0
votes
0answers
21 views

Could an object higher than the stationary orbit be returned to the outgoing point on this orbit?

In the question Centrifuge speed of an object higher than a stationary orbit, I asked: Does an object higher than the stationary orbit move slower or faster around the world than the top of a tower ...
1
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2answers
42 views

Centrifuge speed of an object higher than a stationary orbit

In the question At what altitude above equator do gravitational and centrifugal forces cancel each other?, I asked how high a tower on the equator has to be such that at its top, gravitational and ...
0
votes
2answers
72 views

At what altitude above equator do gravitational and centrifugal forces cancel each other? [on hold]

How high has to be a tower at equator to get on its peak the same - but of course inverted sing - value of gravitational and centrifugal forces?
3
votes
1answer
72 views

Potential that is proportional to distance

Does anybody know of a treatment of the case where a potential field is proportional to the distance, i.e. in 3 dimensions: $$V(\vec{r}) ~\sim ~ |\vec{r}|~?$$ Essentially the question is: What are ...
0
votes
1answer
50 views

Earth-Moon system

While learning about motion of centre of mass, I came across this statement online, It is also more accurate to say that the Earth and Moon together revolve about their common center of mass. ...
1
vote
1answer
340 views

How fast must a torus spin to have a felt gravity? [closed]

Given a rotating torus (like a gyroscope or a rotary) with a radius of 1km, how fast must it rotate to have someone inside the torus feel normal gravity of 1G?
9
votes
1answer
100 views

How can a planet gravitationally capture objects?

I would expect that any asteroid or other object originating far away but passing near a planet would pick up speed and energy as it approaches, but unless it comes into contact with the atmosphere ...
62
votes
5answers
6k views

Where does the extra kinetic energy come from in a gravitational slingshot?

I read in this answer in this site that the KE a free-falling ball acquires is not originated by the attracting body but that energy was actually stored in the ball when it had been lifted to the ...
5
votes
5answers
466 views

Why are orbits elliptical? [duplicate]

Just wanted to know why planetary orbits get to be elliptical? I'm not debating how stable these orbits are (obviously almost completely stable), but why don't planets revolve in the special ellipse ...
1
vote
5answers
111 views

Satellite Collision Problem

I'm stuck on a problem of two satellites going towards each other. The mass of the first satellite is 400kg and the mass of the second satellite is 100kg. The altitude of the satellites is 1000km. I ...
0
votes
4answers
78 views

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 ...
1
vote
1answer
55 views

Reduced mass and harmonic mean

In two-body problems, a reduced mass has the form: $\frac{m_1 m_2}{m_1+m_2}$, which by appearance, is half of the harmonic mean of $m_1$ and $m_2$: ...
9
votes
2answers
1k views

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 ...
4
votes
1answer
454 views

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 ...
1
vote
1answer
42 views

How does acceleration affect the orbit?

I want to know what roughly happens if we hit an orbiting body a little. And how is it possible that most of the objects have seemingly circular orbits around. How do they stabilize? I ask because it ...
13
votes
5answers
1k views

Why are these periods the same: a low earth orbit and oscillations through the center of the earth?

Related: Why does earth have a minimum orbital period? I was learning about GPS satellite orbits and came across that Low Earth Orbits (LEO) have a period of about 88 minutes at an altitude of 160 ...
2
votes
0answers
61 views

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, ...
0
votes
3answers
86 views

Why doesn't an orbiting body keep accelerating?

As a physics newbie I'm trying to get a grip on basic orbital mechanics. I think I'm beginning to get grasp on how bodies interact with each other. When a body approaches another body it accelerates ...
0
votes
1answer
47 views

Launching a unpropelled rocket

I have read about the application of railguns and other ground powered launch, where there is no need to carry any propellant in the rocket. I am wondering, to what velocity should the vehicle ...
3
votes
2answers
91 views

Does the opening angle of the cone matter?

When discussing orbital mechanics, you learn that all orbits roughly follow an ellipse which is obtained as the intersection of a cone with an inclined plane, creating conic sections. Below is a ...
0
votes
1answer
63 views

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, ...
0
votes
0answers
33 views

Can we design the orbit of a satellite with Einstein’s curved space?

