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Using planet Earth's mass of 5.972×10²⁴ kg, the period (in minutes) of a satellite orbiting the planet with a radius of 10,732.000 km is:

User Joe K
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Final answer:

The period of a satellite orbiting Earth can be calculated using Kepler's third law and the formula T^2 = (4π^2/GM) * r^3, where T is the period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the planet. Using the given information, we can calculate the period of the satellite orbiting Earth.

Step-by-step explanation:

The period of a satellite orbiting a planet can be calculated using Kepler's third law, which states that the period is related to the radius of the orbit. The formula is T^2 = (4π^2/GM) * r^3, where T is the period, r is the radius of the orbit, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), and M is the mass of the planet. Given the mass of Earth (5.972×10²⁴ kg) and the radius of the satellite's orbit (10,732.000 km), we can calculate the period as follows:

T^2 = (4π^2/(6.67 x 10^-11 Nm^2/kg^2)(5.972×10²⁴ kg) * (10,732.000 km)^3

T^2 = (4π^2/(6.67 x 10^-11 Nm^2/kg^2)(5.972×10²⁴ kg) * (10,732.000 km)^3

T^2 ≈ 3.974 * 10^9 minutes^2

T ≈ 63002.47 minutes

User Cnnr
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