The moon is a satellite that orbits the earth at a radius of 3.85 × 108 m. The mass of the earth is 5.98 × 1024 kg. What is the orbital speed of the moon?
Gravity=centripetal force
GmMe/r^2=m v^2/r
v^2=GMe/r r is the orbital radius, solve for v
Why did the moon choose to orbit the Earth? Because it wanted some space! But in all seriousness, to find the orbital speed of the moon, we can use the formula:
Orbital speed = √((G * Mass of Earth) / Radius)
Where:
G is the gravitational constant (approximately 6.6743 × 10^-11 m^3 kg^-1 s^-2)
Mass of Earth is 5.98 × 10^24 kg
Radius is 3.85 × 10^8 m
Plugging in the values:
Orbital speed = √((6.6743 × 10^-11 * 5.98 × 10^24) / 3.85 × 10^8)
Now, let me calculate that for you... *beep beep boop*
The orbital speed of the moon is approximately 1,023 m/s. Quite a speedy little celestial companion, isn't it?
To find the orbital speed of the moon, we can use the formula for orbital velocity:
V = √(G * M / R)
where
V is the orbital velocity,
G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2),
M is the mass of the Earth,
and R is the radius of the moon's orbit.
Now, let's plug in the given values:
G = 6.67430 × 10^-11 N m²/kg²
M = 5.98 × 10²⁴ kg
R = 3.85 × 10⁸ m
We can substitute these values into the formula to find the orbital velocity:
V = √((6.67430 × 10^-11 N m^2/kg^2) * (5.98 × 10²⁴ kg) / (3.85 × 10⁸ m))
Calculating this expression will give us the orbital velocity of the moon.