Answer:
2.65×10⁹ seconds, or 84.1 Earth years
Step-by-step explanation:
Don't forget to convert km to m before doing calculations.
Acceleration due to gravity = centripetal acceleration
GM / r² = v² / r
v² = GM / r
v² = (6.67×10⁻¹¹ m³/kg/s²) (1.99×10³⁰ kg) / (2.87×10¹² m)
v² = 4.62×10⁷ m²/s²
v = 6.80×10³ m/s
Period = circumference / velocity
T = 2πr / v
T = 2π (2.87×10¹² m) / (6.80×10³ m/s)
T = 2.65×10⁹ s
Converting to other units:
T = 7.37×10⁵ hr
T = 3.07×10⁴ days
T = 84.1 years