The problem with direct imaging
Telescopes each have an ‘angular resolution’ which describes their ability to distinguish two points clearly from one another. An angular resolution of 1 degree means a telescope is able to clearly separate two points that are 1 degree apart from one another. The actual spatial distance this corresponds to varies depending on how far away the objects are from the observer e.g. if the objects were just 1m away, two points could be distinguished from one another even if they were only 2cm apart. However, if the objects were 380,000km away (the distance of the Moon from the Earth), we could only distinguish two points that were approximately 6,600km apart – this is equal to almost twice the diameter of the Moon itself! As you can tell, this would be a very poor angular resolution indeed, especially given the fact we can see the Moon clearly, with detail, with just our naked eye!
Fortunately, the resolutions of modern telescopes are far, far better than in the example above. The Hubble Space Telescope has an angular resolution of just 0.05 arcseconds, where an arcsecond is 1/60th of an arcminute and an arcminute is in turn 1/60th of a degree (therefore 1 arcsecond equals 1/3,600th of a degree).
To prove the difficulties of direct imaging, try calculating whether a Jupiter sized planet (the largest in our solar system) would be resolvable by Hubble if it were orbiting Proxima Centauri, our nearest star. The following information is needed in the calculation:
- The distance to Proxima Centauri (D) is 4.22 lightyears.
- 1 lightyear is approximately equal to 9,500,000,000,000,000 (9.5 × 1015) metres!
- The diameter of Jupiter (d) is approximately 140,000km.
- The angle (δ) subtended by Jupiter is approximately equal to 'd' divided by 'D', when δ is small, and when δ is given in ‘radians’.
- 1 radian = (360 ÷ 2π) degrees; 1 degree = (2π ÷ 360) radians.
For additional guidance see the relevant section in our guide linked near the top of the page.
To solve, we need determine if the angle subtended by Jupiter is greater than or less that the angular resolution of Hubble. You can imagine trying to separate two points on opposite sides of the planet – they will be separated from one another by the planet’s diameter, d.
First, we must make sure that ‘d’ and ‘D’ are in the same units (easiest to convert everything into km). D = 4.22 × 9.5 × 1012 km = 4 × 1013 km. Using the small angle approximation:
δ = 140,000 ÷ (4 × 1013) radians
δ = 3.5 × 10-9 radians
δ = 2 × 10-7 degrees
δ = 0.0007 arcseconds
This angular separation is less that the angular resolution of Hubble, so the telescope would not be able to make out one side of the planet from the other, making it impossible to directly image the planet.
Note - we observe from space rather than the Earth when possible as the angular resolution is always made worse on the Earth due to the presence of the atmosphere. The air in the atmosphere causes light to bend in unpredictable ways. This has the pleasant effect of causing stars to 'twinkle' in the night sky, but this is a pain for astronomers trying to take clear images of these objects!