Distance to the Sun

It is rather easy to determine distances within the Solar System if you measure them in AU's.

• The planets move around the Sun in orbits.
• The orbits are really ellipses, but for our purposes we can consider them to be circles.
• Call the radius of the orbit a.
  • This is the distance from the planet to the Sun.
  • Let us measure a in AU.
  • Thus for the Earth, a = 1.
• By observing the position of a planet in the sky over a period of months, we can determine the radius a of its orbit.
  • Here is an example.

    

  • This involves trigonometry, which is beyond the knowledge base assumed for this course.
  • But you can see that you could measure the distance to Venus this way by simpling measuring the angle shown in the sky, making a scale drawing on a piece of paper, and measuring the distance between the Sun and Venus on your paper.
• Knowing the distance to Venus in AU, we could measure how big 1 AU is in km if we could measure the distance to Venus in km.
• The most accurate way to do that is to bounce a radar signal off of Venus.
  • Radar is microwave electromagnetic radiation.
  • Therefore it travels at the speed of light, c = 3 x 10⁸m/s.
  • We can measure the time t it takes the signal to get to Venus and back.
  • The distance it went (twice the distance from Earth to Venus) is c t.

Later, we will want to know distances to stars. Getting the distance from the Earth to the Sun right is the first step.