Find the orbital period of a satellite moving around the Moon near its surface if the average density

| September 11, 2021 | education

Find the orbital period of a satellite moving around the Moon near its surface if the average density of the Moon is 3300 kg / m ^ 3.

ρ = 3300 kg / m ^ 3.
R = 1,737,000 m.
G = 6.67 * 10 ^ -11 N * m ^ 2 / kg ^ 2.
T – ?
The satellite’s orbital period T is the time of one complete revolution of the satellite around the Moon.
T = 2 * P * R / V.
The satellite is affected by the force of gravitational attraction F = G * m * M / R ^ 2.
Let’s write 2 Newton’s law for the satellite: m * a = G * m * M / R ^ 2.
Centripetal acceleration a is determined by the formula: a = V ^ 2 / R.
m * V ^ 2 / R = G * m * M / R ^ 2.
V ^ 2 = G * M / R.
V = √ (G * M / R).
M = v * ρ = 4 * P * R ^ 3 * ρ / 3.
V = √ (G * 4 * P * R ^ 3 * ρ / 3 * R) = √ (G * 4 * P * R ^ 2 * ρ / 3) = 2 * R * √ (G * P * ρ / 3).
T = P / √ (G * P * ρ / 3).
T = 3.14 / √ (6.67 * 10 ^ -11 N * m ^ 2 / kg ^ 2 * 3.14 * 3300 kg / m ^ 3/3) = 6500 s.
Answer: the orbital period of the satellite was T = 6500 s.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.