Question

Two planets P1 and P2 orbit around a star S in circular orbits with speeds v1 = 42.6 km/s, and v2 = 56.0 km/s respectively.

(a) If the period of the first planet P1 is 780 years what is the mass, in kg, of the star it orbits around?

(b) Determine the orbital period, in years, of P2.

Answer 1

(a) ; let

• mass of S = M
• mass of P₁ & P₂ = m₁ & m₂
• for part (a)
• 
• 
• ...............(1)
• now r₁ = ?
• given that Time period for P₁ = T = 780 yr , v = 42.6 km/s = 42.6 10³ m/s
• 
• 
• putting in equation 1 we get
• 
• ............................................(2)
• now putting the values
• T₁ = 780 yr = 780 12 30 24 60 60 s = 2.5 10¹¹ s
• 
• 
• 
• .............(Answer)

(b) T₂ = ?

• using equation (2)
• 
• 
• puttimg the values
• 
• 
• 
• 
• .......................(answer)