# How to Calculate the Distances to the Planets From the Sun

The distances to the planets are calculated using the Sun as the primary location point. This distance is often much greater than the distance to Earth but this is not always the case. Learn how to calculate the distances to the planets from the sun in this simple article. You’ll find out how the distances are calculated in astronomical units and years. You can also learn about Bode’s Law which is a basic scientific principle.

## Calculate the distances of the planets from the sun

The distances between the planets are based on their orbital paths around the Sun. The distance between Mercury and Earth for example can be 77 million kilometers at the closest point to almost 222 million kilometers at their furthest. The distance between Mercury and Earth can also vary significantly because the orbits of different planets are not circular. The table below lists the average distance between the planets and their corresponding AU or astronomical units and their orbital distances.

Astronomical units are used to measure distances within the solar system. One astronomical unit equals about 149 million kilometers or 92957000 miles. An astronomical unit is a convenient unit of measurement for distances in our solar system. In this video you will learn how to calculate the distances of the planets from the sun in kilometers and miles. Then you can try your hand at estimating distances in astronomical units to make sure you have a precise number.

Distances between the planets from the sun are calculated using Kepler’s laws. The distances between the Earth and the sun are not equal to the semi-major axis a T of Earth’s orbit and the semi-major axis V of Venus’ orbit. To calculate the distance between Earth and the planet you can use the formula r P = e cos E. The angle ‘e’ represents the position of the planet on its orbit. The orbital radii of the planets are also related to each other.

During the Renaissance scientists began measuring the distances of the planets from the earth. They discovered that the planets were closer to Earth than galaxies far away. The distances between planets and the earth are generally measured in light minutes rather than light years as light minutes and hours are easier to grasp. Mercury is the closest planet to the sun but it is only 36 million miles away – about 0.000006123880620837039 light years away.

## Explain Bode’s Law

It was a famous mathematical rule popularised by Johann Elert Bode in 1772 and predicted the orbital distance of the planets from the sun. Mercury Venus Mars and Jupiter all fit into the predicted pattern. The fifth planet Pluto failed to fit in the law’s neat pattern when it was discovered in 1930. Ultimately the law was considered to be nothing more than a coincidence.

The theory behind the relationship between the planets and the Sun was first developed in 1766 by Titus of Wittenberg and published by Johann Elert Bode six years later. The distances Bode determined were in good agreement with the actual mean distances of the planets at the time. Uranus for example had not been named by Herschel but was named Georgium Sidus after King George III of England. Later Johann Elert Bode suggested calling it Uranus so it would fit in with other planets in the Solar System. The name has a long and interesting history including in classical mythology.

Several theories have been proposed to explain Bode’s law. One of the most popular theories is based on orbital resonance which states that the major orbiting bodies create regions around the Sun that are free of long-term stable orbits. Some recent discoveries of extrasolar planetary systems suggest that Titius-Bode law may be universal but the evidence is weak enough to draw definite conclusions. Ultimately Bode’s law is an uncomfortable science and is best understood as a hypothesis.

Another method for remembering the relative distances of the planets from the Sun is Bode’s Law. This mathematical law states that the distances of Mercury Venus and Mars from the Sun are four times each other. The distances of Jupiter Mars and Saturn are five times farther apart. As we learn more about the relationship between the sun and the planets we can understand where the asteroid belt lies.

## Calculate distances in astronomical units

The average distance between the Earth and the Sun is measured in Astronomical Units which are 93 million miles or 150 million kilometers. The astronomical units are very convenient when dealing with distances within the solar system with Mercury being about a third of an AU and Pluto being about 40 AU. However you may be able to measure the distances of planets and stars using different units.

The astronomical unit was first defined by the International Astronomical Union (IAU) in 1976 when it was determined that the mass of a massless particle would have a period of one year when at that distance. This definition incorporated a Newtonian model of the solar system but proved difficult to apply when general relativity was introduced. Moreover the astronomical unit had a different value depending on the observer’s frame of reference. Also the astronomical unit was dependent on Kepler’s third law of planetary motion and the mass of the Sun which always decreased over time due to conversion of mass to energy.

Distance between the planets and the sun are measured using relative distances to each other. The distance between Jupiter and the Sun is equal to a unit which is ‘a.’ Earth’s orbit is similar to that of Venus which is essentially in the same plane. In this case astronomers use the same unit ‘a’.

After Kepler’s discovery astronomers realized that planets orbit the Sun and were in constant motion. They could thus determine the distances of the planets to the Sun by measuring the differences between two measurements. In addition Kepler’s third law was developed. It states that the ratio of a planet’s period square to its semimajor axis is proportional to its rotational velocity. This law is summarized in the formula a3/p2 = K.

## Calculate distances in years

We measure the distances between planets and the Sun in astronomical units which are millions of kilometers and miles. Distances between planets and the Sun are also measured in lightseconds the amount of time it takes for sunlight to reach a planet. Lightseconds are equivalent to 63178 astronomical units so we can use this distance to find out the exact distances between two planets.

The Earth’s year is 365 days long and the year of Mercury is 0.021 less ‘wide’ than it is long. The Sun is also shifted by about 20.6% from its center to its outermost edge. Kepler’s Harmonic Law ties the length of a planet’s orbital period to the distance between it and the Sun. Hence a period measured in years equals the distance in AU to the power of three.

Earth is the closest planet to the Sun and is approximately 23.8 million light-years from Earth. Its perihelion occurs around the year 2000 and gets one day later each century. Its perihelion position changes one day each century but its average speed is 2.5 days later than the Earth’s orbital radius. Because of leap years Earth is closer to the Sun than Mars is.

While Kepler’s Harmonic Law is accurate the Law of Titius-Bode is also quite accurate. To see the numbers in relation to each other use the table below. The ‘(real)’ column is the average distance of each planet. The ‘(n) column is the number that should go into the formula. Using these two laws will give you the distance between planets and the sun.

## Calculate distances in light years

How do you calculate distances in light years between planets and solar system objects? The distance between two celestial bodies is the distance between the centers of their semi-major axes. Pluto is no longer considered a planet and has an extremely elliptical orbit. The distance between Neptune and Mercury is almost 78 times longer than Mercury’s. Once you have calculated the distance between two objects it’s time to convert it into light years.

Light travels at the speed of about 186000 miles per second or 300000 kilometers per second. One light-year is five trillion miles (or nine trillion kilometers) which is approximately 93 million miles. It takes 1.3 seconds for light to travel from the moon to the earth. That means the distance between Mars and Earth is one minute and twelve seconds. In other words it’s 0.622 AU.

For this reason light years are used to calculate distances. The distance between Earth and the Sun is about 149 million kilometers or 401 million miles. However the distance between the earth and the sun varies as does the distance between a planet and the sun. However astronomers use this unit because it is so much larger than any other unit of measurement. You can find the distance of one planet to another by using this calculator.

How far is Mars from Earth? Mars orbits the sun at a distance of 1.5 astronomical units or 225 million km. This distance is calculated using the speed of light. Considering that light travels at the speed of light this distance would be approximately 11160000 miles for Mars. The distance between Mars and Earth varies as well depending on the planets’ orbits.