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

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.

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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.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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