In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.
Homework Statement
It is required to put a satellite into an orbit with apogee of 5R/2, where R is the radius of the planet. The satellite is to be launched from the surface with a speed Vo at 30degrees to the local vertical. If M is the mass of the planet, show that (Vo)^2 = 5GM/4R. Assume...
Could someone explain the idea, method of how Earth orbit was derived, in non-mathematical terms (well, some math is fine too)? I am more interested in the (ingenious) engineering/experimental approach behind it. I guess it's related to or requires the determination of Earth mass, and from the...
We're doing orbits and such in physics at the moment, and out teacher said "if a geostationary satellite gets further away, it has to go faster". I get this, because with a bigger orbit it would have to move faster to stay above the same point on earth, more distance to travel in the same time...
An Earth satellite remains in orbit at a distance of 6104 km from the center of the Earth. What speed would it have to maintain? The universal gravitational constant is 6.67X10^-11 N m^2/kg^2. The mass of the Earth it 5.88X10^24 kg. Answer in units of m/s.
So again, missed the class. I'm...
Homework Statement
Pluto moves in a fairly elliptical orbit around the sun. Pluto's speed at its closest approach of 4.43x109km is 6.12km/s.
What is Pluto's speed at the most distant point in its orbit, where it is 7.30x109km from the sun?
Homework Equations
Conservation of energy...
Homework Statement
One of the n=5 states of hydrogen is split by spin-orbit coupling into two levels with an energy difference of 0.0039 cm^-1 . Determine the 'l' quantum number for this state and predict the analogous splitting for doubly ionised Li .
Homework Equations
The fine...
Homework Statement
A spaceship of mass m circles a planet (mass = M) in an orbit of radius R. How much energy is required to transfer the spaceship to a circular orbit of radius 3R?
Homework Equations
K=.5mv^{2}
U_{g}=-\frac{GMm}{r}
v=2(pi)r/T
v=(ar)^.5
The Attempt at a Solution
I...
can someone explain how bohr used the mass of the nucleus in helium to develop a ratio of 4.0016 of the original rydberg constant for hydrogen? I can't seem to find the proof anywhere, I read vaguely that he found this value by calculating the increased charge in the nucleus and using the mass...
From Carroll and Ostlie “An Introduction to Modern Astrophysics” prob 2.6 b
After determining angular momentum of sun-jupiter orbit system in part a, the question then asks you “What contribution does the sun make toward the total orbital angular momentum. It says assume Jupiter is in a...
The International Space Station, with a mass of 370,000 kg, is orbiting the Earth at a height 335 km and needs to be boosted to an orbit of 352 km. Calculate the energy needed to boost the ISS to its new height.
m = 370,000 kg
M = 5.98 x 10^24 kg
G = 6.67 x 10^-11 Nm^2/kg^2
Initial...
Hello all:
I'm interested in minor planet.Could you tell me how to calculate the orbit of a minor planet accurately? Is there any software to calculate it?
And how to get the latest information of the minor planets?Any websites of famous international institutes who observe and...
I understand that planets orbit follows a curve in spacetime created by the sun. Most of the planets follow the curve with seemingly a consistent radius. However Pluto follows an ellipse around the sun an appears to be inconsistent with the curve in spacetime created by the sun. Apologies if...
http://www.science27.com/forum/coworbit.jpg
How much relative stronger force would it require to keep a bull in orbit when the radius was 4 times shorter.
And how can this are calculated...?
(The bull only wants to move straight ahead , weight and speed is the same)
4 times ?
2...
Homework Statement
A 600kg satellite moving in a stable circular orbit about the Earth at a height of 4000km (G=6.67x10^-11 NM^2/kg^2, Re=6380km, Me=5.98x10^24kg).
Calculate the speed of the satellite at that height.
Calculate the orbital period (T), the time for one revolution
Calculate...
How much energy would it require (per second or per orbit) to keep the moon in orbit, if gravity did not exist?
Pretend the gravity from Earth did not exist, and the moons still should orbit like it does.
Does it exist a equation to calculate that?
Homework Statement
I am to find the particles trajectory to the first order of r/a knowing it to have the Yukawa potential
v(r)=V_{\circ}r_{\circ}/r * e^{-r/r_{\circ}}
= -k/r * e^{-r/a}
Homework Equations
\theta(r)= \int (1/r^{2})/\sqrt{2\mu (E-U-l^{2}/2\mu r^{2}}) dr...
At radius 1: Acceleration Due to Gravity (ADG) is 16 times as strong as at radius 4.
