Answer :
Answer:
M = 1.38 10⁵⁹ kg
Explanation:
For this problem we will use the law of universal gravitation
F = G m₁ m₂ / r²
Where G is the gravitation constant you are value 6.67 10⁻¹¹ N m2 / kg2, m are the masses and r the distance
In this case the mass of the planet is m = 3.0 10²³ kg and the mass of the start is M
Let's write Newton's second law
F = m a
The acceleration is centripetal
a = v² / r
The speed module is constant, so we can use the kinematic relationship
v = d / t
The distance remembered is the length of the circular orbit and the time in this case is called the period
d = 2π r
a = 2π r / T
Let's replace Newton's second law
G m M / r² = m (4π² r² / T²) / r
G M = 4 π² r³ / T²
M = 4 π² r³ / T² G
Let's calculate
M = 4 π² (3.0 10²³)³ / (3.4 10¹¹)² 6.67 10⁻¹¹
M = 13.82 10⁵⁸ kg
M = 1.38 10⁵⁹ kg