# Measurements between sun and earth

## Main Question or Discussion Point

Hi everyone my name is Fabien
I was wondering is there any accurate way to measure the distance between the earth and the sun without having some professional materiel.
IF yes How accurate are we talking about?
How do you do if you want to know precisely?
How do the scientist do it?
Do you need to use satellite ?
thanks guys

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Matterwave
Gold Member
Well you can get the distance if you already know some of the properties of the sun. If you know the size (radius or diameter) of the Sun, you can construct a pin-hole camera to measure the angular size of the Sun. From this you can easily deduce the distance. Accuracy of this method isn't very high, and it depends on how well your measurements are. I would say you can get the distance to probably within 10-15%.

If you use the mass of the Sun and the period of Earth's rotation, you can get the distance from circular orbits. This will be pretty accurate. After going through a little math you get:

$$r=(\frac{GMT^2}{4\pi^2})^{\frac{1}{3}}$$

Where G is the gravitational constant, M is the mass of the Sun, and T is the period of Earth's rotation. Plugging in known values for this, I get an answer that is within .1% of the real value.

It's not immediately obvious to me how to get the distance without using known properties such as radius or mass...

You can set up experiments to GET the radius; however, that requires a spectroscope since you would need to measure the rotation speed of the Sun.

Well, please forgive me for doing what I love to do which is research! Adding information to this topic from Ask an Astronomer for Kids.

How far away is the sun?
The sun is at an average distance of about 93,000,000 miles (150 million kilometers) away from Earth. It is so far away that light from the sun, traveling at a speed of 186,000 miles (300,000 meters) per second, takes about 8 minutes to reach us. Like all of the other planets in our solar system, Earth does not travel around the sun in a perfect circle. Instead its orbit is elliptical, like a stretched circle, with the sun just off the center of the orbit. This means that the distance between Earth and the sun changes during a year. At its closest, the sun is 91.4 million miles (147.1 million km) away from us. At its farthest, the sun is 94.5 million miles (152.1 million km) away.

Filip Larsen
Gold Member
It's not immediately obvious to me how to get the distance without using known properties such as radius or mass...
The problem is, as you suspect, that the absolute value of such properties are impossible to get with simple techniques that only relates "passive" observable geometric or orbital quantities, since the underlying relations are scale free. The best you can get with that is ratios like mass ratios between orbital bodies and distance ratios like the astronomical unit.

To get an absolute measure, you would need to use an independent relationship that is not scale free, like directly measuring the distance between orbital bodies with radar or measurement of the parallax of one body when simultaneously observed from two positions on another. For the mass ratios, there is (to my knowledge) still a fair bit of uncertainty because the only way to precisely relate mass to orbital mechanics is via precise knowledge of the value of the universal constant of gravity.

Pengwuino
Gold Member
You should look into how 'the ancients' use to measure such distances ;). Or well, maybe not ancient, but before the advent of modern techniques. I'm always amazed to see how accurate people use to find out various astronomical measures "back in the day" :)