Physics Recreations: Helmert’s Equation - pgccphy.net

1 Physics Recreations: helmert s EquationDr. SimpsonDepartment of Physical Sciences and EngineeringPrince George s Community CollegeSeptember 1, 2009We use a value of the acceleration due to gravity (g) of m/s2. But what if wewant to use a more exact value?You might be tempted to use the value given in some reference books:g= ,but that would actually be wrong. This value is just a standard value used for thedefinitions of some units (for example, in the conversion between pounds-force andnewtons). You should never use this value in a Physics formula that containsgas theacceleration due to gravity it s only used when doing certain unit acceleration due to gravitygat the surface of the Earth varies over the surfaceof the Earth for a number of reasons:1.

2 As you get closer to the equator, the Earth s rotation rate gets larger, resulting in agreater centrifugal force that counteracts gravity. This has the effect of reducinggcloser to the Also, the Earth has an equatorial bulge due to its rotation, so that you re fartherfrom the center of the Earth near the equator. This also has the effect of reducinggcloser to the There is also an elevation effect: the higher you are in elevation, the effects can be approximately accounted for using an Equation calledHelmert sequation. According to helmert s Equation , the acceleration due to gravity is given byg= cos 2 + ( 10 5) cos22 ( 10 6)Hm/s2,where is the latitude andHis the elevation (in meters) above sea level.

3 For example,for Largo, Maryland, the latitude is 38 .898and the elevationHis about 174 feet( meters). Substituting these values into helmert s Equation , we findgat Largo isabout m/s2. In other cities around the world, the value ranges from m/s2(Mexico City) to m/s2(Helsinki). For most problems we just use an averagevalue of m/s2. (You shouldneverround this to 10 m/s2unless you re doing a veryrough order-of-magnitude estimation.)1