Good turnout and conversation at EV Breakfast yesterday, Aug 5. In addition to all the discussion about Model 3, there was quite a bit of interest in the Eclipse Mon Aug 21. Jason is going to OR, Sparky, Mark Z, and myself are going to ID. May we all have good clear weather, clouds not allowed.
At the previous breakfast, talking about the eclipse, some opinion was expressed that the Earth's axial rotation was the dominant factor in the speed that the Moon's shadow moves across the country. I was skeptical, so I put on my physicist's hat. My calculations are rough, taking some approximations to keep math simple and avoid 3D vectors which are hard to visualize:
R, lunar orbital radius = .238 10^6 miles
2 Pi R, orbital circumference, = 1.50 10^6 miles
We choose a reference frame centered on the Earth-Moon system, so we can ignore their common motion about the sun, which is almost 100 10^6 miles/hr relative to the Sun. One Lunar month, new Full Moon to next Full Moon, is called the Synodic Period.
T = (Lunar Synodic Period = 29.5 days) * (30 * 24 = 720 hrs/mo) = 708 hrs
Lunar contribution to shadow speed = 2 Pi R/T = 2,120 mi/hr.
Earth rotational speed at Equator = 24.5 10^3 miles/24 hrs = 1,037 mph.
If we look down on the system at Eclipse from above the North pole, we see the Sun, Moon and Earth all in a line, with both the Moon's orbital motion and the Earth's rotation counterclockwise. Note, at this time, the Earth's spin and Moon's motion are in the same approximate direction, so the Earth's spin reduces the speed at which the Moon's shadow moves across the surface. We apply some correction factors to both speeds:
Because the Earth is farther from the Sun than the Moon at a New Moon, the speed of the Lunar shadow is amplified by the ratio of their distances (in 10^6 miles):
(98 + .25)/98 but we can ignore this.
The local latitude determines how far one is away from the Earth's axis, and hence how much speed you have from the spin. It does not affect the Lunar speed. Latitude(Rexburg, ID) = 44 deg,
Cos(44 deg) = .72
Finally, there is the local time of day. If the sun is not directly overhead, the shadow will be elongated by its projection on the surface, an enlargement of 1/Cos(angle from zenith). The speed of the shadow along the surface will be affected by east-west tilt, but not north-south tilt.
In Idaho, Eclipse Totality is at 11:30 am MDT, 10:30 MST, 1.5 hrs before Noon.
Cos( 360 * (1.5/24) = 22 deg ) = .92
This factor reduces the spin speed while amplifying the lunar speed.
Putting these all together, we have:
Net speed of shadow measured along Earth's surface =
Moon's contribution - Earth spin contribution
= (2,120/Cos(22)) - (1,037 * Cos(44) * Cos(22)) =
2304 - 687 = 1620 mph
Again, this is only approximate, since the angles interact somewhat, but it gives the idea.
LEAF Ocean Blue SL, "100 % Electric" decals, Delivered June 3, 2011
Sold June 2014 27K miles, 18% capacity loss, 1 bar, 5.0 mi/kWh.
Solar 4.6 KW DC with both string and micro-inverters.