Measurement of distance of Heavenly Bodies

 

1.    

1.  Parallax Method: In this method, a planet P is observed simultaneously from two distant place A and B. The angle Ɵ (= angle APB) is measured.

                                 

              

           Ɵ = AB/AP

           AP = AB/Ɵ   

           D = b/Ɵ

     If Ɵ is in radian and AB is in A.U, then distance AP of the planet from the earth will be in A.U.

           1 A.U = 1.496x 10¹¹ m.

2. Radio – Echo Method: A radio signal is sent towards the planet and the reflected signal is received. The time interval between the transmission and reception of the signal is accurately determined. If the time interval is ‘t’ seconds, then distance ‘S’ of the planet from earth is given by:

 

     S = ct/2       where c = 3x10⁸ ms^-1

 

3. Copernicus Method: The distance of inferior planet from earth is measured. In this method, the sun is considered at the centre of the solar system and the planets orbit around the sun in circular paths. Let the inferior planet P and the earth E revolves around the sun in circular orbits of radii r₁ and r respectively.

                  

   

              r = sun - earth distance = 1 A.U

              r₁ = distance of the planet from sun

              r₂ = distance of the planet from earth  

               

                r₁ = rsin€

                r₂ = rcos€

 The value of can be determined by radio-echo method and is given by:

                  r₂ = ct/2

         Since c = 3x10

                   t = known

                    r = 1 A.U

Therefore the value of € and r₁ can be calculated.

 

4. Kepler’s Law: according to Kepler’s third law, the ratio of squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distance from the sun. Thus if T₁ and T₂ represent the time needed for one revolution about the sun of two planets 1 and 2. Also r₁ and r₂ represent their average distance from the sun, then,

 

                  (T₁)² / (T₂)² = (r₁)³ / (r₂)³

 

If distance r₁ (i.e average distance of planet 1 from the sun) and the periods T₁ and T₂ are known, then distance r₂ (i.e average distance of planet 2 from the sun) can be determined.