Moon is a natural satellite of the Earth, circling it with period (time of one revolution), T = 27,3 days. Radius of Moon’s orbit = 384,000 km. Find the acceleration of the Moon toward the Earth.
a= w^2*r= (2PI/period)^2 * r
change the period in days to seconds.
To find the acceleration of the Moon toward the Earth, we can use Newton's law of universal gravitation, which states that the force of gravity between two objects is given by:
F = G * (m1 * m2) / r^2
where:
F is the force of gravity,
G is the gravitational constant (approximately 6.67 x 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the two objects (in this case, the Earth and the Moon),
r is the distance between the centers of the two objects.
In this case, we want to find the acceleration, which is the force per unit mass (a = F/m). Rearranging the equation, we can solve for acceleration:
a = (G * (m1 * m2) / r^2) / m
Now, let's plug in the values given:
T = 27.3 days = 27.3 * 24 * 60 * 60 s (convert to seconds)
r = 384,000 km = 384,000 * 1000 m (convert to meters)
The mass of the Earth is approximately 5.97 x 10^24 kg, and the mass of the Moon is approximately 7.35 x 10^22 kg.
Plugging in these values, we can calculate the acceleration:
a = (G * (m1 * m2) / r^2) / m
a = (6.67 x 10^-11 * (5.97 x 10^24 * 7.35 x 10^22) / (384,000,000)^2) / (7.35 x 10^22)
Simplifying the expression, we can calculate the value of 'a'.