Q58P - University Physics with Modern Physics

Question

 .. It has been proposed to use an array of infrared telescopes spread over thousands of kilometers of space to observeplanets orbiting other stars. Consider such an array that has an effective diameter of  and observes infrared radiation at a wavelength of . If it is used to observe a planet orbiting the star Virginis, which is   from our solar system, what is the size of the smallest details that the array might resolve on the planet? How does this compare to the diameter of the planet, which is assumed to be similar to that of Jupiter ? (Although the planet of  Virginis is thought to be at least  more massive than Jupiter, its radius is probably not too different from that of Jupiter. Such large planets are thought to be composed primarily of gases, not rocky material, and hence can be greatly compressed by the mutual gravitational attraction of different parts of the planet.)

Step-by-Step Solution

Answer

the size of the smallest details on the planet is 1130km 

Step 1 : About Gravitational acceleration of jupiter

The gravity on Jupiter is greater than the gravity on Earth because Jupiter is more massive. Although Jupiter is a great deal larger in size, its surface gravity is just 2.4 times that of the surface gravity of Earth.

Step 2 : Determine the size of the smallest details on the planets

IDENTIFY and SET UP:

This problem concerns resolving power of an array of infrared telescopes- We use Eq- (36.17) to find the angular separation 0

of the smallest (resolvable) details on the planet of 70 Vlrginis- The distance betWeen the planet and our solar system is 

 

planet is w = L0, which is the ratio 10 / d of the diameter of the planet (the diameter the planet of 70 Virginis is -

EXECUTE:

From Eq- (36.17) the angular separation 0 of the smallest details on the planet of 70 Virginis is

 

Hence, the size of the smallest details on the planet is

 

The ratio of the size of the smallest details on the planet to the diameter of the planet is

 

 

EVALUATE:

The large aperture diameter of very large telescopes minimises diffraction effects. The effective diameter of a telescope can

be increased by using arrays of smaller telescopes. The array of telescopes in our problem gives a limit of resolution of  at an infrared wavelength of If your eye had this angular resolution you could read the  line on an 

eye chart on the moon from where you are on the earth!

Therefore the size of the smallest details on the planet is 1130km