Einstein’s Theory of Relativity

1. The Sun’s radiation is derived by fusing hydrogen into helium, which converts mass to energy. How many years does it take the Sun to reduce its mass by an amount equal to the mass of Earth? Show how you got your answer.

(A) 1 million years

(B) 5 million years

(C) 25 million years

(D) 45 million years

(E) 90 million years

Calculations

In this question Einstein’s equation E = mC2 is used

Where: E = 3.8 x 1026 Watts (Energy produced by the sun)

            C = 3.0 x 108 m/s velocity of energy

            m = Mass converted per second.

Substituting the values in the equation we get;

3.8 x 1026 = m x (3.0 x 108)2

m =  = 4.222 x 109 kg/s

From Rose (2017) astronomy paper the mass of Earth is estimated at 5.972 x 1024kg. Therefore, the time taken by the Sun to reduce its mass by an amount equal to the mass of Earth would be:

Time (seconds) =  = 1.4145 x 1015 s

Time (years) =  = 4.485 x 107 years

                                           ≈ 45 million years.

2. Some of the stars visible tonight are the same as our Sun, but they look very faint because they are much farther away. If a star like our Sun is 10 parsecs from Earth, how bright is it compared to our Sun? Show how you got your answer.

(A) 10-7

x Sun’s brightness

(B) 10-9

x Sun’s brightness

(C) 10-11

x Sun’s brightness

(D) 10-13

x Sun’s brightness

(E) 10-15

x Sun’s brightness

Calculation

Since the star is like the sun its brightness will be equal to that of the sun moved to 10 parsecs from the earth.

Therefore, brightness of star (bstar) = Brightness of sun at distance of 10 parsecs (bsun10)

Using the relationship b =  

Where: b = brightness

            L = luminosity of the sun

            d = distance from the earth in parsecs.

Now, bsun = ,  where, d = 4.848 x 10-6 parsecs

bsun

=  

However, the bstar = bsun10

                                        bsun10

=

Implying  =  = 2.35 x 10-13

Therefore, the star is 10-13 x Sun’s brightness.

References

Rose, S. (2017). Modeling the Earth-Moon Distance for Different Theories of Gravitation.