What is the distance between the sun and Neptune? What is the formula used to calculate this distance?

Question

What is the distance between the sun and Neptune?  What is the formula used to calculate this distance?

Owen Atkinson · Accepted Answer

Neptune is about 30 AU from the Sun.

Neptune's distance from the Sun is approximately 29.82 astronomical units (AU) at perihelion and 30.32 AU at aphelion, for an average of roughly 30 AU. The distance cannot be calculated exactly, but since planetary orbits are approximately elliptical, two of the ellipse's parameters can be determined. Since its discovery, Neptune has actually only completed one full orbit. Planet positions are determined through the numerical integration of observational data obtained from satellites, deep space probes, and Earth-based observations.

Levi Alexander · Answer

undefined The average distance between the Sun and Neptune is about 4.5 billion kilometers or 2.8 billion miles. The formula used to calculate this distance is based on Kepler's third law of planetary motion:

$$ r = a(1-e^2) $$

where:
- $ r $ is the distance between the Sun and Neptune,
- $ a $ is the semi-major axis of Neptune's orbit (30.07 astronomical units),
- $ e $ is the eccentricity of Neptune's orbit (0.009456).

Using this formula:

$$ r = 30.07 AU \times (1 - 0.009456^2) $$

$$ r = 30.07 AU \times 0.9906 $$

$$ r = 29.79 AU $$

1 astronomical unit (AU) is the average distance from Earth to the Sun, which is about 149.6 million kilometers or 92.96 million miles. Therefore, the distance between the Sun and Neptune is approximately:

$$ r = 29.79 AU \times 149.6 million km $$

$$ r \approx 4.45 billion kilometers $$

$$ r \approx 2.77 billion miles $$

This is an average value, as Neptune's orbit is slightly elliptical, so its distance from the Sun varies during its orbit.