# Tagged Questions

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### Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
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### Put a bullet into orbit around the moon

While I was watching this beautiful video, the absence of air friction pushed me to ask myself: While standing on the surface of the moon, what is the initial velocity by which you can fire a bullet ...
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### The motion of the particle satisfies $\textbf{v} = \textbf{c}\times \textbf{r}$

Why does a particle with position $\textbf r(t)$ that satisfies $\textbf{v}(t) = \textbf{c}\times \textbf{r}(t)$ follow a circle that lies in a plane perpendicular to $\textbf{c}$ with centre on a ...
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### How to show that the gravitational potential energy of a two particle system is -2 times the total kinetic energy, without using the virial theorem?

Consider a two-particle system with identical masses, orbiting in circles about their center of mass. I'm supposed to prove that: $$U_p = -2U_k$$ With $U_p$ potential energy of the system, and $U_k$ ...
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### Gravitational slingshot maximum

I have recently read an article about gravitation slingshot assist used by Voyagers 1-2, and was thinking on why this hasn't been used for travel between solar and other systems. I mean sligshot can ...
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### Can an elliptical orbit take the same time as a circular obit?

In the picture below you can see two orbits of potential pbjects. The main aspect of the orbits is that they have a collision point at the maximum of the elliptical orbit. My question is, could the ...
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### How to calculate launch angle for tangentially launched satellites?

What is the value of theta for a satellite not falling back to the Earth if it is launched from the direction tangent to the surface of the Earth? I have found the escape velocity which is 11.18km/s, ...
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### Leaving a stellar black hole's orbit [closed]

Say Earth is orbiting a black hole 1900 km in diameter, 1.5E33 kg in mass, and has a gravitational pull of 110,858,725,761.77 m/s^2. It's around 40 AU away Earth's orbital speed is 129,305.15664 m/s. ...
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### Calculate orbit height from tangential velocity

Is it possible to calculate the altitude of a satellite orbiting a planet, just from the planet's mass and the satellite's velocity, assuming that the satellite is in a perfect circular orbit? If so, ...
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### Which planet in the solar system is it?

It is known that the period of revolution of the earth about the sun is $365.3$ days and that the semimajor axis of the earth's orbit is $1.495 \times 10^{11}$ m. An astronomer notes that the ...
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### Finding at a distance from the Earth speed of satellite [closed]

A satellite at 8000 km from Earth where gravity is 6.4 m/s^2. What is the velocity of satellite? I don't the formula to find speed of satellite.
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### Satellites and gravitation

A satellite with mass $m$ orbits a planet of mass $M$ in a circular path with radius $r$ and velocity $v$. Due to some internal technical failure, the satellite breaks into two, similar parts with ...
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### Kepler's law of periods question, application [closed]

I'm a year 12 student studying in Sydney Australia. I would like to ask about a physics question which I'm currently troubled on. I have made several attempts of answering the question but no luck. ...
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### Center of mass and gravitational force

Say we have a two star system with both stars of equal mass $M$. The center of mass of this system is by definition in the center of the two stars. There is a small asteroid with mass m in orbit ...
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### A change in the mass of the moon [closed]

Would a change in the mass or radius of the moon have any effect on its speed? When asked this question in an assignment, I stated that it did not. My reasoning being that a change in the mass or ...
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### A satellite in orbit fires it's engines for a short interval. Is the new orbit closer or further away?

A satellite is in a circular orbit when its engines turn on to exert a small force in the direction of the velocity for a short time interval. Is the new orbit further or closer to the Earth? The ...
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### Mathematical model for this graph of a simplified binary star system?

