This program estimates Earth’s gravitational acceleration given the latitude and elevation (in meters).

For this calculation, consider the absolute value of the latitude. Gravity acceleration is the a given the northern latitude north and the corresponding southern latitude. (Example: gravity is about 9.79325 m/s² at 30° north and 30° south).

Sources: Bislin, Walter. “Earth Gravity Calculator” September 1, 2018. https://walter.bislins.ch/bloge/index.asp?page=Earth+Gravity+Calculator Retrieved January 15, 2026.

Glover, Thomas J. and Richard A. Young Desk Ref Sequoia Publishing, Inc. Anchorage, AK. 4th Edition, 2022. Soft Cover ISBN 978-1-885071-60-6. pg. 587

“Gravity of Earth” Wikipedia. Last edited January 31, 2026. https://en.wikipedia.org/wiki/Gravity_of_Earth Retrieved February 1, 2026.

from math import *

# constants
# equator: radius, gravity
a=6378137
ga=9.7803253359
# poles: radius, gravity
b=6356721.3142
gb=9.8321849378

print("Latitude:","\nNorth or South")
d=eval(input("Decimal? "))
m=eval(input("Minutes? "))
s=eval(input("Seconds? "))
phi=radians(d+m/60+s/3600)

print("Height (m)?")
h=eval(input("? "))

gs=a*ga*cos(phi)**2+b*gb*sin(phi)**2
gs/=sqrt((a*cos(phi))**2+(b*sin(phi))**2)

print("Gravity on the surface:")
print(str(gs)," m/s**2")

print("At altitude: ",str(h)," m")
ge=(100*gs-0.3086*h/1000)/100
print(str(ge)," m/s**2")