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Orbits

An orbit is the gravitationally curved path of an object around a point in space. The current understanding of orbital motion is from Albert Einstein’s general theory of relativity. This accounts for gravity due to curvature of space-time which orbits following geodesics.

There are some common ways to understand orbits:

- As objects move sideways, it falls toward the central body. However, it moves so quickly that the central body will curve away beneath it.
- A force, like gravity, pulls the object into a curved path as it attempts to fly off in a straight line.
- As the object moves tangentially, it falls toward the central body. However, it has enough tangential velocity to miss the orbited object and will continue falling indefinitely.

Our solar system there is many things which orbit the Sun, planets, dwarf planets, asteroids, comets and space debris. The Sun is called the barycenter in elliptical orbits. Some bodies, such as comets, are not gravitationally bound to the star and therefore are not considered part of the star’s planetary system.

Orbit of Comets

A comet is observed at a distance "D" AU from the Sun and is moving tangentially with a speed "S" times the Earth's average orbital speed. Show that the orbit will be a hyperbola if DS^2>2, a parabola for DS^2=2, or an ellipse for DS^2<2. Thank you very much for your help!

Bohr Atom Relativity

The Bohr atom derived from de Broglie'.r relation. Here is another development of Bohr's results for hydrogen. based directly onthe de Broglie relation. If a de Broglie wavelength can be associated with an electron in orbit. then it seems reasonable to suppose that the circumference of an orbit be equal to an integral number of

Quantum Numbers & Electron Configurations

Would highly appreciate detailed work shown/ explanation on how you got your answer. This entire chapter makes little sense to me. (P.S. If answers are hand written, please do not write in cursive for I have a difficult time reading it) 1. What is the maximum number of electrons that can occupy each of the following subshells

The gravitational attraction between a planet and a star

A star has a planet held in orbit by gravitational attraction. a) if the mass of the star was doubled, what effect would this have on the gravitational attraction between the star and its planet? Explain. b) If the distance between the star and the planet were three times as great, what effect would this have on their gr

Charged Particle in Magnetic Field. House Wiring.

1. A magnetic field can change the direction of motion of a charged particle yet in doing so it has done no work on the particle. Why? Give another example of a force causing an object to change direction without doing any work on it. 2. Explain why it takes more fuel for a spacecraft to travel to the Moon from Earth than it ta

Relative Initial Speed Calculated

Vanguard 1, launched in 1958, is the oldest human artefact/satellite in orbit. It weighs 1.47 kg and orbits the Earth every 134.2 minutes. At its closest distance it is 654 km from the surface of the Earth. Assume that it is in a circular orbit and due to a collision with some space junk it loses 20% of its velocity. a) Calc

Burnside Counting, Isometry

1) Let E1, E2, E3, and E4 denote, respectively, the edges ab, bc, cd, and da of the square in the figure below. Write the permutation induced on {E1, E2, E3, E4} by each isometry (symmetry) of the square. [Example: ρH ↦ (E1E3).] Does the symmetry group of the square act faithfully on {E1, E2, E3, E4} 2) The group G = 〈(

Calculating the Earth's travel distance

What arc length does the Earth travel in a three-month period in its nearly circular orbit around the Sun? (The radius of the Earth's orbit is 1.5 x 10^11 m.) Please provide a detailed explanation.

Solving a Physics Problem

The hydrogen atom consists of a proton of mass 1.67 x 10 -27 kg and an orbiting electron of mass 9.11 x 10-31 kg. In one of its orbits, the electron is 5.3 x 10-11 m from the proton. What is the mutual attractive force of gravitation between the electron and proton? Please provide detailed explanation and reflect your wor

Group Operations

The symmetric group Sâ?? operates on two sets U and V of order 3. Decompose the product set UÃ?V into orbits for the diagonal action g(u,v)=(gu,gv), when a) the operations on U and V are transitive, b) the operation on U is transitive, the orbits for the operation on V are {vâ?} and {vâ??,vâ??}.

Electron Velocity Problem

Find the velocity an electron in a circular orbit would require at a distance of 2.098 Angstroms from a proton. Find the deBroglie wavelength of this electron. Determine whether the corresponding probability wave would 'fit' the circumference of the orbit without undergoing destructive interference. [ The mass of an electron

Solution of energy transfer for orbital electron

How much energy will an electron in orbit about a hydrogen atom lose in a transition from orbit # 2 to orbit # 4, where orbits are counted from the closest outward? If this lost energy is carried away by a photon, what will be its wavelength?

Rate at which area is swept out by a planet or satellite

Area is measured in m^2, so the rate at which area is swept out by a planet or satellite is measured in m^2/s. a. How fast is area swept out by Earth in its orbit about the Sun? b. How fast is area swept out by the Moon in its orbit about Earth? Use 3.9 x 10^8 m as the average distance between Earth and the Moon, and 27.33

Dipole moment and bohr radius

Look up the magnetic dipole moment of a hydrogen atom and the bohr radius, and use the assumption of uniform circular motion to calculate the effective current with in a hydrogen atom. Compare this current to that of a scanning tunneling microscope 1nA. Which is greater and by how many orders of magnitude? Magnetic dipole m

Geosynchronous Orbit Satellites

Many satellites are moving in a circle in the earth's equatorial plane. They are at such a height above the earth's surface that they always remain above the same point. Such an orbit is said to be geosynchronous. Find the altitude of these satellites above the earth's surface.

