The period of a satellite is the primary way that the mass of planets is determined. The equation used for this calculation uses the fact that gravity of the planet provides the centripetal force to keep the satellite in orbit. The distance from the Earth to the Moon is 3.8 x 108 m and the period of the moon is approximately 27.3 days. Use the formula derived for this purpose to calculate the mass of the Earth.2 r3 )/(G T2 ) where T is the period of the moons orbit rotation.
To calculate the mass of the Earth using the given equation, we can plug in the known values and solve for the mass of the Earth. The equation is:
M = (4π^2 * r^3) / (G * T^2)
Where:
M = Mass of the Earth
π = Pi (approximately 3.14159)
r = Distance from the Earth to the Moon (3.8 x 10^8 meters)
G = Gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
T = Period of the Moon's orbit (27.3 days)
First, we need to convert the period of the Moon's orbit from days to seconds.
T_seconds = T_days * 24 hours/day * 60 minutes/hour * 60 seconds/minute
T_seconds = 27.3 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute
T_seconds = 27.3 * 24 * 60 * 60 seconds
Next, we substitute the known values into the equation:
M = (4π^2 * (3.8 x 10^8)^3) / (6.67430 x 10^-11 * (27.3 * 24 * 60 * 60)^2)
Calculating this expression will give us the mass of the Earth.