Given that the Earth’s mass is 5.98X10^24kg, and the radius of the moon’s orbit around the Earth is approximately 3.85X10^8m, calculate:
a) The speed with which the moon orbits the Earth.
b) The Orbital period of the moon in seconds.
c) The centripetal acceleration of the moon in its orbit around the Earth.
m v^2/R = G m M /R^2
so
v^2 = G M / R = 6.67*10^-11 * 5.98*10^24 / 3.85 * 10^8
a) take the square root of v^2
b) Period time * v = 2 pi R
c) v^2/R
Thank you this was helpful
To calculate the answers to these questions, we can use some basic physics formulas. Here's how you can find the answers:
a) The speed with which the moon orbits the Earth can be determined using the formula for the circumference of a circle (C = 2πr) and the formula for the speed of an object in uniform circular motion (v = C / T), where C is the circumference of the orbit and T is the orbital period.
First, we need to find the circumference of the moon's orbit. The radius of the moon's orbit around the Earth is given as approximately 3.85X10^8 m. Using the circumference formula, we can calculate the circumference (C) as follows:
C = 2πr
C = 2π(3.85X10^8)
C ≈ 2.42X10^9 m
Now we can use the formula for the speed of an object in uniform circular motion to calculate the moon's speed (v):
v = C / T
Since we don't have the orbital period (T) yet, we'll move to the next question to calculate it.
b) The orbital period of the moon in seconds can be determined using the formula for the period of an object in uniform circular motion (T = 2πr / v), where r is the radius of the orbit and v is the speed of the moon.
We already have the radius of the moon's orbit (3.85X10^8 m), and we need to find the speed of the moon (v). To calculate the speed, we'll use the answer from the previous question.
c) The centripetal acceleration of the moon in its orbit around the Earth can be determined using the formula for centripetal acceleration (a = v^2 / r), where v is the speed of the moon and r is the radius of the orbit.
Again, we will use the values we have already calculated in the previous answers to solve for the centripetal acceleration.
Now, let's calculate the answers step by step:
a) The speed with which the moon orbits the Earth:
v = C / T
v = 2.42X10^9 / T
b) The orbital period of the moon in seconds:
T = 2πr / v
T = 2π(3.85X10^8) / v
c) The centripetal acceleration of the moon in its orbit around the Earth:
a = v^2 / r
a = v^2 / (3.85X10^8)
Plug in the values we have and solve for the answers.