Physics
Gravity on Different Planets
Gravity on different planets varies based on their mass and radius. The acceleration due to gravity is stronger on larger, more massive planets and weaker on smaller, less massive ones. This means that an object's weight would be different on each planet, even though its mass remains constant.
Written by Perlego with AI-assistance
Related key terms
1 of 5
10 Key excerpts on "Gravity on Different Planets"
- Thais Russomano, Gustavo Dalmarco, Felipe Prehn Falcao(Authors)
- 2022(Publication Date)
- Springer(Publisher)
Compared to the other three fundamental interactions in nature, gravitation is the weakest one. It, however, acts over great distances and is always present. Gravitation is interpreted differently by classic mechanics, relativity, and quantum physics. In classic mechanics, gravitation arises out of the force of gravity. In general relativity, it is the mass that curves space time, not a force. In quantum gravity theories, the gravitation is the postulated carrier of the gravitational force, time space itself is envisioned as discrete in nature, or both. The gravitational attraction of the Earth endows objects with weight that causes them to fall to the ground when dropped (the Earth also moves toward the object but only by an infinitesimal amount). FIGURE 1.1: The gravitational force keeps the planets in orbit about the sun (http://en.wikipedia .org/wiki/Gravity). GENERAL CONCEPTS IN PHYSICS—DEFINITION OF PHYSICAL TERMS 3 The Universal Law of Gravitation was postulated by the English physicist and mathemati- cian Sir Isaac Newton (1642–1727). There is a popular story that the origin of this theory happened when Newton was sitting under a tree and an apple fell on his head. This is almost certainly not an exact truth, with embellishment of details, as what happens in most legends. Probably, the more correct version of the story is that Newton, upon observing (or imagining!) an apple fall from a tree, began to think that the apple is accelerated because its velocity changes from zero as it is hanging on the tree then moves toward the ground. He then considered that the same force that pulled the apple toward the Earth is the same one that makes the Moon to orbit our planet. Newton’s theory of how a celestial body can orbit another celestial body can be illustrated by his well-known example shown in Figure 1.2. Suppose that a cannon ball is fired horizontally from a high mountain on top of the Earth.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
Then, because 376 CHAPTER 13 GRAVITATION The Law of Gravitation Any particle in the universe attracts any other particle with a gravitational force whose magnitude is F = G m 1 m 2 r 2 (Newton’s law of gravitation), (13-1) where m 1 and m 2 are the masses of the particles, r is their separation, and G (= 6.67 × 10 −11 N · m 2 /kg 2 ) is the gravitational constant. Gravitational Behavior of Uniform Spherical Shells The gravitational force between extended bodies is found by adding (integrating) the individual forces on individual particles within the bodies. However, if either of the bodies is a uniform spherical shell or a spherically symmetric solid, the net gravitational force it exerts on an external object may be computed as if all the mass of the shell or body were located at its center. Superposition Gravitational forces obey the principle of super- position; that is, if n particles interact, the net force F → 1,net on a particle labeled particle 1 is the sum of the forces on it from all the other par- ticles taken one at a time: F → 1,net = ∑ n i =2 F → 1i , (13-5) in which the sum is a vector sum of the forces F → 1i on particle 1 from particles 2, 3, . . . , n. The gravitational force F → 1 on a particle from Review & Summary an extended body is found by dividing the body into units of differential mass dm, each of which produces a differential force d F → on the particle, and then integrating to find the sum of those forces: F → 1 = ∫ d F → . (13-6) Gravitational Acceleration The gravitational acceleration a g of a particle (of mass m) is due solely to the gravitational force acting on it. When the particle is at distance r from the center of a uniform, spherical body of mass M, the magnitude F of the gravitational force on the particle is given by Eq. 13-1. Thus, by Newton’s second law, F = ma g , (13-10) which gives a g = GM r 2 .