Comet Hyakutake: Semi-major axis; compare to distance to Pluto, Alpha Centauri

One of the brightest comets of the 20th century was Comet Hyakutake, which passed close to the sun in early 1996. The orbital period of this comet is estimated to be about 30,000 years. a) Find the semi-major axis of this comet's orbit. r= ? m b) Compare it to the average sun-Pluto distance. (r / r_pluto) = ? Expres

Hohmann transfer of satellite from one orbit to a higher orbit

For a circular orbit around a massive gravitating body, the speed depends on the radius according to Equation 8.3; for elliptical orbits, the speed varies according to the equation V squared=2GM{(1/r)-(1/2a)}, where r is the distance from the massive body and a is the semi major axis of the ellipse(i.e., half the sum of the clos

Heliocentric Model

Who rediscovered the heliocentric model? Who had proposed it earlier? What two observations about the planets did this theory explain without the use of complicated epicycles and deferents? What is an inferior planet? What is a superior planet?

Displacement and Equations of Kinematics in Two Dimensions

The following problems and conceptual questions are from chapter 3 of "Physics, 7th edition by Cutnell and Johnson". It pertains to displacement, velocity, and acceleration; equations of kinematics in two dimensions; and projectile velocity. Please consider significant figures and if possible, draw visual graphics. Concept

Bohr Theory: Finding a Quantum Number

Consider the Earth-Sun system as a giant-sized hydrogen atom, the objects interacting, however, by the gravitational force. (a) What is the quantum number, according to Bohr Theory, for the Earth's orbit about the Sun? (b) If the Earth were to make a transition to the next lowest quantum state, by what amount would its distance

Combination of four quantum numbers

Please see the attached file for full problem details. 6. What does the combination of four quantum numbers (QN) specify? What does the combination of two quantum numbers specify? List the possible values of l if n = 3 List the possible values of ml if l = 3 Which of the following combination of quantum n

(see attached file for calculations)

1. (a) 35800 km and 22240 mi. (b) 3070 m/s and 10090 ft/s. 2. (a) 6.67 m/s. (b) 0.0755. I have the answers to the questions. I need help with understanding the steps it takes to get to the solution. 1. Communication satellites are placed in a geosynchronous orbit, i. e., in a circular orbit such that they complete one f

Semi-major axis of a comet's orbit & greatest distance from sun

Chapter 13, Problem 51 Suppose that a comet that was seen in 574 A.D. by Chinese astronomers was spotted again in year 1998. Assume the time between observations is the period of the comet and take its eccentricity as 0.20. What are (a) the semimajor axis of the comet's orbit and (b) its greatest distance from the Sun?

Magnetic Moment and Current associated with an Electron in a Hydrogen Atom

In the Bohr model of the Hydrogen atom, we assume that the electron makes a circular orbit about a proton. Recall that for uniform circular motion F=mv^2/r and where F is the Coulomb force, use the Bohr radius 0.529 angstroms to compute the current due to an orbiting electron. What is the associated magnetic moment?

Primitive Cubic, Body Centered Cubic and Face Centered Cubic

1. Describe the primitive cubic, body centered cubic and face centered cubic unit cells. 2. Compare quantum mechanical and bohr model of atom. 3. Draw molecular orbital energy diagrams for Li2 and Be2. What is the bond order in each of these species? 4. When calcium hydride (CaH2) reacts with water, hydrogen gas is evo

Reasons for the Seasons

The attached image of the Earth was made by the Galileo spacecraft while en route to Jupiter. South America is at the center of the image and Antarctica is at the bottom of the image. 1. In which month of the year was this image made? Please explain. 2. When this image was made, was the Earth relatively close to the Sun

Masses in Equilateral Triangle and Net Forces Exerted

Problem 12.16 Part A What is the acceleration due to Earth's gravity at a distance from the center of the Earth equal to the orbital radius of the Moon? ANSWER: = Answer not displayed Problem 12.12 Suppose that three astronomical objects (1, 2, and 3) are observed to lie on a line, and that t

Newton's form of Kepler's third law

The orbital period of the binary system containing A0620-00 is 0.32 day, and Doppler shift measurements reveal that the radial velocity of the X-ray source peaks at 457 km/s (about 1 million miles per hour). a) Assuming that the orbit of the X-ray source is a circle, find the radius of its orbit in kilometers. (This is act

Angular speed of race car, tangential speed, loop-the-loop

1. A race car makes two and a half laps around a circular track in 3 mins. What is the car's average angular speed? Answer: - 0.087 rad/s 2. A wheel of radius 1.5m rotates at a uniform speed. If a point on a rim of the wheel has a centripetal acceleration of 1.2m/s^2, what is the point's tangential speed? Answer: - 1.3m/s

Moon Circular Orbits

Approximately one billion years ago, the moon orbited the Earth much closer that it does today. The radius of the orbit was only 24 400 km. The orbital period was only 23 400s. Today the average radius is 385,000km; and the present period is 2.36x106s. Assuming that the orbit of the moon is circular, calculate the ratio of the s