The object at radius 1 has 4 times so much KE and 4 times so little time to change the course (into a continues circular orbit) hence ADG must be 4*4 times so strong, = ADG 16 at radius 1,- to keep the...
Homework Statement
An Earth's satelite is in equatorial orbit at 352,000 km above earth. What is the orbital velocity (m/s) of the satelite (4 sig figs)
Homework Equations
g1d1^2=g2d2^2 to find gravity at the height of the satellite
The Attempt at a Solution
I don't really know...
Homework Statement
A distant star has a single planet circling it in
a circular orbit of radius 3.33 × 1011 m. The
period of the planet’s motion about the star
is 836 days.
What is the mass of the star? The
value of the universal gravitational constant
is 6.67259 × 10−11 N · m2/kg2...
Homework Statement
High above the surface of the Earth, charged particles (such as electrons and protons) can become trapped in the Earth's magnetic field in regions known as Van Allen belts. A typical electron in a Van Allen belt has an energy of 55 keV and travels in a roughly circular orbit...
Homework Statement
Ok so i had all of this typed up and some work typed out and then the page refreshed and i lost it all so this one is going to be shorter and more brief.
I have to create a spreadsheet and graph of altitude vs time and speed vs altitude. My goal is to place a rocket into a...
If you were to measure the area of a sector that a planet would sweep out in one week around the sun. It would be the same no matter what time of the year it was. What conservation principle is this example demonstrating? Linear, angular or both? and why?
Hallo, i have a question here, hope someone can answer it. :)
As we know, two object attract each other. The closer the object, the stronger the force of attraction. This explain why Earth is attract by sun, but moon is attract by earth. (i guess.)
But here i got a question, we know that...
The following is the equation for a Keplerian stable orbit at the equator around a Kerr black hole-
\tag{1}v_s=\frac{\pm\sqrt{M}(r^2\mp2a\sqrt{Mr}+a^2 )}{\sqrt{\Delta}(r^{3/2}\pm a\sqrt{M})}
where M=Gm/c^2,\ a=J/mc and \Delta=r^2-2Mr+a^2
which for a static black hole would reduce to -...
At what horizontal velocity would a satellite have to be launched from the top of Mt. Everest (elevation 8848 m) to be placed in a circular orbit around Earth?
I'm not sure where I'd start here, any tips?
Every time Neptune scatters bodies to Jupiter, Neptune gains energy and its
orbit becomes larger. How much mass would Neptune have to scatter to Jupiter
for Neptune’s orbit to have changed from a circular orbit at 22AU to a circular
orbit at 30AU? Give the answer in terms of Neptune’s mass...
Homework Statement
The equation of the elliptical orbit of Earth around the sun in
polar coordinates is given by
r =ep/1 − e cosa
where p is some positive constant and e = 1/60. Let r0 and r1
denote the nearest and the furthest distance of the Earth from
the sun. Calculate r1/r0...
Can we detect any coriolis forces induced from our circular orbit around the Sun ?
We're going in a big circle so we should be able to detect some coriolis if we deviate from that circle - ie if we move around a bit instead of following a perfect circular path.
Considering the Earth is...
Homework Statement
Prove that:
r=a(cos E-e)(ihat,xi)+(sqrt(a*p)) *sin E (ihat,eta)
Homework Equations
E=eccentric anomaly
e=eccentricity
The Attempt at a Solution
Rotational matrices come into play here, but I'm not sure to what extent. alpha=beta*gamma*delta, with their...
For this problem, I have to find all orbits of given permutation.
\sigma: \mathbb{Z} \rightarrow \mathbb{Z}
Where,
\sigma(n)=n-3
Now, the problem is I do not know how to approach this permutation in the given format.
All the permutations I dealt with were in the form:
\mu...
Homework Statement
Consider Comet Halley. At a particular instant in time, its position and velocity
are given below, in units of AU and AU/yr relative to the centre of the Sun.
(x,y,z) = 0.331060, -0.455488, 0.166180)
(vx,vy,vz) = (-9.01154, -7.02645, -1.30645)
There are a number...
I would like to know the Earth Date or Julian Date of the Periapsis, Vernal Equinox or any other point in the orbit for every planet in the solar system excluding Earth.
Homework Statement
Consider a spherical, nonrotating planet of mass M, and radius R, with no atmosphere. A satellite is fired from the surface of the planet with speed v0 at 45o from the local vertical. In its subsequent orbit the satellite reaches a maximum distance of 5R/3 from the centre...
