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from flask import Flask, request, jsonify |
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import math |
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import os |
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app = Flask(__name__) |
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C = 299792458 |
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G = 6.67430e-11 |
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def gravitational_time_dilation(mass, radius, t0): |
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""" |
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Calculate gravitational time dilation factor based on mass and radius. |
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t0: Proper time for observer (seconds) |
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Returns: Dilated time (seconds) |
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""" |
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try: |
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rs = (2 * G * mass) / (C ** 2) |
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factor = math.sqrt(1 - rs / radius) |
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if factor <= 0 or math.isnan(factor): |
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return None |
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return t0 / factor |
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except Exception: |
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return None |
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def relativistic_time_dilation(velocity, t0): |
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""" |
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Calculate relativistic time dilation due to velocity. |
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velocity: Speed of observer (m/s) |
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t0: Proper time for observer (seconds) |
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Returns: Dilated time (seconds) |
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""" |
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try: |
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beta = velocity / C |
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if beta >= 1: |
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return None |
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factor = math.sqrt(1 - beta ** 2) |
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return t0 / factor |
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except Exception: |
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return None |
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@app.route('/') |
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def home(): |
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return """ |
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<html> |
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<head> |
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<title>Time Dilation Calculator</title> |
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<style> |
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body { font-family: Arial, sans-serif; margin: 20px; } |
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.container { max-width: 800px; margin: auto; } |
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.input-group { margin: 20px 0; } |
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label { |
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display: inline-block; |
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width: 200px; |
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cursor: pointer; |
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color: #007bff; |
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text-decoration: underline; |
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} |
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label:hover { color: #0056b3; } |
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input { padding: 5px; width: 200px; margin-left: 10px; } |
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button { |
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padding: 10px 20px; |
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margin: 20px 0; |
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background-color: #007bff; |
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color: white; |
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border: none; |
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cursor: pointer; |
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} |
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button:hover { background-color: #0056b3; } |
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#result { margin-top: 20px; padding: 10px; border: 1px solid #ddd; } |
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.popdown { |
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display: none; |
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margin-top: 5px; |
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padding: 10px; |
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background-color: #f8f9fa; |
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border: 1px solid #ddd; |
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border-radius: 4px; |
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max-width: 400px; |
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font-size: 14px; |
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} |
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.popdown.show { display: block; } |
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</style> |
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</head> |
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<body> |
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<div class='container'> |
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<h1>Time Dilation Calculator</h1> |
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<p>Calculate gravitational and relativistic time dilation for two observers.</p> |
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<div class='input-group'> |
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<h3>Observer 1</h3> |
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<div> |
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<label onclick="togglePopdown('mass1-info')">Mass (kg):</label> |
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<input type='number' id='mass1' value='5.972e24'> |
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<div id='mass1-info' class='popdown'> |
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The mass of the object (e.g., planet or star) affecting Observer 1, in kilograms. |
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This determines the strength of the gravitational field. For example, Earth's mass is approximately 5.972 × 10²⁴ kg. |
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Larger masses cause greater gravitational time dilation, slowing time for the observer. |
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</div> |
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</div> |
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<div> |
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<label onclick="togglePopdown('radius1-info')">Radius (m):</label> |
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<input type='number' id='radius1' value='6.371e6'> |
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<div id='radius1-info' class='popdown'> |
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The distance from the center of the massive object to Observer 1, in meters. |
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This is typically the radius of the planet or star. For example, Earth's radius is about 6.371 × 10⁶ m. |
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Smaller radii (closer to the mass) increase gravitational time dilation. |
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</div> |
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</div> |
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<div> |
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<label onclick="togglePopdown('velocity1-info')">Velocity (m/s):</label> |
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<input type='number' id='velocity1' value='0'> |
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<div id='velocity1-info' class='popdown'> |
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The speed of Observer 1 relative to a stationary reference frame, in meters per second. |
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This affects relativistic time dilation. For example, a velocity of 0 m/s means no relativistic effects, |
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while high speeds (e.g., 0.5 × speed of light) significantly slow time. Must be less than 299,792,458 m/s. |
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</div> |
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</div> |
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</div> |
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<div class='input-group'> |
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<h3>Observer 2</h3> |
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<div> |
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<label onclick="togglePopdown('mass2-info')">Mass (kg):</label> |
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<input type='number' id='mass2' value='5.972e26'> |
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<div id='mass2-info' class='popdown'> |
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The mass of the object affecting Observer 2, in kilograms. |
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For example, a planet 100 times Earth's mass would be 5.972 × 10²⁶ kg. |
