Final answer:
To find the mass of the planet, we can use Newton's law of gravitation and the equations for centripetal force. By equating the gravitational force to the centripetal force, we can eliminate the mass of the satellite and solve for the mass of the planet. Plugging in the given values, we can calculate the mass of the planet.
Step-by-step explanation:
To find the mass of the planet, we can use Newton's law of gravitation. The satellite is in a circular orbit around the planet, so we can equate the gravitational force to the centripetal force. The gravitational force is given by the equation F = (G * m₁ * m₂) / r², where G is the gravitational constant, m₁ is the mass of the planet, m₂ is the mass of the satellite, and r is the radius of the orbit. The centripetal force is given by the equation F = m₂ * v² / r, where v is the velocity of the satellite. Since the satellite is in a circular orbit, we can also relate the velocity to the period of the orbit using the equation v = (2 * π * r) / T, where T is the period of the orbit.
By equating the gravitational force and the centripetal force, we can eliminate the mass of the satellite and solve for the mass of the planet. The final equation will be: m₁ = (v² * r) / (G * T²).
Plugging in the given values, we get: m₁ = ((2 * π * r) / T)² * r / (G * T²) = (4 * π² * r³) / (G * T²).
Substituting the values of r = 9,000,000 meters and T = 10,000 seconds, and using the value of G = 6.67430 × 10^-11 N m²/kg², we can calculate the mass of the planet.