Question

What equation do astronomers use to calculate the sun-earth distance?

Answer 1

Kepler's third law:

1. The squares of the planetary' orbital periods were precisely proportional to the cube of their semi-major dimensions.
2. According to Kepler's Third Law, the period required for a planet to orbit the Sun grows exponentially well with the radius of its orbit.

Mathematically, this can be represented as:

${\mathrm{T}}^2={\mathrm{a}}^3$

Here,

T is the planet's orbital period.

a is the semi-major axis distance.

Explanation:

1. We may readily estimate the orbital periods of the planets in AU by monitoring their locations. To establish the exact length of an AU, we require one more piece of information. The simplest method is to calculate the distance between Earth and Venus. Originally, this was done with parallax.
2. We could now determine distances with excellent precision using radar. The distance is determined by the time it takes radio waves to bounce off Venus.
3. We can calculate Venus's distance from the Sun utilizing Kepler's law. The distance between Earth and Venus is therefore $0.27\mathrm{AU}$.
4. We could calculate the distance between Earth and Venus utilizing observations, which is around $42,000,000\mathrm{kilometers}$. We may deduce from this that $1\mathrm{AU}$, the distance between the Earth and the Sun, is approximately $150,000,000\mathrm{km}$.

Therefore, the earth-sun distance is determined using Kepler's 3rd law.