If the mass of the Sun were to double its current value, with Earth maintaining its same orbit, the time interval of one Earth year would

Question

a. remain the same 

b. decrease by a factor of √2 

c. increase by a factor of √2 

d. increase by a factor of 2 

e. decrease by a factor of 2 

Answer 1

GMm/r² = mv²/r, after reducing we have v² = GM/r. On the other hand v = 2πr/T, where T is period

4π²r²/T² = GM/r, T = (4π²r³/GM)^1/2_.

If mass of Sun became 2M then period T_new = (4π²r³/2GM)^1/2

So, T_new/T = 1/2^1/2; Tnew = T/√2. Period decrease by factor √2.

Answer is b.^