B.)A Waning Crescent moon occurs when the Moon is between the Earth and the Sun, just BEFORE it reaches New Moon Phase.
A Waxing Gibbous moon occurs when the Earth is between the Moon and the Sun, just BEFORE it reaches Full Moon Phase.
The length of the year (i.e. Earth's orbital period) is given
by Kepler's third law:
(semimajor axis in AU)3 = (period in years)2
A3 = P2
if A=1/2, then A3 =1/8. So P2 = 1/8, and P=the square root of 0.125 = 0.35 years
It would take only 0.35 years for Earth to orbit. In fact, a "year" would then be defined as 0.35 of our current years. So, after 35 of our years had passed, you would celebrate your 100th birthday!
There would also be changes to Earth's temperature: it would be much hotter as Earth would receive 4 times more light (inverse square law). The seasons would also last 2.8 times shorter. Winter would not be very cold, in either hemisphere.
Kepler's 2nd law says that a planet sweeps through equal areas in equal times. To do this a planet must move fastest when it is closest to the Sun, (perihelion) and slowest when farthest from the Sun (aphelion) So on July. 4th, when Earth reaches aphelion, it is moving the slowest, and on Jan 4th, when it reaches perihelion, it is moving fastest, as predicted by Kepler's 2nd law.
A planet or asteroid's semi major axis is its "average distance from the Sun". This is a measure of how big its orbit is. It is related to the Period via Kepler's Third Law (see above). In this case:
(period in years)2 = 46.42 = 2153
So, (a)3 = 2153
The semi-major axis, a, is thus the cube root of: 2153
Looking for an integer whose cube is about 2153 we might guess: 12 3 = 1728. (too low) while 13 3 = 2197 is high, but pretty close. The semimajor axis of this asteroid's orbit is 12.9 AU.
B.) Both of these measurements are much smaller than a grain of sand, which has diameter of 0.2 millimeters (mm) or 200 micrometers. Each micrometer = 1000 nanometers, somewhat larger than 1 wave of red light. So a sand grain is about 200-500 times larger than red light and almost 1000 times smaller than violet light! This website has some nice perspectives: Scale of the Universe
The two main types of radiation which reach Earth are radio waves and visible light. Almost all telescopes on Earth are designed to collected one of these two types. Some Ultraviolet light leaks through Earth's atmosphere to the surface, especially where the Ozone Layer is weakened. While greenhouse gasses absorb and block much of the Infrared light, small amount also leaks through.
Light Gathering Power is proportional to the Area of the light collecting surface (eg the mirrors). Area is proportional to the diameter squared. A = PI * r2 = 3.14 * (d/2)2
The Palomar telescope is 5 meters, while the human
eye is 5 mm or 5 x 10-3 m.
So Palomar's light gathering power is greater by a factor of: 52/0.0052 = 106 = 1,000,000. The 5m Palomar telescope can see stars one million times fainter than the human eye.