Questions tagged [celestial-mechanics]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
3answers
41 views

Would Earth always face Sun the same way if Earth didn't rotate around it's axis?

Imagine for a second that Earth no longer rotates around its axis. It still revolves around the Sun. However, would the Earth: face the same way towards the Sun as it goes around it (permanent time ...
0
votes
1answer
29 views

How can these two definitions of the eccentric anomaly give the same answer?

The eccentric anomaly,$E$, is defined via the equation, $$ r = a(1-e \cos E) \tag{1} $$ for radius $r$, semi-major axis $a$ and eccentricity $e$. It is ALSO defined in terms of the Kepler Equation ...
0
votes
0answers
20 views

Angular speed of Mercury [closed]

I have to calculate Mercury's angular speed ratios in the perihelion and in the aphelion $\left(\frac{\omega_a}{\omega_p}\right)$, using given eccentricity $ e = 0.206 $. I have no idea what ...
2
votes
0answers
35 views

Is this a valid way to estimate the solar system's orbital velocity around the galactic center?

I know there are better ways to derive this, such as finding orbital velocities of other stars at approximately the same radius from the GC as ourselves and finding our own velocity $v_0$ as within ...
-1
votes
1answer
54 views

Vis viva equation - finding how change in velocity changes the semi-major axis distances - math trick [closed]

I'm reading about how to deorbit. I stumped upon a trick here. In the question, we wish to find how a chance in orbital speed changes the semi-major axis distances. So in the answer we start with the ...
0
votes
1answer
126 views

Analytical proof for Kepler's first law using cartesian co-ordinates

Many detailed proofs are available for Kepler's first law, like this one. But all of them use polar co-ordinates. There is one which doesn't even use differential equations. I'm looking for a proof ...
0
votes
1answer
21 views

Lorenz System in reference to Astrophysics / Planetary orbits

From my research I have found that there are a system of ordinary differential equations for atmospheric convection. What I am seeking are any Lorenz equations that apply to any areas of Astrophysics ...
0
votes
0answers
14 views

Transform from Cartesian coordinates to Delaunay elements

Place a central mass $M = 1/G$ at the origin $(0,0,0)$. We know that for a test particle moving in the $xy$-plane, we can transform $(x,y,p_x,p_y)$ to the Delaunay elements $(\theta_\lambda, \theta_\...
0
votes
0answers
39 views

How wide is the $L_4$ and $L_5$ Moon-Earth Lagrangian point?

How far would an object need to be displaced from the $L_4$ and $L_5$ Lagrangian points so that it can escape returning to those points?
-1
votes
0answers
48 views

About Simple Harmonic Motion [duplicate]

the earth is revolving around the sun in a fixed orbit does this motion execute Simple harmonic motion
0
votes
0answers
11 views

Find first lagrange point from potential energy of binary system [duplicate]

I am trying to solve a question of a course that I need to TA tomorrow and I am not sure what I am missing here. You first have to derive the potential energy of a test source in a binary system, ...
0
votes
0answers
60 views

It is about spacetime and Gravity [duplicate]

if the gravity is the curvature in Spacetime due to this the earth revolves around the sun so does the curvature of spacetime applies force on the earth to move around the sun?
0
votes
1answer
42 views

Two-body problem: reduced mass velocity to individual velocity

I asked a question on finding the initial velocity of two objects of equal mass in order to follow a keplerian orbit with a given eccentricity but I am still having some trouble. I have seen the ...
0
votes
1answer
49 views

Subjective Zenith and Nadir

I apologize if this is similar to existing questions asked by others, but I was asked to post it instead of asking for clarification of the 'answers' given on silimar questions asked by others... How ...
0
votes
1answer
25 views

Validity of the two-body system approximation in astrophysics

I'm taking an intro course in astrophysics and studying Kepler's Laws of planetary motion - all of which are built over the assumption that we can approximate our system to one where there's only two ...
2
votes
2answers
52 views

If I use the Earth as my point of reference on a model, would it be valid if I said that the Sun orbits the Earth? (in my model)

What the title says. If I create a model, and I use the Earth as my point of reference, is it valid to say that the Sun orbits the Earth inside my model? Or is claiming that invalid?
2
votes
1answer
48 views

What is the fastest moving macroscopic object people have made? [closed]

The Parker Solar Probe will move at 690,000 km/h (430,000 mph), or 0.064% the speed of light, at its closest approaches to the sun. Parker Solar Probe top speed Will that be the highest speed yet ...
0
votes
1answer
55 views

Is this a viable way to calculate the mass of the sun?