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
372 What Is Physics? One of the long-standing goals of physics is to understand the gravitational force—the force that holds you to Earth, holds the Moon in orbit around Earth, and holds Earth in orbit around the Sun. It also reaches out through the whole of our Milky Way Galaxy, holding together the billions and billions of stars in the Galaxy and the countless molecules and dust particles between stars. We are located somewhat near the edge of this disk-shaped collection of stars and other matter, 2.6 × 10 4 light-years (2.5 × 10 20 m) from the galactic center, around which we slowly revolve. The gravitational force also reaches across intergalactic space, holding together the Local Group of galaxies, which includes, in addition to the Milky Way, the Andromeda Galaxy (Fig. 13.1.1) at a distance of 2.3 × 10 6 light-years away from Earth, plus several closer dwarf galaxies, such as the Large Magellanic Cloud. The Local Group is part of the Local Supercluster of galaxies that is being drawn by the gravitational force toward an exceptionally massive region of space called the Great Attractor. This region appears to be about 3.0 × 10 8 light-years from Earth, on the opposite side of the Milky Way. And the gravitational force is even more far-reaching because it attempts to hold together the entire universe, which is expanding. This force is also responsible for some of the most mysterious structures in the universe: black holes. When a star considerably larger than our Sun burns out, the gravitational force between all its particles can cause the star to collapse in Gravitation 13.1 NEWTON’S LAW OF GRAVITATION Learning Objectives After reading this module, you should be able to . . . 13.1.1 Apply Newton’s law of gravitation to relate the gravitational force between two particles to their masses and their separation.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter-5 Gravitation Gravitation keeps the planets in orbit around the Sun. (Not to scale) Gravitation , or gravity , is a natural phenomenon in which objects with mass attract one another. In everyday life, gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, thus accounting for the existence of the Earth, the Sun, and most of the macroscopic objects in the universe. Gravitation is responsible for keeping the Earth and the other planets in their orbits around the Sun; for keeping the Moon in its orbit around the Earth; for the formation of tides; for natural convection, by which fluid flow occurs under the influence of a density gradient and gravity; for heating the interiors ________________________ WORLD TECHNOLOGIES ________________________ of forming stars and planets to very high temperatures; and for various other phenomena observed on Earth. Gravitation is one of the four fundamental interactions of nature, along with the strong force, electromagnetism and the weak force. Modern physics describes gravitation using the general theory of relativity, in which gravitation is a consequence of the curvature of spacetime which governs the motion of inertial objects. The simpler Newton's law of universal gravitation provides an accurate approximation for most calculations. History of gravitational theory Scientific revolution Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. In his famous (though possibly apocryphal) experiment dropping balls from the Tower of Pisa, and later with careful measurements of balls rolling down inclines, Galileo showed that gravitation accelerates all objects at the same rate. This was a major departure from Aristotle's belief that heavier objects accelerate faster.
eBook - PDFGravity from the Ground Up
An Introductory Guide to Gravity and General Relativity
- Bernard Schutz(Author)
- 2003(Publication Date)
- Cambridge University Press(Publisher)
Gravity on Earth: the inescapable force 1 G ravity is everywhere. No matter where you go, you can’t seem to escape it. In this chapter: the simplest observations about gravity – it is universal and attractive, and it affects all bodies in the same way – have the deepest consequences. Galileo, the first modern physicist, founded the equivalence principle on them; this will guide us throughout the book, including to black holes. Galileo also introduced the principle of relativity, used later by Einstein. We begin here our use of computer programs for solving the equations for moving bodies. Pick up a stone and feel its weight. Then carry it inside a building and feel its weight again: there won’t be any difference. Take the stone into a car and speed along at 100 miles per hour on a smooth road: again there won’t be any noticeable change in the stone’s weight. Take the stone into the gondola of a hot-air balloon that is hovering above the Earth. The balloon may be lighter than air, but the stone weighs just as much as before. This inescapability of gravity makes it different from all other forces of nature. Try taking a portable radio into a metal enclosure, like a car, and see what happens to its ability to pick up radio stations: it gets seriously worse. Radio waves are one aspect of the electromagnetic force, which in other guises gives us static electricity and magnetic fields. This force does not penetrate everywhere. It can be excluded Remember, terms in boldface are in the glossary. from regions if we choose the right material for the walls. Not so for gravity. We could build a room with walls as thick as an Egyptian pyramid and made of any exotic material we choose, and yet the Earth’s gravity would be right there inside, as strong as ever.
