DuckieDai Universal Gravitation Python Program

physics · MIT License

Overview

Solve gravitational force, either mass, or separation distance using Newton's law of universal gravitation.

Tested on a TI calculator
Downloaded 37 times
Version 1.0.0
4832 bytes
Uses math

Download GRAVLAW.py Read the source How to install

Before you run it

TI-84 Plus CE Python · tested on OS 5.8.3, Python App 5.8.3.0048
TI Connect CE .py conversion to a Python AppVar in RAM; physically verified one program at a time
Bodies are treated as point masses and G is 6.674E-11.
All numeric inputs must be positive and below 1e100.
Zero and negative inputs are rejected.

Try the DuckieDai calculator screen

Follow the reviewed program's real menu, prompts, validation, calculation, and result flow before downloading.

JavaScript is required for the optional browser simulation. Source viewing and downloading remain available without it.

Simulation boundary: This preview uses a reviewed browser adapter. It does not execute the downloaded Python and does not prove TI-Python or calculator compatibility.

Learn the math

How universal gravitation works

The idea

Every pair of masses attracts. The force is larger for bigger masses and falls off with the square of the distance between their centers.

This is the law that describes orbits, tides, and the weight of an object at any distance from a planet.

The formula

Fg = G*m1*m2/r^2

Fg: gravitational force (N)
G: 6.674 x 10^-11 N*m^2/kg^2, built into the program
m1, m2: the two masses (kg)
r: distance between their centers (m)

Using the program

Choose what to solve for: 1 force, 2 mass 1, 3 mass 2, or 4 distance.
Enter the known values, then press Enter for the answer.

Worked example

Two masses of 1000 kg and 2000 kg are 10 m apart. Choose 1 and enter 1000, 2000, and 10.

Fg = 6.674e-11 x 1000.0 x 2000.0 / 10.0^2

The program shows Fg = 1.3347999999999997e-06 newtons, which is about 1.33 x 10^-6 N. Gravity between everyday objects is tiny.

Tips and common mistakes

An answer ending in e-06 means times 10 to the power -6.
Measure r between the centers of the objects, not their surfaces.
For objects near the Earth's surface, PE = m*g*h and weight = m*g are simpler.

Where this comes up

It comes up in the gravitation and orbits unit of physics and in introductory astronomy, for finding the pull between planets, moons, and satellites or the value of g on another world.

Exact reviewed bytes

Source code

Download .py

View source below, copy it when JavaScript is available, or download the exact .py bytes.

"""DuckieDai Universal Gravitation for TI-84 Plus CE Python."""

from math import sqrt


def duckiedai_intro(program_name, wait=True):
    """Show the reusable DuckieDai program opening."""
    title = program_name[:16]
    empty = 16 - len(title)
    left = empty // 2
    right = empty - left

    print("+----------------------+")
    print("|   " + " " * left + title + " " * right + "   |")
    print("|                      |")
    print("|       __             |")
    print("|   ___(o )>  quack!   |")
    print("|   \\ <_. )           |")
    print("|    `---'             |")
    print("|     by DuckieDai     |")
    print("+----------------------+")
    print("Loading...")

    if wait:
        input("Press enter to start ")
        print("\n" * 6)


def positive_number(prompt):
    """Ask until a positive finite number is entered."""
    while True:
        try:
            value = float(input(prompt))

            if value > 0 and value < 1e100:
                return value

        except ValueError:
            pass

        print("Enter a number above 0.")


def show_answer(name, value, unit):
    input("Press enter for answer ")
    print("\n" * 6)
    print("ANSWER")
    print(name + " = " + str(value))
    print(unit)


def main():
    duckiedai_intro("UNIVERSAL GRAV")

    G = 6.674e-11

    print("UNIVERSAL GRAVITY")
    print()
    print("Formula:")
    print("Fg = G*m1*m2/r^2")
    print()
    print("G = 6.674E-11")
    input("Press enter for menu ")
    print("\n" * 6)
    print()
    print("What do you need?")
    print()
    print("1. Gravity force")
    print("2. Mass 1")
    print("3. Mass 2")
    print("4. Distance")
    print()

    choice = input("Choose 1-4: ")

    print()