By measuring the Earth’s distance from the Sun, and knowing its orbital period, Newton’s Law of Universal Gravitation and Newton’s 2nd Law can I calculate the mass of the sun?
2
votes
2answers
104 views

Mistake in proof of virial theorem for gravity

I'm having trouble proving the virial theorem for gravity. I get an extraneous term, but I think my work is correct. Starting with the Lagrangian: $$\frac{1}{2}m\dot{r}^2+\frac{1}{2}mr^2\dot{\theta}^...
1
vote
1answer
54 views

Time that a comet comes closer than earth [closed]

I had to solve the following problem on an exam today: A comet is travelling on a parabolic path $r$ to the 'west', crosses the orbit of the earth (assume the orbit of the earth is circular with ...
0
votes
1answer
38 views

Rotation of satellite at Lagrange point $L_1$

What rotations occur due to gravitation for a body placed/anchored at Lagrange point $L_1$ in the Sun-Earth system, which is an unstable equilibrium point? Is the rotation axis vector normal to the ...
2
votes
2answers
78 views

Circular trajectories and Kepler's law [duplicate]

I'm studying about the central force and Kepler's law, and I was wondering: by the first law, the trajectories of planets suppose to be elliptical. but from what I understood, most physical ...
1
vote
1answer
87 views

Why don't the galaxies collide due to gravity?

Why doesn't the galaxies collide due to gravitational attraction and why doesn't all the matter in the universe stick together due to gravitational attraction?
4
votes
2answers
116 views

How Can I Calculate the Speed Required for an Orbiting Planet to Pass Through a Given Point in Space?

I've been trying to derive an equation for this for a while now, but I haven't had much success. Let us set up the equation. There is a star with mass $M$ and a planet that is distance $d$ from the ...
2
votes
2answers
62 views

Gravitationally bound system

I have a question concerning an $N$-body gravitationally bound system. It is quite simple and straight forward but I have not found an answer to it yet. I'm not even sure if the question is actually ...
-1
votes
2answers
105 views

Why is the orbital velocity tangent to the ellipse?

Why is the orbital velocity tangent to ellipse? And at perigee and apogee the orbital velocity has velocity tangential to the radius vector joining the planet and the star around which it is ...
2
votes
2answers
2k views

Would the moon eventually fall into Earth if we reduce its tangential velocity slightly?

Would the moon eventually fall into Earth if we reduce its velocity slightly?
2
votes
3answers
338 views

Conservation Laws that apply to a hyperbolic trajectory

I don't understand why the answer choice is D, I thought for unbound orbits, none of these principles applied? Could someone clear this up for me?
-2
votes
2answers
96 views

Moon is receding from Earth approximately 4cm per year [closed]

According to the theory of relativity the universe is styled as a fabric which is depressed by a large mass and a moon, still following a straight path ever 'curves inward' toward the large mass. Now ...
1
vote
1answer
34 views

Boost to satellite in elliptical orbit in order to reach the maximum radius? [closed]

If there were a satellite in an elliptical orbit, at what point in its orbit should a booster rocket be fired to kick it to its max radius? I was thinking whennit was closest to the plant/object ...
2
votes
1answer
68 views

On the limits of Kepler’s second law

Does Kepler’s second law hold true if the shape of the orbit is not closed? Let’s say, for example, a spiral?
0
votes
0answers
21 views

Gravothermal catastrophe, how to understand it?

I would like to study the phenomenon of gravothermal catastrophe. Could you suggest some papers or books about it and the books I should check for prerequisites (astrodynamics, statistical mechanics, ...
1
vote
1answer
54 views

Why can't we have trinary or multiple sytems, like binary systems?

We usually come across close binary systems in Astrophysics. Also, we can have hierarchical systems in which there is a close binary. The Alpha Centauri is an example of an hierarchical triple. But ...
1
vote
1answer
30 views

Why are planet's maximal/minimal angular speed ratio harmonic?