- Raymond Serway, John Jewett(Authors)
- 2018(Publication Date)
- Cengage Learning EMEA(Publisher)
CONNECTIONS We first studied gravity in Section 2.8, where we talked about freely falling objects. There, and in Section 4.3 on projectile motion, we con- sidered the effects of gravity on objects near the surface of the Earth. In Section 5.5, we related the gravitational force on such objects to their weight. In Chapter 7, we related the gravitational force on an object near the surface of the Earth to grav- itational potential energy of the object–Earth system. In this chapter, we remove the assumption that objects are near the surface of the Earth. How does the gravitational force on an object vary as we move the object far from the surface of the Earth? The answer to that question will allow us to understand the motion of planets around the Sun and has allowed scientists to place many objects in orbit around the Earth, the Moon, and Mars. The principle that allows this understanding Hubble Space Telescope image of a spiral galaxy, NGC 1566, taken in 2014. In the spiral arms of the galaxy, hydrogen gas is compressed to create new stars. It is theorized that our own galaxy, the Milky Way, has a similar structure with spiral arms. (ESA/Hubble & NASA) Copyright 2019 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. 13.1 Newton’s Law of Universal Gravitation 333 is the law of universal gravitation. We emphasize a description of planetary motion because astronomical data provide an important test of this law’s validity. After introducing this law, we will show connections between it and the angular momen- tum of Chapter 11 and the energy techniques in Chapters 7 and 8.
- Peter Kosso(Author)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
1 Introduction: What to Expect from a Science of Gravity Gravity dominates our lives and attracts our attention like no other force of nature. First thing in the morning, just getting up and out of bed, lifting your head from the pillow and dropping your feet to the floor, it’s gravity that works with you and works against you, and you know it. You will spend your day opposing and cooperating with gravity, lifting the coffee pot, pouring the coffee, and so on. There is no up or down without gravity. This most basic direction is defined, not by some cosmic or even planetary coordinate system, but by the force of attraction between the Earth and things. The force is generally directed toward the center of the spherical planet; that’s down. The other direction is up. A builder deter- mines that a wall is vertical by using a plumb-line, a mass hanging free in the field of gravity. And for all of us, getting up in the morning amounts to changing our orientation in the gravitational field from horizontal to vertical, from lying down to standing up. Gravity is the force we all notice and the one we can all identify explicitly. This is despite the fact that physicists describe gravity as the weakest of the four funda- mental forces in nature. The electromagnetic force is responsible for holding the atoms and molecules together in everything we touch, but this is largely overlooked as we go about our days. Two versions of nuclear force are responsible for stabi- lizing the core of matter, the atomic nucleus, or in some cases for destabilizing it, perhaps the start of the process of heating your coffee if your electricity comes from a nuclear power plant. But the nuclear glue holds at such short range as to go un- detected unless you know what to look for. It’s only gravity that we all experience and we all know. The force of gravity is always attractive. It is a force pulling together any two things that have mass.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Moreover, this “stuff” always attracts other “stuff,” never repelling it (or a hard sneeze could put us into orbit). In the past people obviously knew that they were being pulled downward (especially if they tripped and fell over), but they fig- ured that the downward force was unique to Earth and unrelated to the apparent movement of astronomical bodies across the sky. But in 1665, the 23-year-old Isaac Newton recognized that this force is responsible for holding the Moon in its orbit. Indeed he showed that every body in the universe attracts every other body. This tendency of bodies to move toward one another is called gravi- tation, and the “stuff” that is involved is the mass of each body. If the myth were true that a falling apple inspired Newton’s law of gravitation, then the attraction is between the mass of the apple and the mass of Earth. It is appreciable because the mass of Earth is so large, but even then it is only about 0.8 N. The attraction between two people standing near each other on a bus is (thankfully) much less (less than 1 N) and imperceptible. The gravitational attraction between extended objects such as two people can be difficult to calculate. Here we shall focus on Newton’s force law between two particles (which have no size). Let the masses be m 1 and m 2 and r be their separation. Then the magnitude of the gravitational force acting on each due to the presence of the other is given by F = G m 1 m 2 _____ r 2 (Newton’s law of gravitation). (13.1.1) G is the gravitational constant: G = 6.67 × 10 −11 N · m 2 /kg 2 = 6.67 × 10 −11 m 3 /kg · s 2 . (13.1.2) In Fig. 13.1.2a, F → is the gravitational force acting on particle 1 (mass m 1 ) due to particle 2 (mass m 2 ). The force is directed toward particle 2 and is said to be an attractive force because particle 1 is attracted toward particle 2.