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This influences gravitational time dilation, with larger masses causing greater time dilation. |
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</div> |
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</div> |
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<div> |
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<label onclick="togglePopdown('radius2-info')">Radius (m):</label> |
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<input type='number' id='radius2' value='6.371e6'> |
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<div id='radius2-info' class='popdown'> |
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The distance from the center of the massive object to Observer 2, in meters. |
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For example, using Earth's radius (6.371 × 10⁶ m) assumes Observer 2 is on the surface. |
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Smaller distances amplify gravitational time dilation effects. |
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</div> |
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</div> |
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<div> |
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<label onclick="togglePopdown('velocity2-info')">Velocity (m/s):</label> |
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<input type='number' id='velocity2' value='0'> |
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<div id='velocity2-info' class='popdown'> |
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The speed of Observer 2 relative to a stationary reference frame, in meters per second. |
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High velocities cause relativistic time dilation, slowing time for the observer. |
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Set to 0 for no relativistic effects. Must be less than the speed of light (299,792,458 m/s). |
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</div> |
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</div> |
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</div> |
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<div class='input-group'> |
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<div> |
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<label onclick="togglePopdown('proper_time-info')">Proper Time (s):</label> |
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<input type='number' id='proper_time' value='86400'> |
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<div id='proper_time-info' class='popdown'> |
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The time experienced by a reference observer in a weak gravitational field and at rest, in seconds. |
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For example, 86,400 seconds equals 1 day. This is the baseline time used to calculate how much |
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time each observer experiences after dilation effects are applied. |
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</div> |
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</div> |
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</div> |
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<button onclick='calculate()'>Calculate</button> |
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<div id='result'></div> |
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</div> |
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<script> |
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function togglePopdown(id) { |
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const popdown = document.getElementById(id); |
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popdown.classList.toggle('show'); |
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} |
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async function calculate() { |
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const data = { |
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mass1: parseFloat(document.getElementById('mass1').value), |
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radius1: parseFloat(document.getElementById('radius1').value), |
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velocity1: parseFloat(document.getElementById('velocity1').value), |
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mass2: parseFloat(document.getElementById('mass2').value), |
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radius2: parseFloat(document.getElementById('radius2').value), |
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velocity2: parseFloat(document.getElementById('velocity2').value), |
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proper_time: parseFloat(document.getElementById('proper_time').value) |
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}; |
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const response = await fetch('/calculate', { |
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method: 'POST', |
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headers: { 'Content-Type': 'application/json' }, |
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body: JSON.stringify(data) |
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}); |
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const result = await response.json(); |
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document.getElementById('result').innerHTML = result.message.replace(/\\n/g, '<br>'); |
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} |
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</script> |
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</body> |
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</html> |
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""" |
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@app.route('/calculate', methods=['POST']) |
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def calculate(): |
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try: |
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data = request.get_json() |
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mass1 = data.get('mass1') |
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radius1 = data.get('radius1') |
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velocity1 = data.get('velocity1', 0) |
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mass2 = data.get('mass2') |
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radius2 = data.get('radius2') |
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velocity2 = data.get('velocity2', 0) |
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t0 = data.get('proper_time') |
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if not all([mass1, radius1, mass2, radius2, t0]) or any(x <= 0 for x in [mass1, radius1, mass2, radius2, t0]): |
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return jsonify({"message": "Invalid input: All values must be positive numbers."}), 400 |
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t1_grav = gravitational_time_dilation(mass1, radius1, t0) |
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t2_grav = gravitational_time_dilation(mass2, radius2, t0) |
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if t1_grav is None or t2_grav is None: |
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return jsonify({"message": "Error: Invalid gravitational parameters (e.g., within event horizon)."}), 400 |
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t1_rel = relativistic_time_dilation(velocity1, t0) if velocity1 > 0 else t0 |
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t2_rel = relativistic_time_dilation(velocity2, t0) if velocity2 > 0 else t0 |
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if (velocity1 > 0 and t1_rel is None) or (velocity2 > 0 and t2_rel is None): |
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return jsonify({"message": "Error: Velocity exceeds speed of light."}), 400 |
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t1_total = t1_grav if velocity1 == 0 else t1_grav * (t1_rel / t0) |
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t2_total = t2_grav if velocity2 == 0 else t2_grav * (t2_rel / t0) |
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time_diff = abs(t1_total - t2_total) |
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message = ( |
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f"Results for proper time {t0:.2f} seconds:\n" |
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f"Observer 1:\n" |
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f" Gravitational dilated time: {t1_grav:.2f} seconds\n" |
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f" Relativistic dilated time: {t1_rel:.2f} seconds\n" |
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f" Total dilated time: {t1_total:.2f} seconds\n" |
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f"Observer 2:\n" |
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f" Gravitational dilated time: {t2_grav:.2f} seconds\n" |
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f" Relativistic dilated time: {t2_rel:.2f} seconds\n" |
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f" Total dilated time: {t2_total:.2f} seconds\n" |
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f"Relative time difference: {time_diff:.2f} seconds" |
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) |
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return jsonify({"message": message}) |
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except Exception as e: |
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return jsonify({"message": f"Error: {str(e)}"}), 500 |
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if __name__ == '__main__': |
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port = int(os.environ.get("PORT", 7860)) |
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app.run(host='0.0.0.0', port=port) |
