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How to Calculate the Distance From Mars to the Earth

Astronomers have been observing planets for hundreds of years, not only to track their orbits but to measure distances between them. In the 17th century, Giovanni Cassini calculated the distance between Mars and Earth, and was only 7 percent off. Distances between planets change every moment, but to get a rough number it's best to start with Earth's distance from the Sun and the distance of Mars from the Sun. Then you can easily calculate the relative distance of Mars from Earth.

Instructions

- 1
  Note the distance from the Earth to the Sun. A website such as AstronomyforBeginners.com will help you find this distance. Earth's distance from the Sun is considered to be 1 AU, or one astronomical unit. Scientists have determined that 1 AU equals an average of 149,598,000 kilometers.
- 2
  Figure out Mars's average distance from the Sun using the Kepler method. You will need to know how long Mars's orbit takes, so look in astronomy books or visit Nasa.gov to find that number. Once you know that Mars's orbit takes 688 days, or 1.88 Earth years, you're ready to figure out how far Mars is from the Sun.
- 3
  Apply the Kepler Method. Square the orbital period of Mars (multiply it times itself) and then find the cube root. So, 1.88 times 1.88 equals 3.5378. The cube root of that is 1.5237. This means that Mars is on average 1.5 times Earth's distance from the Sun.
- 4
  Subtract the average distances from the Sun of Mars and Earth. Since Mars is 1.5 times farther from the Sun than Earth, subtract 1.5 from 1, which equals .5. Multiply that by the average distance of the Earth to the Sun, which will be .5 times 149,598,000 kilometers. The product of the multiplication will be your answer. Note that these numbers are almost always measured in kilometers.
- 5
  Determine the distance between Mars and Earth if the planets are on opposite sides of the Sun. The above calculation only works if Mars and Earth are on the same side of the Sun, which means they are fairly close to one another. To determine the farthest away they could be from each other, add their average distances from the Sun (1.5 AU plus 1 AU = 2.5 AU) instead of subtracting. Then multiply the average distance of Earth from the Sun by 2.5, and you have your answer.

Astronomy