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
Although the gravitational force is still not fully understood, the starting point in our understanding of it lies in the law of gravitation of Isaac Newton. Newton’s law of gravitation Before we get to the equations, let’s just think for a moment about something that we take for granted. We are held to the ground just about right, not so strongly that we have to crawl to get to school (though an occasional exam may leave you crawling home) and not so lightly that we bump our heads on the ceiling when we take a step. It is also just about right so that we are held to the ground but not to each other (that would be awkward in any classroom) or to the objects around us (the phrase ‘catching a bus’ would then take on a new meaning). The attraction obviously depends on how much ‘stuff’ there is in ourselves and other objects: Earth has lots of ‘stuff’ and produces a big attraction, but another person has less ‘stuff’ and produces a smaller (even negligible) attraction. Moreover, this ‘stuff’ always attracts other ‘stuff’, never repelling it (or a hard sneeze could put us into orbit). In the past people obviously knew that they were being pulled downward (especially if they tripped and fell over), but they figured that the downward force was unique to Earth and unrelated to the apparent movement of astronomical bodies across the sky. But in 1665, 23‐year‐old Isaac Newton recognised that this force is responsible for holding the Moon in its orbit. Indeed, he showed that every body in the universe attracts every other body. This tendency of bodies to move towards one another is called gravitation, and the ‘stuff’ that is involved is the mass of each body. If the myth were true that a falling apple inspired Newton to his law of gravitation, then the attraction is between the mass of the apple and the mass of Pdf_Folio:241 CHAPTER 13 Gravitation 241 Earth. It is appreciable because the mass of Earth is so large, but even then it is only about 0.8 N.
eBook - PDF- Rodney Hill(Author)
- 2016(Publication Date)
- Pergamon(Publisher)
C H A P T E R 1 GRAVITATIONAL THEORY OF PLANETARY SYSTEMS 1.1 Introductory Remarks For philosophical and methodological reasons the subject of dynamics is best entered by way of Newton's gravitational theory. The primary function of this theory is to synthesize observational data on the motions of the solar system (sun, major and minor planets, satellites and comets) and of stars in the galaxy, and then to predict future movements. During three hundred years numerous implications of the theory have been verified over a rapidly widening range of phenomena and in progressively finer detail. This is a con-tinuing process depending on improvements in mathematical techniques, in instrumental accuracy, and in interpretation of the observations (which often involve, in an intricate manner, various physical hypotheses). In the solar system there remains just one discordant observation with apparent significance, but even this is quantitatively unimportant except as a long-term effect. It concerns the slow rotation of certain planetary orbits. The perihelion of Mercury, for example, advances at the rate of about 9-6 minutes of arc in a century. Perturbations of the orbit by the other known planets leave 0-7 minutes of arc unaccounted for, and so far only the more general theory of gravita-tion due to Einstein has yielded a tenable explanation for this and similar residuals. When reduced to essentials, Newton's postulates have an especially simple structure, as scientific theories go, logically as well as analytic-ally. Although not evident from the time-honoured presentation, their context is essentially kinematical, and ideas of 'force' and Mnertial mass' are not in fact needed. The remaining elements are easily separated and made transparent. In this way one gains a firm conceptual base prior to studying the more complex system of Newtonian laws of motion for non-gravitational phenomena.
Index pages curate the most relevant extracts from our library of academic textbooks. They’ve been created using an in-house natural language model (NLM), each adding context and meaning to key research topics.
