Planetary Centripetal Acceleration Calculator

Calculate the centripetal acceleration of a planet orbiting a star based on orbital parameters

Input Parameters

Default: Sun's mass (1.989 × 10^30 kg)

Calculation Results

Calculation Formula

a = (4π²r) / (T²)

Where:
a = centripetal acceleration (m/s²)
r = orbital radius (m)
T = orbital period (s)

Planetary Centripetal Acceleration Calculator Usage Guide

Learn how to use the calculator to determine the centripetal acceleration of planets

How to Use This Calculator

  1. Enter the orbital radius of the planet in kilometers (km)
  2. Enter the orbital period of the planet in days
  3. The mass of the central body (star) is set to the Sun's mass by default (1.989 × 10^30 kg), but can be adjusted if needed
  4. Click the "Calculate" button to compute the centripetal acceleration
  5. The result will be displayed in both standard and scientific notation formats

Understanding Centripetal Acceleration

Centripetal acceleration is the acceleration that causes an object to follow a curved path and is always directed toward the center of the curve. For planets orbiting a star, this acceleration is what keeps them in their orbits.

The formula used in this calculator is:
a = (4π²r) / (T²)
where:
a = centripetal acceleration (m/s²)
r = orbital radius (m)
T = orbital period (s)

Example Calculation

If Earth orbits at an average distance of approximately 149.6 million kilometers from the Sun with an orbital period of 365.25 days, the centripetal acceleration can be calculated as:

a = (4π² × 149.6 × 10^6 × 1000) / (365.25 × 24 × 60 × 60)²
a ≈ 0.00593 m/s²

Note: For more accurate astronomical calculations, consider using astronomical units (AU) instead of kilometers for the orbital radius.