    # ==========================================
    # 1. SOLVE GRAVITATIONAL FORCE
    #
    # Fg = G*m1*m2/r^2
    # ==========================================

    if choice == "1":

        m1 = positive_number("Mass 1 (kg): ")
        m2 = positive_number("Mass 2 (kg): ")
        r = positive_number("Distance (m): ")

        force = (
            G * m1 * m2 /
            (r ** 2)
        )

        print()
        print("Using:")
        print("Fg = G*m1*m2/r^2")
        print()
        print("Fg =")
        print(str(G) + " x")
        print(str(m1) + " x")
        print(str(m2))
        print("/ " + str(r) + "^2")

        show_answer(
            "Fg",
            force,
            "newtons"
        )

    # ==========================================
    # 2. SOLVE MASS 1
    #
    # m1 = Fg*r^2 / (G*m2)
    # ==========================================

    elif choice == "2":

        force = positive_number("Gravity force (N): ")
        m2 = positive_number("Mass 2 (kg): ")
        r = positive_number("Distance (m): ")

        m1 = (
            force * r ** 2 /
            (G * m2)
        )

        print()
        print("Using:")
        print("Fg = G*m1*m2/r^2")
        print()
        print("Rearranged:")
        print("m1 = Fg*r^2")
        print("     /(G*m2)")

        show_answer(
            "m1",
            m1,
            "kg"
        )

    # ==========================================
    # 3. SOLVE MASS 2
    #
    # m2 = Fg*r^2 / (G*m1)
    # ==========================================

    elif choice == "3":

        force = positive_number("Gravity force (N): ")
        m1 = positive_number("Mass 1 (kg): ")
        r = positive_number("Distance (m): ")

        m2 = (
            force * r ** 2 /
            (G * m1)
        )

        print()
        print("Using:")
        print("Fg = G*m1*m2/r^2")
        print()
        print("Rearranged:")
        print("m2 = Fg*r^2")
        print("     /(G*m1)")

        show_answer(
            "m2",
            m2,
            "kg"
        )

    # ==========================================
    # 4. SOLVE DISTANCE
    #
    # r = sqrt(G*m1*m2/Fg)
    # ==========================================

    elif choice == "4":

        force = positive_number("Gravity force (N): ")
        m1 = positive_number("Mass 1 (kg): ")
        m2 = positive_number("Mass 2 (kg): ")

        r = sqrt(
            G * m1 * m2 /
            force
        )

        print()
        print("Using:")
        print("Fg = G*m1*m2/r^2")
        print()
        print("Rearranged:")
        print("r = sqrt(")
        print("G*m1*m2/Fg)")

        show_answer(
            "r",
            r,
            "meters"
        )

    else:
        print("Invalid choice.")

    print()
    print("DuckieDai says: done!")


# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

"""DuckieDai Universal Gravitation for TI-84 Plus CE Python."""
from math import sqrt
def duckiedai_intro(program_name, wait=True):
"""Show the reusable DuckieDai program opening."""
title = program_name[:16]
empty = 16 - len(title)
left = empty // 2
right = empty - left
print("+----------------------+")
print("| " + " " * left + title + " " * right + " |")
print("| |")
print("| __ |")
print("| ___(o )> quack! |")
print("| \\ <_. ) |")
print("| `---' |")
print("| by DuckieDai |")
print("+----------------------+")
print("Loading...")
if wait:
input("Press enter to start ")
print("\n" * 6)
def positive_number(prompt):
"""Ask until a positive finite number is entered."""
while True:
try:
value = float(input(prompt))
if value > 0 and value < 1e100:
return value
except ValueError:
pass
print("Enter a number above 0.")
def show_answer(name, value, unit):
input("Press enter for answer ")
print("\n" * 6)
print("ANSWER")
print(name + " = " + str(value))
print(unit)
def main():
duckiedai_intro("UNIVERSAL GRAV")
G = 6.674e-11
print("UNIVERSAL GRAVITY")
print()
print("Formula:")
print("Fg = G*m1*m2/r^2")
print()
print("G = 6.674E-11")
input("Press enter for menu ")
print("\n" * 6)
print()
print("What do you need?")
print()
print("1. Gravity force")
print("2. Mass 1")
print("3. Mass 2")
print("4. Distance")
print()
choice = input("Choose 1-4: ")
print()
# ==========================================
# 1. SOLVE GRAVITATIONAL FORCE
#
# Fg = G*m1*m2/r^2
# ==========================================
if choice == "1":
m1 = positive_number("Mass 1 (kg): ")
m2 = positive_number("Mass 2 (kg): ")
r = positive_number("Distance (m): ")
force = (
G * m1 * m2 /
(r ** 2)
)
print()
print("Using:")
print("Fg = G*m1*m2/r^2")
print()
print("Fg =")
print(str(G) + " x")
print(str(m1) + " x")
print(str(m2))
print("/ " + str(r) + "^2")
show_answer(
"Fg",
force,
"newtons"
)
# ==========================================
# 2. SOLVE MASS 1
#
# m1 = Fg*r^2 / (G*m2)
# ==========================================
elif choice == "2":
force = positive_number("Gravity force (N): ")
m2 = positive_number("Mass 2 (kg): ")
r = positive_number("Distance (m): ")
m1 = (
force * r ** 2 /
(G * m2)
)
print()
print("Using:")
print("Fg = G*m1*m2/r^2")
print()
print("Rearranged:")
print("m1 = Fg*r^2")
print(" /(G*m2)")
show_answer(
"m1",
m1,
"kg"
)
# ==========================================
# 3. SOLVE MASS 2
#
# m2 = Fg*r^2 / (G*m1)
# ==========================================
elif choice == "3":
force = positive_number("Gravity force (N): ")
m1 = positive_number("Mass 1 (kg): ")
r = positive_number("Distance (m): ")
m2 = (
force * r ** 2 /
(G * m1)
)
print()
print("Using:")
print("Fg = G*m1*m2/r^2")
print()
print("Rearranged:")
print("m2 = Fg*r^2")
print(" /(G*m1)")
show_answer(
"m2",
m2,
"kg"
)
# ==========================================
# 4. SOLVE DISTANCE
#
# r = sqrt(G*m1*m2/Fg)
# ==========================================
elif choice == "4":
force = positive_number("Gravity force (N): ")
m1 = positive_number("Mass 1 (kg): ")
m2 = positive_number("Mass 2 (kg): ")
r = sqrt(
G * m1 * m2 /
force
)
print()
print("Using:")
print("Fg = G*m1*m2/r^2")
print()
print("Rearranged:")
print("r = sqrt(")
print("G*m1*m2/Fg)")
show_answer(
"r",
r,
"meters"
)
else:
print("Invalid choice.")
print()
print("DuckieDai says: done!")
# TI-Python imports the selected AppVar rather than
# setting __name__ to main.
main()

Filename: GRAVLAW.py
Size: 4832 bytes
SHA-256: fe76a2435c9044e26b40e145a1cc5cdc6f3b2ec7bc16e529200ea5bd415f20b4

Usage

Inputs

Requested unknown: gravitational force, mass 1, mass 2, or distance
Three known positive values in SI units

Outputs

Requested gravitational quantity with formula and labelled unit

Units: Masses use kilograms, distance uses metres, and force uses newtons.

Assumptions and limitations

Assumptions

Bodies are treated as point masses and G is 6.674E-11.

Constraints

All numeric inputs must be positive and below 1e100.

Known failures

Zero and negative inputs are rejected.
The point-mass model may be inappropriate at small separations for extended bodies.

Compatibility and review

Review status: Tested on a TI calculator
Tested on: TI-84 Plus CE Python; OS 5.8.3; Python App 5.8.3.0048; exact paginated .py transferred through TI Connect CE into RAM and tested individually
What happened: Passed: branded intro, paginated menu, universal gravitation workflow, formula display, and answer screen ran on the physical calculator
Dependencies: math
Suggested calculator name: GRAVLAW — you can give it another valid, unique name when you transfer it
Desktop test cases: Not available for this interactive-only source

This exact source auto-launches an interactive calculator session, so compatibility evidence comes from the recorded physical-device review rather than an importable desktop fixture.

Transfer and launch

Download the .py file, send it to your calculator with TI Connect CE as GRAVLAW or another name, then open the Python App and try the worked example on this page first.

Full installation and troubleshooting guide. Check your teacher's or exam's rules before using any program.

Version history

1.0.0 — current version, published 2026-09-23. Download this reviewed version

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