GRAVITATION 10th Grade – Physics 10th - Physics

INTRODUCTION Why is Moon going around the earth in a circular orbit? Why doesnt it fall down to the earth? Why doesnt it go away from earth? Images from: Daily.am, bionicbong.com 10th - Physics

Newton and the Apple Sir Isaac Newton got answers for all these questions, when he was sitting under an apple tree. He explained the answers for these questions as Universal law of gravitation 10th - Physics

The law of Gravitation What made that Apple fall to the ground? Every object on the surface of the Earth is attracted towards the center of the Earth. This force is called as Gravitational force. The gravitational force is directly proportional to the mass of the object. The gravitational force is inversely proportional to the square of the distance between the objects. This helps us arrive at the formula 𝐹∝mo/d2 Where mo - mass of the object d - distance from the centre of the Earth Image from : http://mail.colonial.net/~hkaiter/Gravity_Inertia.html 10th - Physics

The law of Gravitation The object exerts an equal and opposite force on the Earth 𝐹∝ME/d2 Where ME is the mass of the Earth Combining the two equations, we get 𝐹∝MEmo/d2 Newton Generalized that there is a force between any two objects and proposed his universal law of Gravitation , Every particle in the universe attracts every other particle 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 acts along the line joining the two particles. 10th - Physics

The law of Gravitation where: F1, F2  are the force between the masses, G is the constant of proportionality m1 is the first mass, m2 is the second mass, and r is the distance between the centers of the masses. G is called as the universal Gravitational constant. It has the same value for all the objects. Its accepted value is 6.67 x 10-11Nm2kg-2 10th - Physics

The law of Gravitation The centripetal force provided to the Moon is the gravitational force given by the formula 𝐹=𝐺MEmo/d2 Gravitational force is independent of: Intervening Medium and their masses Change in temperature, Pressure or any other physical condition The law is valid for small and large masses and distances Holds good for celestial bodies also Hence the law of gravitation is an universal law , Here mo - mass of the object ME- mass of the Earth d - distance from the centre of the Earth 10th - Physics

Weight and Weightlessness Weight(W) of an object with mass m is given by the formula W=mg where g is the acceleration due to gravity at the Earth’s surface We exert a Gravitational force on the Earth. The ground in turn provides an equal and opposite reaction. This reaction is weight. This force called weight is defined by the universal law of gravitation as: 𝐹=𝐺MEm/RE2 where ME is the Mass of the Earth and RE radius of the Earth Hence, mg =𝐺MEm/ RE2 g = 𝐺ME/RE2 , Remember, weight of a body is measured by the reaction exerted on the body. In the space, the distance from the Earth is so huge that the Gravitational force of the Earth is very less and hence the body experiences weightlessness. Image from: http://www.physicsonlinetutor.com.au/resource-library/resource-view.aspx?rscid=11 10th - Physics

Weight and Weightlessness Astronauts experience Weightlessness when their space craft orbits around the Earth. The gravitational pull is used in providing the necessary centripetal force to the space craft. Due to the centripetal force, there is no reaction on the occupant in a space craft. This condition of zero reaction is called Weightlessness. , Imagine a lift falling freely under gravity. A person inside it experiences no reaction and hence weightless. Image from: www.accessscience.com The value of g at a distance of 3.84 x 105 km (distance of the moon), the value is found to be nearly 2.7 x 10-3 ms-2 10th - Physics

Variation of ‘g’ If a body is at a height h above the ground, then the value of gravity gh , the acceleration due to gravity is given by: gh=𝐺ME/ (RE + h)2 Value of g is independent of mass of the object, but depends on the mass of the Earth and the distance of the object from the Earth Value of g is slightly higher at the poles and than that at the equator, because of the geoid shape of the Earth Image from: http://www.school-for-champions.com/science/gravity_constant.htm 10th - Physics

Motion of planets around the Sun Johannes Kepler is best known for his discovery of the three laws of planetary motion. These laws are based on his observations and the data collected by Tyco Brahe. Kepler’s First Law: The orbits of the planets are ellipses, with the Sun at one focus of the ellipse. Some story on Brahe's Data and Kepler Kepler and Brahe did not get along well. Brahe apparently mistrusted Kepler, fearing that his bright young assistant might eclipse him as the premiere astonomer of his day. He therefore let Kepler see only part of his voluminous data.He set Kepler the task of understanding the orbit of the planet Mars, which was particularly troublesome. It is believed that part of the motivation for giving the Mars problem to Kepler was that it was difficult, and Brahe hoped it would occupy Kepler while Brahe worked on his theory of the Solar System. In a supreme irony, it was precisely the Martian data that allowed Kepler to formulate the correct laws of planetary motion, thus eventually achieving a place in the development of astronomy far surpassing that of Brahe. http://csep10.phys.utk.edu/astr161/lect/history/kepler.html 10th - Physics

Motion of planets around the Sun Kepler’s Second Law: An imaginary line drawn from the sun to a planet, sweeps equal areas in equal intervals of time. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse. Kepler's second law is illustrated in the preceding figure. The line joining the Sun and planet sweeps out equal areas in equal times, so the planet moves faster when it is nearer the Sun. Thus, a planet executes elliptical motion with constantly changing angular speed as it moves about its orbit. The point of nearest approach of the planet to the Sun is termed perihelion; the point of greatest separation is termed aphelion. Hence, by Kepler's second law, the planet moves fastest when it is near perihelion and slowest when it is near aphelion. Helion refers to Sun. Peri means nearer. The term ‘Ap’ refers to farther. Aphelion refers to the farthest position from the Sun. http://csep10.phys.utk.edu/astr161/lect/history/kepler.html 10th - Physics

Planets around the Sun Kepler’s Third Law: The cube of the average distance (r) of a planet from the sun is proportional to the square of its period (T) of revolution. r3 ∝ T2 Applying the equation to Earth and Planet: rP 3/rE 3= Tp2/TE2 Using AU for distance and year for time as units rP 3 = Tp2 (1AU3/1Yr2) AU = astronomical unit = 1.5 x 108 km 10th - Physics

Planets around the Sun Kepler’s third law can be used to find Mass of the sun Distance of a planet Period of revolution of a planet Newton showed that Kepler’s laws can be derived from the universal law of gravitation. , Centripetal force = gravitational force mv2/r = 𝐺Mm/r2 v2 = 𝐺M/r But v = 2𝜋𝑟/𝑇 (2𝜋𝑟/𝑇) 2 = GM/r ∴ r3 = (GM/4𝜋2) 𝑇2 10th - Physics

Importance of the law of Gravitation The law of gravitation successfully explained several phenomena: The force that binds us to the Earth The motion of moon around the Earth The motion of planets around the sun The tides due to the Moon and the Sun The law of gravitation successfully predicted The existence of planets beyond the Uranus Observations in the deviations in the orbit of Uranus led to the discovery of Neptune in the nineteenth century Smaller deviations in the orbit of Neptune led to the discovery of Pluto in 1930 Pluto though was initially considered as planet, now has been given the status of a dwarf planet, because of its size which is only twice of its Moon. , 10th - Physics

Exercise State the universal law of Gravitation What led Newton to develop the law of Gravitation? Why is the law of gravitation called a universal law? What is weight? How does the acceleration due to gravity vary with height? Explain Mention three points successfully explained by the law of Gravitation What led to the discovery of the planet Neptune? What led to the discovery of planet Pluto? What is meant by Weightlessness? Explain with an example. , 10th - Physics