Enter the orbital period and the eccentricity into the Calculator (this method assumes a heliocentric orbit and uses the AU-years form of Kepler’s 3rd law). The calculator will evaluate the Aphelion Distance. 

Aphelion Distance Calculator

By Orbital Period
By Perihelion Distance

Enter exactly 2 values to calculate the missing variable (elliptical orbits: 0 ≤ e < 1). Orbital-period method assumes an orbit around the Sun (a³ = T² when a is in AU and T is in years).

Aphelion Distance Formula

AD = T^{2/3}\,(1+e)

Note: This form uses Kepler’s 3rd law for objects orbiting the Sun, where a³ = T² when a is in AU and T is in years, and where aphelion distance is AD = a(1+e).

Variables:

  • AD is the Aphelion Distance (AU)
  • T is the orbital period (years)
  • e is the eccentricity (for an ellipse, 0 ≤ e < 1)

To calculate the Aphelion Distance, compute T2/3 (the semi-major axis in AU for a heliocentric orbit when T is in years), then multiply by (1+e).

How to Calculate Aphelion Distance?

The following steps outline how to calculate the Aphelion Distance.

  1. First, determine the orbital period (years). 
  2. Next, determine the eccentricity (0 ≤ e < 1 for an ellipse). 
  3. Next, gather the formula from above = AD = T2/3 * (1+e).
  4. Finally, calculate the Aphelion Distance.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

orbital period (years) = 8

eccentricity = 0.5

Aphelion Distance (AU) = 82/3 × (1 + 0.5) = 4 × 1.5 = 6 AU

FAQs

What is the significance of the Aphelion Distance in astronomy?
The Aphelion Distance is significant in astronomy as it represents the farthest point in an object’s orbit around the Sun. This distance can influence the object’s climate and visibility from Earth.

How does eccentricity affect an orbit?
Eccentricity measures the deviation of an orbit from being circular. A higher eccentricity means the orbit is more elongated, affecting the object’s speed and distance from the Sun at different points in its orbit.

Can the Aphelion Distance change over time?
Yes, the aphelion distance of an object can change over time due to gravitational interactions with other bodies (orbital perturbations) and, for some objects like comets, non-gravitational effects such as outgassing.

Why is it important to calculate the Aphelion Distance accurately?
Accurately calculating the Aphelion Distance is important for understanding the dynamics of celestial bodies in our solar system, predicting climate variations on planets and moons, and planning space missions.