DuckieDai Universal Gravitation Python Program

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physics · MIT License

Overview

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

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.

Browser preview

Try the DuckieDai calculator screen

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

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.

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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

Transfer and launch

Confirm that your calculator is the Python-capable model named above. Check that its OS and Python App versions match the reviewed record.
Download the .py source above and verify its SHA-256 digest if your computer provides that option.
Use TI Connect CE to send the Python file to a compatible calculator. GRAVLAW is a suggested name; you may choose another valid, unique calculator name.
Open the Python App, select the program, and check sample inputs before relying on other results.

Read the complete installation, launch, troubleshooting, and removal guide.

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Version history

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

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