Unnecessary background for question: I had a school assignment asking us to relate a quadratic equation to a real life example relating to our future dream career, making sure to express the accuracy ...
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### Time it takes two oppositely charged particles to collide

I think this is supposed to be a simple problem but I am having a hang up converting it to a one-body problem. It's one-dimensional. +q and -q a distance d apart, held stationary then let go at t=0. ...
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### Collision of two asteroids in the main belt [closed]

If there are two asteroids $A$ and $B$ of equal mass (and density of 3000kg/m^3), with the same semi major axis of $a=$2.2 AU with asteroid $A$ having a circular orbit and no inclination, and ...
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### Calculation of 12000 Lunar Orbits/Earth Day [closed]

I am really interested in the calculation of the following speed value in meter-per-second unit: Speed of something that is able to travel in one earth day the distance that it would take for the ...
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### Calculating specific orbital energy, semi-major axis, and orbital period of an orbiting body

Is it possible to calculate the specific orbital energy $Ïµ$, the semi-major axis $a$, and the orbital period $T$ (or $P$) without any of them being available to you? The values I do have available to ...
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### Relative angular momentum in two-particle problem

Assume the two particle problem i.e. two particles with equations of motions as follows: $\ddot{x_i} = -\frac{1}{m_i}\frac{\partial}{\partial x_i}V(|x_1 - x_2|)$ Since the angular momentum is ...
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### Solving differential Equation for the Two-Body Problem

So, I'm following the derivation in D. Morin, Introduction to Classical Mechanics, of the equations for a two-body system. I understand all of it, aside from this one step. When he's talking about ...
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### Newtons Cannon ball problem [closed]

Let's I have a Newton's Cannon ball of 15 kg and want to fire so it will round the earth and back to me. My query is which law can evaluate the speed that cannon ball will revolve round the sun ...
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We are supposed to show that orbits in 4D are not closed. Therefore I derived a Lagrangian in hyperspherical coordinates $$L=\frac{m}{2}(\dot{r}^2+\sin^2(\gamma)(\sin^2(\theta)r^2 \dot{\phi}^2+r^2 ... 1answer 88 views ### Why doesn't this equation for orbital motion change with position in the orbit? The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ... 1answer 109 views ### Vector cross product of \mathbf{r} and \ddot{\mathbf{r}} in polar coordinates I'm struggling with the following question: Question 6 A planet of mass m moves under the gravitational attraction of a central star of mass M. The equation of motion of the planet is ... 0answers 137 views ### Mercury's Orbital Precession in Special Relativity I am researching Mercury's orbital precession. I have considered most perturbations and general relativity. I am still not satisfied. I need your help. I need a solution to Exercise 13, Chapter 6, in ... 1answer 165 views ### Understanding Kepler's 2^{nd} law in terms of angular momentum conservation A) Explain how Kepler's 2^{nd} law - "The radius vector from the Sun to a planet sweeps out equal areas in equal time intervals" - can be understood in terms of angular momentum conservation. I ... 1answer 102 views ### What Speed Would an object need to leave the earth at to reach L1? [closed] Let's say the Earth is an airless sphere. What speed would an object weighing 1 kg need to leave the surface at in order to get to and be motionless at L1, where the Moon's gravity becomes stronger ... 3answers 204 views ### Condition for closed orbit [closed] I'd like to know when an orbit is closed. I know that, to have a closed orbit, there is a ratio that must be a rational number, but I don't know other things.. 1answer 683 views ### How can a satellite's speed decrease without its orbital angular momentum changing? I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences. 1answer 156 views ### Lagrange L4 L5 points and perifocal plane I have 2 satellites at the L4 and L5 points and these are watching an object. Each satellite provides the angle to the object from its own position from a line parallel to the \text{x-axis} of ... 1answer 412 views ### Finding orbital eccentricity I have this problem: They give me, from a satellite that is in orbit in earth, a value for the period, and the closest height to earth surface, the ask me what the eccentricty of the orbit is. I have ... 1answer 119 views ### What is the orbital motion where both foci are located at one point? What is the orbital motion where both foci are located at one point? I know that an ellipse orbit is motion with two distinct foci. 1answer 691 views ### Satellite Orbital Period [closed] I know I can calculate the period of a satellite orbit by Kepler's third law, but somehow it does not work out. The sattelite is 20200km from surface of the earth. r=orbits radius=earths ... 1answer 360 views ### Condition for circular orbit I am a little confused about the condition for circular orbit. Goldstein's Classical Mechanics has the condition for circular orbit as$$f'=0\tag1 where $f'$ is the effective force. I understand ...
I am trying to solve the following problem from Goldstein's Classical Mechanics: A planet of mass $M$ is in orbit of eccentricity $e=1-\alpha$ where $\alpha<<1$, about the Sun. Assume that the ...