Homework Statement
Two moons orbit a planet in nearly circular orbits. Moon D has orbital radius r, and moon E has orbital radius 4r. Moon D takes 20 days to complete one orbit. How long does it take for moon E to complete one orbit
Homework Equations
None - I think
The Attempt...
Homework Statement
A 10,000 kg satellite is rbiting the Earth in a geostationary orbit. The height of the satellite above the surface of the Earth is ?
Homework Equations
V = \omega r
Newtons gravitational force equation
Keplers third law equation
The Attempt at a...
I was looking at this link: http://en.wikipedia.org/wiki/File:Universe_Reference_Map_%28Location%29_001.jpeg" and wondered to myself why the asteroid belt just outside of Mars is a ring...as opposed to a sphere.
Then I thought, why do all the planets seem to orbit the sun on a similar plane...
Hi,
i need to solve the orbit equations that leads to Kepler's third law.
The equations are :
l = r * [e * cos(theta - theta0) - 1]
and
l = r * [e * cos(theta - theta0) + 1]
where l = (J * J) / (m * k)
Homework Statement
A satellite is in a circular polar orbit 240 km altitude. When the satellite is over the South Pole the engine is fired to achieve a polar orbit that has apogee directly over the North Pole. After the impulsive burn an observer on the North Pole observes the satellite has...
So I know this is the orbit-stabilizer theorem. I saw it in Hungerford's Algebra (but without that name).
So we want to form a bijection between the right cosets of the stabilizers and the orbit. Could I define the bijection as this:
f: gG/Gx--->gx
Where H=G/Gx
f(hx)=gx h in H
^ Is that...
Homework Statement
A spacecraft is inserted into a lunar orbit. It varied from 101.5 km to 11,741,8 km above the surface of the moon. Later it was transferred into a circular orbit 96.6 km above the moon. Compute the delta v total for a 2 maneuver sequence to transfer the spacecraft...
Homework Statement
A satellite is in a circular orbit very close to the surface of a spherical planet. The period of the orbit is T = 1.78 hours.
What is density (mass/volume) of the planet? Assume that the planet has a uniform density.Homework Equations
T^{2}=4*PI^2*r^3/G*M
Density =...
Homework Statement
The orbit of a particle moving on a central field is a circle passing through the origin, namely, r = r_0cos(\theta). Show that the force law is inverse fifth power.
Homework Equations
\frac{d^2u}{d\theta^2} + u = \frac{-mF(u^{-1})}{L^2u^2}
u=r^{-1}
The Attempt...
Homework Statement
see attachment #12.106
Homework Equations
V=R\sqrt{}(g/r) (for a circular orbit)
where R is the radius of the Earth and r is the radius of the orbit from the center of the earth
conservation of momentum for elliptical orbits:
Vara=Vbrb
The Attempt at a Solution...
Homework Statement
A GEO spacecraft crosses the earth’s equatorial
plane when its true anomaly is 30 deg. The
eccentricity of the orbit is 0.1 and its initial
inclination is 5 deg with respect to the equator.
What minimum velocity increment is required to
transfer this GEO to an...
Homework Statement
On July 1, 2004, the Cassini spacecraft approached
Saturn with hyperbolic excess velocity 5.5 km/s to
swing by the planet at the closest approach distance
rp = 80,680 km. Compute the impulsive ΔV
required for a maneuver performed at the closest
approach to Saturn to...
Homework Statement
Given data: A moon of Mars orbits with a period of 459 minutes. The radius of the moon's orbit is 9.4x10^6 m. What is the mass of mars?
Homework Equations
The Attempt at a Solution
The only relevant equation I could find was Fmars on moon= (G*m1*m2)/(r2)...
Well, the question is that what happen when an electron changes orbits? if it cannot have states in between those orbits, how can it 'move through' those restricted areas? Do the go through those states? or just disappear and reappear without any time lapse, at two different places??
please...
Hello there! Long time no see!
I've been struggling with this thing for a long time, and finally I've been able to write something down and wonder whether it is correct or not. Unluckily, I am trying to do something that may be more difficult than it seems, so I need your help.
I am going...
Why is the total energy of an elliptical orbit given by:
E_{tot}=\frac{-GMm}{2a}
Where a=semi major axis.
I agree for a circular orbit I can do the following:
F_c=F_g
ma_c=\frac{GMm}{r^2}
\frac{v^2}{r}=\frac{GM}{r^2}
v^2=\frac{GM}{r}
Since the total energy also equal to the kinetic plus...