Chapter 7: Gravitational Force & Field Strength

University:
California State University, Northridge
Course:
PHYS 100A | General Physics I
Academic year:

2023
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1
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Gravitation 7.1 Gravitational Force & Field Strength 1. Every particle in the Universe attracts every other particle with a force, Fg 2. Newton’s Law of gravitation – a magnitude of an attractive force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them 9. 𝑀𝑚 𝑟2 G = 6.67 x 10-11 N m2 kg-2 F21 = F by 2 on 1 Fg = G 7.2 Gravitational Potential 8. Gravitational potential, V - the work done by an external force in bringing a test mass from infinity to a point per unit the test mass 𝑊 𝑉= 𝑚 Work done by the external force dW = F dr cos ,  = 0o 𝑀𝑚 Fg varies with r dW = Fg dr, Fg = G 2 𝑟 1 1 𝑊𝑟1  𝑟2 = 𝐺𝑀𝑚 ( 2 − 2 ) , = (+)𝑣𝑒 𝑟1 𝑟2 r1 = initial distance, r2 = final distance 𝑊 1 1 From 𝑉 = and 𝑊 = 𝐺𝑀𝑚 ( 2 − 2 ) , 𝑟1 = , r2 = r 𝑚 𝑟1 𝑟2 𝐺𝑀 V=− 𝑟 10. Gravitational field - a region where a body having a mass experiences gravitational force if a test mass placed in the region 11. Gravitational field strength, ag (a.k.a gravitational acceleration) – the gravitational force per unit mass of a body (test mass) placed at a point (i) Outside the Earth ( r > R) 12. Variation of gravitational field strength on the distance from the centre of the Earth 𝑎𝑔 = (ii) On he earth (r = R) 𝑎𝑔 = 𝐺𝑚 1 ,𝑎  𝑟2 𝑔 𝑟2 9. The gravitational potential difference between point A and B (VAB) in the Earth’s gravitational field is defined as the work done in bringing a test mass from point B to point A per unit the test mass. 𝑊𝐵𝐴 𝑉𝐴𝐵 = = 𝑉𝐴 − 𝑉𝐵 𝑚 𝐺𝑀 But 𝑉 = − 𝑟 1 1 𝑉𝐴𝐵 = 𝐺𝑀 ( − ) 𝑟𝐵 𝑟𝐴 And 𝑊𝐴𝐵 𝑉𝐵𝐴 = = 𝑉𝐴 − 𝑉𝐵 𝑚 (iii) Inside the Earth (r < R) 𝐺𝑚 , 𝑔 = 9.81 𝑁 𝑘𝑔−1 𝑟2 𝑎𝑔 = 𝐺𝑚 , 𝑎 r 𝑅3 𝑔 Newton’s Law of gravitation Gravitational field strength Gravitation Gravitational potential Satellite motion For satellite: http://www.suntrek.org/ 7.3 Satellite Motion In a Circular Orbit 10. Tangential velocity, v: Fg = Fc = mac 𝑀𝑚 𝑚𝑣 2 G 2 = 𝑟 𝑟 𝐺𝑀 v=√ 𝑟 For satellite close to Earth r  R, v = √𝑔𝑟 11. T = 2√ 𝑟3 𝐺𝑀