Question

A star of mass 8.5x1030 kg has a single planet of mass 6.2x1023 kg. The star and planet each orbit around the center of mass of the star-planet system. If the star and planet are separated by a distance of 4.4x1012 m from each other, what is the radius of the star’s orbit? a) 103 km b) 175 km c) 248 km d) 321 km e) 394 km

Answer 1

If the star and planet are separated by a distance from each other, then radius of star’s orbit will be given as -

we know that, M_total X = (m_s x₁ + m_p x₂)

X = (m_s x₁ + m_p x₂) / M_total

X = (m_s x₁ + m_p x₂) / (m_s + m_p)

where, m_s = mass of star = 8.5 x 10³⁰ kg

m_p = mass of planet = 6.2 x 10²³ kg

x₁ = distance from center to star = 0

x₂ = distance from center to planet = 4.4 x 10¹² m

then, we get

X = [(8.5 x 10³⁰ kg) (0 m) + (6.2 x 10²³ kg) (4.4 x 10¹² m)] / [(8.5 x 10³⁰ kg) + (6.2 x 10²³ kg)]

X = [(2.728 x 10³⁶ kg.m) / (8.50 x 10³⁰ kg)]

X = 320941.1 m

converting m into km :

X = 320.9 km

X 321 km

Option (d) : it will be correct.