The moon has a mass of 7.4 x 10^22 kg and completes an orbit of radius 3.8x10^8 m about every 28 days. The Earth has a mass of 6 x 10^24 kg and completes an orbit of radius 1.5 x 10^11 m every year.
What is the speed of the Moon in its orbit? Answer in units of m/s.
What is the kinetic energy of the Moon in orbit? Answer in units of J.
What is the kinetic energy of the Earth? Answer in units of J.
2007-04-11 10:23:08 · 4 answers · asked by p.b 1 in Science & Mathematics ➔ Physics
I assume you're not expected to calculate anything but circular orbits (that would require more information than you were given). The formula for the circumference of a circle is just pi times diameter, or 2 pi r. Kinetic energy, of course, is 1/2 m v^2.
Starting with the Moon, that's 2 x 3.14 x 3.8 x 10^8 m = 2.39 x 10^9 m. It has 28 days, which is 28 d x 24 hr/d x 60 min/hr x 60 s/min = 2,419,200 seconds. So in m/s that's 986 m/s (about 2,000 miles per hour).
Since we took the trouble to put it all in standard units (meters, seconds, and kg), it's easy to figure KE in joules: 0.5 x 7.4 x 10^22 x 986^2 = 3.6 x 10^28 J. You can see that most of that comes from the Moon just being really massive, not its speed.
To figure the KE of Earth, we're going to need to know its velocity too. And in the same way. 2 x 3.14 x 1.5 x 10^11 = 9.42 x 10^11 m. It has 365.25 days (leap year is every four years) so that's 365.25 d x 24 hr/d x 60 min/hr x 60 s/min = 31,557,600 seconds. That's 29,865 m/s (about 30 times faster!).
KE is also the same way. 0.5 x 6 x 10^24 x 29865^2 = 2.7 x 10^33 J. Still mostly from mass.
And if I can take a moment to point out something interesting... the Earth is about 100 times heavier than the Moon but moving 30 times faster. Even though the weight is the biggest part of each body's KE, most of the DIFFERENCE in KEs is actually coming from the velocity! If Earth was moving the same speed as the Moon, its weight would give it 100 times the KE. But if it weighed the same as the Moon, its speed would give it 900 times (30^2) the KE. Velocity is having a bigger effect! Given the square thing, maybe that's not too surprising.
2007-04-11 10:38:41 · answer #1 · answered by Doctor Why 7 · 0⤊ 0⤋
about 2000/mph
2014-11-15 01:57:06 · answer #2 · answered by Pappa 1 · 1⤊ 0⤋
Real fast!
2007-04-11 10:26:46 · answer #3 · answered by rico3151 6 · 0⤊ 2⤋
do your own homework
an its slow
2007-04-11 10:26:54 · answer #4 · answered by scenicgg 2 · 0⤊ 2⤋