Explain the significance of Kepler’s laws for planetary motion. Name and describe the work of at least 2 other scientists who contributed to the theory of gravity which helped explain Kepler’s observations.

A train, travelling with velocity v = 0.8c, enters a tunnel. The train has proper length 100m and the tunnel has proper length 80m. When the center of the train coincides with the center of the tunnel, two gates located at either end of the tunnel come crashing down. The three events (the center of the train reaching the center of the tunnel, the front gate closing and the rear gate closing) occur simultaneously in the stationary reference frame. a) Describe the order of the events in the train’s reference frame. b) Where are the two ends of the train (from the point of view of each reference frame) when each of the events occurs?

Explain at least three characteristics of the Sun that contribute to its solar activity. (Please answer in your own words and type answer, thanks).

Consider 100 g of aluminum (p = 2700 kg/m^3) and 100 g of lead (p = 11,300 kg/m^3). a. Which as a greater volume? Show why this is true mathematically. b. Which contains a larger number of moles? Show why this is true mathematically. c. Which contains more atoms? Show why this is true mathematically.

A 685-liter oxygen tank contains oxygen gas at 20℃ . When the tank is full, the pressure gauge reads 3000 psi. a. How many oxygen molecules are in the cylinder? b. What is the number density of the oxygen? c. How much does the oxygen in the tank weigh?

2. A 15-MΩ resistor and a 48-nF capacitor get connected in series to a 15-V battery. a. How long will it be until the capacitor is “fully” charged? b. If the battery is then disconnected from the circuit, how long will it be until the capacitor’s voltage is 9.0 V? What is the charge of the capacitor at that moment? c. If we’d like the capacitor’s voltage in this circuit to decrease from 15-V to 9.0-V in 1.5 seconds after the battery gets disconnected, how should the capacitance of the capacitor change (increase or decrease, and by how much)?

Define and describe the following, if you can, site some example/simple analogy.

1. Wave-particle duality of light
2. Energy quantization
3. Black body
4. Ultraviolet catastrophe

The LIGO experiment, which historically detected gravitational waves for the first time in September 2015, uses a pair of highly sensitive Michelson interferometers. These have arms that are 4.00 km long and use powerful Nd:Yag lasers with 1064 nm wavelength. The beams traverse the arms both ways 280 times before recombining, which effectively lengthens the arm length to 1120 km. The devices are tuned so that the beams destructively interfere when they recombine if no gravitational wave is present. (a) The beam has a power of 100 kW, concentrated into an area of a square centimeter. Calculate the amplitude of the electric field in the beam. (b) LIGO can detect a gravitational wave that temporarily lengthens one arm by the minuscule amount of 10^-18 m! When this happens, the beams combine with a phase difference of π+δ. Estimate the shift δ in radians. Note that the phase difference accumulates during both traversals of each round trip. (c) Use Eq. (35.7)to estimate the sensitivity of the photodetector in terms of the minimal electric field strength needed to detect a gravitational wave.

Eqn 35.7

E_p = 2E |cos (theta/2) |

explanation pleasssssee.

Thanks in advance!

Explain the following terms: (1) Spontaneous emission (2) Stimulated emission (3) Metastable state and (4) Population inversion.

The Federation space cruiser Execrable is floating in Federation territory at rest rel-

ative to the border of Klingon space, which is 6.0 min away in the +x direction.

Suddenly, a Klingon warship flies past the cruiser in the direction of the border at

speed B = 3/5. Call this event A and let it define time zero in both the Klingon and

cruiser reference frames. At tB = 5.0 min according to the cruiser clock, the Klingons

emit a parting phasor blast (event B) that travels at the speed of light back to the

cruiser. The phasor blast hits the cruiser and disables it (event C), and shortly later

(according to cruiser radar measurements) the Klingons cross the border into Klingon

territory (event D).

a. Draw a 2-system space-time diagram of the situation, taking the cruiser to de_ne

the stationary frame and the Klingon to define the moving frame. Draw and

label the world-lines of the cruiser, the Klingon territory boundry, the Klingon

warship, and the phasor blast. Draw and label events A,B,C,D as points on

your diagram.

b. When does the phasor blast hit, and when do the Klingons pass into their own territory, according to clocks in the cruiser's frame? Read these events directly

from the diagram.

c. The Klingon-Federation Treaty states that it is illegal for a Klingon ship in Fed-

eration territory to damage Federation property. When the case comes up in

Interstellar court, the Klingons claim that they are within the letter of the law,

since according to measurements made in their reference frame, the damage to

the Execrable occurred after they crossed back into Klingon territory-hence

they were not in Federation territory at the time. Did event C really happen

after event D in the Klingon's frame? Check your answer with the Lorentz Transformation equations.

1. (a) Explain HGL and EGL with figure for different condition (b) discuss Poiseuille equation.

A plane has a heading relative to the air of speed 121 m/s and direction 23.5° East of North. The air is moving relative to the ground with wind speed 49 m/s and direction 33.4° North of West.

a) If the plane is flying at an altitude of 5560 m and drops a package directly above a city, what distance away from the city will the package land?

(b) If the plane begins a journey from one city to another located 195 km away in these wind condition, then how far from their destination will the plane be once they have traveled the amount of time it would take to get to the city without wind? Note that the straight path between the cities is the exact heading of the plane relative to the air.

5. The difference between a solar day on Earth and a sidereal day is about 4 minutes. If the Earth orbited the Sun at 0.5 AU, what would the difference be? (Assume the Earth’s orbit is circular and the rotation rate is the same.)

Please explain clearly and provide explanations for how you solve this so I can learn. Thank you.

1. Suppose we discover a new stealth planet that orbits the Sun in the same plane and the same direction as the known planets. The planet has a circular orbit, orbits twice as far from the Sun as Earth. The equator of this planet is perfectly aligned with its orbital plane. Answer the following questions about the new planets. Show your work for full credit.

   1. How long is a year on the new planet?

   2. Does the new planet have seasons?

   3. How quickly does it orbit (km/s)

2. In 1 billion years, predict how the following quantities would be different from their current values. Answers should be qualitative (e.g. shorter, longer, no change) but you must explain your reasoning for full credit. [15 points]

   1. Earth-moon separation

   2. Length of the day

   3. Length of the month

   4. The height of ocean tides.

   5. Frequency of eclipses