity? 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 cv.nrao.edu 1

2 Concept What is Gravity Assist? Image source: NASA, STSI Source: wikipedia How to increase velocity of a spacecraft without using fuel? Source: wikipedia Gravity Assist An Alternative viewpoint of Gravity 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 2

3 Einstein and Relativity Einstein ( ) Noticed that Newton s laws of motion are only correct in the limit of low velocities (speeds <<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 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 3

4 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 Einstein view on Gravity 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 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. 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 4

5 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. 5