Swiss Micros DM32: Estimating Earth’s Acceleration at Latitude

Swiss Micros DM32: Estimating Earth’s Acceleration at Latitude

Introduction

Earth’s gravitational force is usually set a constant of 9.80665 m/s², usually shortened to 9.8 m/s² or 9.81 m/s² in publications such as physics text books. However, in reality gravity on Earth is not constant. There are many ways to calculate (estimate) the gravitational acceleration depending where you are on Earth. Gravity depends on many factors including latitude (degrees North or South) and the elevation. The blog focuses on the effect of latitude on Earth’s gravity.

The is part of the Acceleration Due to Gravity table from the Desk Ref book (see the Source section). The column for m/s² is added.

Degrees Latitude (North or South)	Gravity Acceleration (cm/s²)	Gravity Acceleration (m/s²)
0 (Equator)	978.0327	9.780327
15	978.3786	9.783786
30	979.3249	9.793249
45	980.6199	9.806199
60	981.9178	9.819178
75	982.8698	9.828698
90	983.2186	9.832186

[Glover, Young, pg. 587]

There are many ways to estimate the gravitational acceleration depending where you are on Earth. Gravity depends on many factors including latitude (degrees North or South) and the elevation.

Earth’s gravity tends to be at the strongest at the poles. However, gravity weakens at higher elevations, where we are further away from the center of the planet.

Gravity Estimate – (Univ. of Illinois)

The formula that is presented by The Grainger College of Engineering Physics Van [Univ. of Illinois] is a simple but pretty accurate estimation of gravity:

g = g_45 – 1 / 2 * (g_poles – g_equator) * cos(2 * latitude * π ÷ 180)

where:

g_poles = 9.832 m/s²

g_45 = 9.806 m/s²

g_equator = 9.78 m/s²

lat = latitude, north or south

2 * latitude is converted to radians. (as it is multiplied by π ÷ 180)

Simplifying the equation leads to:

1 / 2 * (g_poles – g_equator) = 1 / 2 * (9.832 – 9.78) = 0.026

2 * latitude * π ÷ 180 = latitude * π ÷ 90 (in radians)

Then:

g = 9.806 – 0.026 * cos(latitude * π ÷ 90)

(in radians)

DM32 Program: Gravity Estimate

Input L as D.MS (degrees/minutes/seconds) format.

E01 LBL E
E02 RAD
E03 INPUT L
E04 →HR
E05 90
E06 ÷
E07 π
E08 ×
E09 COS
E10 0.026
E11 ×
E12 +/-
E13 9.806
E14 +
E15 STO G
E16 RTN

World Geodetic System 84 Ellipsoidal Gravity Formula

The formula is presented by the World Geodetic System (WGS): [Wikipedia]

g = Ge * ((1 + k * sin² L) ÷ √(1 – e² * sin² L))

L: latitude in decimal degrees

with the constants:

Ge = 9.7803253359 m/s²

k = 0.001931852652

e² = 0.0066943799901

Input L as D.MS (degrees/minutes/seconds) format.

DM32: WEG ‘84

G01 LBL G
G02 DEG
G03 INPUT L
G04 →HR
G05 SIN
G06 x²
G07 STO T
G08 0.001931852652
G09 ×
G10 1
G11 +
G12 1
G13 RCL T
G14 0.0066943799901
G15 ×
G16 -
G17 SQRT
G18 ÷
G19 9.7803253359
G20 ×
G21 STO G
G22 RTN

Table of Values

Sources

“Gravity of Earth” Wikipedia. (2026, January 31).

https://en.wikipedia.org/wiki/Gravity_of_Earth Retrieved March 9, 2026.

Grainger Engineering Office of Marketing and Communications. (answer written by Rebecca H.) (2016, November 21). “How gravitational force varies at different locations on Earth.” Illinois. https://van.physics.illinois.edu/ask/listing/64061. Retrieved March 10, 2026.

Glover, Thomas J. and Richard A. Young. Desk Ref. Sequoia Publishing, Inc. Anchorage, AK 4^th Edition. 2022 pg. 587

Eddie

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Review: "Cosmic Numbers: The Numbers That Define Our Universe" by James D. Stein

Cosmic Numbers

One of the books I purchased recently was “Cosmic Numbers: The Numbers That Define Our Universe” by James D. Stein.  What attracted me to the book is that I am fascinated by mathematical constants (my favorite number is π) and how they came about. Stein talks about the following constants in the book: 

1.    The Gravitational Constant (G)

2.    The Speed of Light (c)

3.    The Ideal Gas Constant

4.    Absolute Zero

5.    Avogardo’s Number

6.    Electricity and the Proportionality Constant

7.    The Boltzmann Constant

8.    The Plank Constant

9.    The Schwarzschild Radius (which the value depends on the object’s mass)

10.  The Efficiency of Hydrogen Fusion

11.  The Chandrasekhar Limit

12.  The Hubble Constant

13.  Omega

While I have not yet finished the book (got three more chapters to go), I recommend this book.  Stein writes in a straight-forward, entertaining matter.  Here of some of my favorite highlights of the book:

Gravitational Constant:

* The concept of the gravitational constant comes from Issac Newton’s Principia (1687), and as we are aware, we have two constants:  Big G for the universal constant and little g for the local constant. 

* Little g (local gravity) was fairly easy to get, at least for Earth, using the relationship d = 1/2*g*t^2.  It would take until the mid-1700s before Henry Cavendish would propose a way to calculate big G, and even later before the first values of G were found.

Speed of Light:

* The first calculation of the speed of light was inspired by Galileo Galilei’s discovery of moons in front of Jupiter in 1610, which inspired Ole Rømer to come up with the first estimation of the speed of light.

* Albert Michelson is most connected with the speed of light, which will lead to the famous Michelson-Morely experiment, in which a beam of light was split into two separate, divergent beams.  Each of the diverged beams would reach two separate mirrors, and the difference between the wave’s speeds were calculated.

* An interesting paradox was presented in the chapter, involving lighthouse and a beach with the wall behind the lighthouse, and the speed of light is calculated using the distance between the lighthouse and the beam, in which the speed would reach a limit.

Absolute Zero:

* I know how refrigerators keep its food cold:  Liquid chlorine circulates in coils which evaporates into chlorine hydrate from the surrounding environment.  An electric pump pressurizes the gas, allowing the chlorine to turn back into a liquid, and the absorbed heat is released into the refrigerator.  Thank you Michael Faraday.  (OT?)

* In practice, temperatures near absolute zero have been reached (0 K, -273.15°C), both using a Bose-Einstein condensate and lasers to atoms almost to the point where atoms are completely still.

Electricity and the Proportionality Constant:

* Ever notice how similar the force of gravity and the force of electricity are similar?  For gravity, F = G*m*M/r^2 and for electricity, F = k*q*Q/r^2.

Boltzmann Constant:

* If you want a good mnemonic for the equation of work, just get mad:  W = m*a*d.

* Using the relationship of a monatomic molecule’s transitional energy and it’s kinetic energy, Ludwig Boltzmann solved for his constant (k) by solving 3/2*k*T = 1/2*m*v^2

Efficiency of the Hydrogen Fusion:

* I’m thankful that hydrogen fuses at a constant rate (.007 weight loss per nuclei).  If it didn’t, life may have not been possible.

* Measuring the fusion came first came from Lord Kelvin asking “How does the sun keep shining?”  The greatest contributions came during the decade of 1895-1905, and a value was finalized before the beginning of World War II. 

If you want a good read, check “Cosmic Numbers” out.

Eddie

This blog is property of Edward Shore.  2015.