HCI 07 Gravitation Lecture Notes

Hwa Chong Institution (College) H2 Physics C1 2023 1 Chapter 7 Gravitational Field Playlist of Lecture Examples and Concept Videos can be found at https://youtube.com/playlist?list=PL_b5cjrUKDlbcIl2_xwdbabhxq0fs40Xw. Alternative resource (with videos) at xmphysics: https://xmphysics.com/xmGravitation/

Hwa Chong Institution (College) H2 Physics C1 2023 2 Chapter 7: Gravitational Field H2 Physics Syllabus 9749 Content  Gravitational field  Gravitational force between point masses  Gravitational field of a point mass  Gravitational field near to the surface of the Earth  Gravitational potential  Circular orbits Learning Outcomes Candidates should be able to: (a) show an understanding of the concept of a gravitational fie ld as an example of field of force and define the gravitational field strength at a point as the gravi tational force exerted per unit mass placed at that point. (b) recognize the analogy between certain qualitative and quant itative aspects of gravitational and electric fields (will be done in the chapter on electric fields). (c) recall and use Newton’s law of gravitation in the form 2 21 r mGmF  . (d) derive from Newton’s law of gravitation and the definition of gravitational field strength, the equation 2r GMg  for the gravitational field strength of a point mass. (e) recall and apply the equation 2r GMg  for the gravitational field strength of a point mass to new situations or to solve related problems. (f) show an appreciation that near the surface of the Earth, gr avitational field strength is approximately constant and equal to the acceleration of free fall. (g) define the gravitational potential at a point as the work d one per unit mass in bringing a small test mass from infinity to the point. (h) solve problems by using the equation r GM for the gravitational potential in the field of a point mass. (i) analyse circular orbits in inverse square law fields by rel ating the gravitational force to the centripetal acceleration it causes. (j) show an understanding of geostationary orbits and their app lication.

Hwa Chong Institution (College) H2 Physics C1 2023 3 7.1 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation states that: Every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Consider two point masses of m 1 and m2 separated by a distance r. Each will exert a force F on the other, and its magnitude is given by 2 21 r mmGF  where F : gravitational force between the two point masses. m1, m2 : masses of the two point masses. r : distance between the two point masses. G : gravitational constant The two forces form an action-reaction pair and have the following characteristics,  are equal in