Rafaela de Figueiredo
Mr. Davis
Algebra 8
March 18, 2011

Out of this world project

A brief from the past…
The planets look like little points of light in the dark sky at night, and we can't simply look up at them and tell how far they are from Earth or from each other, or even from the sun. But astronomers and mathematicians have come up with some ways to discover their distances.

500 years ago, everyone thought Earth was the center of the solar system. By the time Johannes Kepler was born in 1571, people were starting to get the idea that the planets go around the Sun. Kepler discovered that the motions of the planets could be described by some simple mathematical formulas. The closer a planet is to the Sun, the faster it travels.

If only astronomers could determine the distance from Earth to any other planet or the Sun, they could use that to find the distances to all the planets, and their understanding of how the solar system would be greatly improved.
One of the first people to make good measurement of the distance to a planet was the astronomer Gian Domenico Cassini. In 1672, Cassini used a technique called parallax to measure the distance to Mars.

If you hold your thumb up at arm's length and looking at it first with one eye, and then your other. Notice how your thumb seems to shift back and forth against the objects that are farther away. Because your two eyes are separated by a few inches, each views your thumb from a different position. The amount that your thumb appears to move is its parallax. When astronomers measure the parallax of an object and know how separate they are, and with that, they can calculate the distance to the object.

Although he didn't get the exact right answers, Cassini's results were very close to the correct values. The Sun is about 93 million miles from Earth. As Earth and Mars move in their separate orbits, they never come closer than 35 million miles to each other. Saturn, that was the most distant planet at that time, is around 900 million miles away.

Now a days, astronomers have technologies that could measure distances to other orbits and other universes. When we have a spacecraft at another planet, we know the time it takes for it to get there and to come back and so it is easy to find how far planets are from each other. We can also send a powerful radar signal toward a planet and time how long it takes for the echo to return. We know how fast these signals travel (the speed of light), so measuring how long they take makes it easy to calculate the distance.

What we know about planets that are further from the Sun:
• They move more slowly
• Take more time to complete an orbit
For example, Mercury, the closest planet to the Sun, takes just 88 Earth days to complete an orbit. But Neptune, that is the furthest takes 164 Earth years to complete an orbit.

The graph shows the distances of the planets from the Sun and the time it takes them to orbit once around it. The shape of the curve shows that the further out a planet is the longer it takes to orbit the Sun.

Scientists and Mathematicians use the formula :
Distance= rate X time
d= r x t

The rate equals distance divided by time and time equals distance divided by rate.
And thats how we know hot to find the distance between planets