Diameter of Astronomical Object Using Magnification

Question

I took a picture of Jupiter through my telescope, using an iPhone. I know the magnification of the telescope lens I used, and can Google to get the magnification of the iPhone lens (the magnification without zooming). Using a standard Photo Editor, I also know the pixels across of Jupiter in my image.

Can I, using all of this information above, calculate how many kilometres one pixel represents, and consequently the diameter of Jupiter?

Answer 1

You could use your image to estimate the angular size of Jupiter that night. To find the actual diameter of Jupiter you would also need to know the distance that Jupiter is from Earth, and since Jupiter and Earth are both orbiting the sun, this distance changes.

You can find the distance with software (Eg Stellarium) or using Nasa's Horizons web interface (You will need to use the column labeled "delta" which gives distance in astronomical units). To find the diameter you will need to do some trigonometry. (Diameter = distance $\times$ angular size in radians)

Alternatively you could use the published Diameter of Jupiter (70000km) and use your observations to calculate the distance.

To calculate the distance to Jupiter without knowing it's diameter requires more than a single observation. You will need to have:

1. A long enough series of observations to establish the orbital period and elements of Jupiter.
2. Knowledge of Kepler's laws of planetary motion
3. Knowledge of the distance of Earth from the sun, and to get this you can fund a expedition to the South Pacific during a transit of Venus.
4. A sharp pencil to do all the maths.

I'm being a little glib... The point is that it took more than 150 years of research between the broad acceptance of heliocentric solar system, and our knowledge of its scale, or the actual sizes of planets.