Aphelion and Perihelion distance calculations

[ExoP]

Hi!

I was wondering how you can calculate the distance to a planet simply by looking at images when it is at aphelion and perihelion? is it even possible? Thanks!

 

[SteamKing]

How do you know the planet is at aphelion and perihelion?

 

[BobG]

If you knew the aphelion distance and the perihelion distance, the average distance (semi-major axis) would just be the two of them added together and divided by two. Getting those two distances is the challenge.

A more realistic way:

A planet's orbital period is measurable and Kepler's Third Law relates orbital period to distance from the Sun. For example, Jupiter's orbital period is almost 12 times longer than the Earth's. Since the square of the period is proportional to the cube of the distance, Jupiter must be a little more than 5 times further from the Sun than the Earth.

If you can figure out how far the Earth is from the Sun, then you know how far every other planet is. Figuring out how far Earth is from the Sun is the challenging part (hence the tradition of giving planets' radius in terms of astronimical units, with astronomical units being the distance between the Earth and the Sun - we didn't know how long an astronomical unit was, but we knew Jupiter's radius was about 5.25 of them, however long they were).

Fortunately, you can measure the distance between the Earth and the Sun. Every once in a while, Venus crosses between the Earth and the Sun (instead of over or below the Sun from our point of view). Eight years later, it crosses the Sun again. Then you have to wait either another 121.5 years or another 105.5 years for the sequence to occur again.

By timing the transit of Venus from widely separated points on the Earth, and with a knowledge of how big the Earth's diameter is, you can figure out how far away the Earth is from the Sun based on the idea of similar triangles.

In fact, the first international science project was in 1761 when astronomers traveled all over the world to observe the transit of Venus from several points as widely separated from each other as possible. And then they did it again in 1769 (which is why Capt Cook went to Tahiti).

The last transit was just last year (and it was very cool). The next will be in 2117, followed by another in 2125.

 

[ExoP]

Hello,

Thanks! I have already calculated the AU by using images of the Venus transit :) How do I do it with other planets , for example calculate the distance to Mars? I need something orbiting in front of it right? :S

 

[ExoP]

Or, may I ask this. I have 2 images of the Sun, one when Earth is at aphelion and the other one at perihelion. By using the images, and using helpful data, how can I calculate these distances? :S

 

[BobG]

Let's try the Moon. It's close and easy to photograph.

Even if the distances weren't printed on the picture, you could figure out that apogee is x times further away than perigee. Don't know what those distances are, but you can still compare their relative sizes and relative distances.

Likewise, Kepler figured out the relative distances of each planet (i.e. Mars is x times further away from the Sun than Earth, etc).

You still have to calculate at least one actual distance. Once you do, you essentially know all the other distances you're interested in. Because we already knew the relative distances of each planet, and the shape of their orbit, once we figured out the distance between the Earth and Sun, we knew all the other distances were interested in for all of the planets known at that time.

In other words, comparing the images at apogee and perigee (or aphelion and perihelion) alone won't give you enough information. Somehow, you need to calculate a real distance; not just a relative distance.

So, if "and using helpful data" means measuring the distance between the Earth and Moon at apogee or perigee, then the images would enable you to measure the distance of the other. But you'd actually have to measure the distance somewhere.