See this Wikipedia page for Harmonices Mundi, a book by Kepler (yes, he was the one to discover the three Kepler's laws). The author writes: He found that the difference between the maximum and ...
1
vote
2answers
81 views

What is orbit that could place satellite to be always under the Sun?

I just thinking that, if we could place satellite to orbit earth in opposite direction of earth rotation, inverse of geostationary orbit. If we carefully choose a speed to sync with earth rotation, it ...
2
votes
2answers
87 views

Misunderstanding of how the Sun losing mass makes the Earth orbit increases in size

The radius of the Earth orbit increases by about 15 cm per year. One of the main argument found online to explain this is the fact that the gravitational pull of the Sun on the Earth diminishes over ...
0
votes
0answers
29 views

Matrix Used for Orbital Motion [duplicate]

this question is by no means a new question, however previous questions have been unable to exactly answer my question. I'm attempting to obtain analytical results and then plot the results of a ...
0
votes
0answers
36 views

Why doesn't the Sun gravitate Mercury so that in following years, Mercury goes inside the Sun? [duplicate]

There has been news in public about Mercury that passes in front of Sun which happens very rarely every 100 years, here. So people on Earth can see it through special kind of telescope, of course, ...
2
votes
3answers
75 views

Will August be always summer in the northern hemisphere?

Is the Earth orbit precessing, or are there other effects which will create a shift between our calendar (day counting), and the Earth's orbit? I imagine these effects to be small, but I'm asking for ...
-4
votes
2answers
250 views

Is Newton’s gravitation law able to explain the circular motion of the earth around the sun?

I have read in Forbes website that the orbit of the earth around the sun is expanding (by 1.5 cm in 2019). I have also heard that big bang theory suggests that the universe would collapse into ...
0
votes
1answer
34 views

Motions of planets from a non-rotating earth frame

Suppose you are hovering just above the earth at a fixed distance such that you are not rotating with it (the earth is obviously rotating about its own diametrical axis) but you are orbiting the sun ...
0
votes
1answer
64 views

How to decrease satellite's orbital radius?

According to the equation $v²=GM/r$ to decrease the orbital radius of a satellite currently in orbit, you'd want to increase its speed. However intuitively this doesn't make sense to me, surely if you ...
0
votes
0answers
20 views

Converting units for N-body simulation for the solar system

I am implementing a test particle integrator for the solar system, now I've gotten to the phase where I want to test the orbits it integrates. I want to start with the Sun and the Earth (massless), ...
-1
votes
1answer
35 views

Where does the radial velocity component come from?

Any object under the influence of a central force will have two components of velocities: Radial and rotational I understand that the rotational velocity is there due to the centripetal force. But ...
1
vote
3answers
105 views

Physical reason for $T^2=a^3$ when $T$ is in years and $a$ is in AU

Kepler's third law states $$T^2\propto a^3$$ When $T$ is in years and $a$ is in AU, the proportionality constant becomes $1$. This can't be a coincidence; I would like to know the physical reason for ...
0
votes
1answer
54 views

Satellites orbiting around any planet's [closed]

Suppose a satellite is revolving around a planet with radius r. Now if we increase the value of r then the angular velocity and kinetic energy will decrease, but the total energy & potential ...
0
votes
1answer
60 views

Can dark matter explain the unusual orbit of transnettunian objects? [closed]

While we are struggling to find an hypothetical planet 9 to explain the unusual orbit of transnettunian objects, I was wondering if it could be just dark matter. We know that the universe is mostly ...
-1
votes
1answer
69 views

Is space-time fabric around Uranus tilted?

I am completely new in this field, so please pardon me if I am asking something which makes no sense at all :) The Situation: According to Einstein's theory of relativity, there is a 4th dimension ...
0
votes
2answers
65 views

Creating a Gravitational 2-body simulation

I am trying to create a simulation for a gravitational 2 body problem. But I am kind of having trouble to define the equations that can be solve numerically. From an inertial frame I defined the ...
0
votes
1answer
51 views

Could a planet have terminal velocity greater than its escape velocity?

I've had 2 semesters of college-level physics (1 of Mechanics and 1 of E&M) and was wondering after exploring a bit about terminal velocity: Is it physically possible for a planet to have a ...

1
2 3 4 5
10