9950-GravityInverseSquareLaw.doc

9950-GravityInverseSquareLaw.doc - Gravity and the Inverse...

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Gravity and the Inverse Square Law Gravity is a great real life application of the inverse (indirect) square law , or, y is inversely proportional to the square of x ’. The gravity field of a body (comet, planet, star etc) is inversely proportional to the distance from the centre of the body squared. As an equation this is: 2 1 r g 2 r k g Where: g = gravity field of a body (acceleration due to gravity in ms -2 ) r = distance from centre of the body (in m) Task 1 For each of the bodies listed below, use the figures for surface gravity and radius to find equations for their gravity fields. (Expect large k values!): Planet Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto* Surfac e Gravity (ms -2 ) 3.7 8.87 9.81 3.69 24.79 3.69 8.69 11.15 0.81 Radius (1000 m) 2,439 6,051 6,378 3,39 6 71,492 60,268 25,550 24,764 1,151 *Pluto is no longer called a planet but rather a ‘ dwarf planet ’. Nevertheless it is still a body with a gravity field that obeys the inverse square law. You could also try this for the Moon (surface gravity=1.622ms -2 , radius=1,738,140m) or the Sun (surface gravity=274ms -2 , radius=6.955x10 8 m). Task 2 - The constant k . In each of your equations the constant k actually represents the mass ( m ) of each planet multiplied by the gravitational constant ( G ), as discovered by Sir Isaac Newton . As an equation this is: Gm k and hence 2 r Gm g The gravitational constant is a very small number measured in Newtons or kgms -2 : 11 10 674 . 6 G
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We can use this to find the mass of each planet. Divide each of your constant k values by G to find the mass (in kg’s) of each planet (and Moon and Sun).
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