I think that the most successful theory of gravity is that the orbit of planet can be explained with this theory and the orbit of satellite was designed with this theory. To design an orbit of a ...
1
vote
1answer
49 views

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.
1
vote
2answers
119 views

Why does earth have a minimum orbital period?

Using the equation for Kepler's constant for Earth $K$: $$K = \frac{GM}{4\pi^2}$$ $$K = 1.01 \times 10^{13} \;\rm m^3/s^2$$ Finding time ($r = 6.4 \times 10^{6} \;\rm m$ (radius of Earth)): $$K = ...
1
vote
0answers
100 views

Application of trigonometry to the slingshot effect/gravity assist

I have been trying to understand the formula $$v_f^{2}=v_i^{2}+2V(V(1-\cos\beta)+v_i(\cos(\alpha-\beta)-\cos\alpha))$$ as it relates to Fig. 2 on page 5 of this exposition: ...
0
votes
0answers
28 views

Ideal suborbital hop

This is actually regarding Kerbal Space Program, but it's more of a physics question than one about the game. If I have a rocket on the surface of a rotating spherical body without an atmosphere, ...
1
vote
1answer
54 views

Help for orbits of planets

Suppose that an asteroid) that moves at a velocity $v$ passes near to a planet: now I know that the gravity force of the planet will curve the trajectory of the asteroid so I tried to make a draw of ...
5
votes
3answers
451 views

Derivation of Kepler's laws

How can analytically be derived the Kepler's laws? I found some extremely synthetic equations which from the Newton's laws (in particular $\mathbf{F} = m \mathbf{a}$) tried to obtain the Kepler's ...
0
votes
0answers
92 views

Alternative derivations of vis-viva equation?

The proof of the vis-viva equation of orbital mechanics found on wikipedia looks, in my opinion, somewhat convoluted and unenlightening. Considering the simplicity and importance of the vis-viva ...
2
votes
3answers
72 views

Question about (complex) motion of Moon

In an ideal situation, we can use a simple formula to determine the velocity at which a body revolves around a massive body at a particular distance. I was wondering if there is an intuitive way to ...
0
votes
2answers
47 views

Velocity required for orbit of satellite

I am very confused about orbital velocity for satellite launched from earth. It is states that: $$ v=\sqrt{\frac{GM}{r}} $$ Some says that it is equal to 8000 m/s and some say 3.1 km/s. Please remove ...
4
votes
3answers
136 views

Why aren't there more natural satellites orbiting the Earth than just the Moon?

Considering that there's a lot of debris in space and that impacts fling out rocks into space all the time, why do we only have one large natural satellite - the Moon? Shouldn't there be all kinds of ...
3
votes
1answer
64 views

multibody problem and determinism

Given that there is no exact general solution to the $N$-body problem, can it be concluded that the Universe is non-deterministic, even for the Newtonian case (ignoring relativistic and quantum ...
0
votes
3answers
70 views

Orbital motion with varying radius

The model of a orbital motion in many Physics textbooks and online resources (e.g., Wikipedia on circular motion) assumes that the orbit is a circle, i.e. the radius is constant and the speed is ...
0
votes
1answer
96 views

Gravitation - why is it so confusing?

First, does gravity emit from all directions around a star or planet equally. Secondly, how is it that gravity pulls a planet closer, then it goes further out, without the planet changing orbit ...
1
vote
1answer
82 views

What are Lagrange points in gravitation fields? [closed]

What are Lagrange points in gravitation fields? Additionally, what are their properties? For example, if a satellite or asteroid rested at a Lagrange-point.
0
votes
2answers
85 views

A small object on the opposite side of the earth's orbit with 0 velocity,“in line” with the core - would it collide with the earth?

If a small object (say mass 1 kg), at the opposite side of the earth's orbit (six months away), was placed in the same orbital position as the earth's core, at zero velocity in all directions, would ...
2
votes
2answers
204 views

Why do the planets orbit the Sun? [duplicate]

Why do the planets orbit the Sun? If it's because the gravity of Sun then why don't they just fall in and burn up?
0
votes
0answers
90 views

Calculate trajectory of projectile with gravity from disk planets in 2D?

I'm making a 2D game where you control a spaceship and fly between disk-formed planets of differing size (mass/pull). The planets are small and you can fly near several at once. I need to calculate ...
1
vote
2answers
64 views

Finding sphere of influence in multibody system

I would like to draw a boundary illustrating the sphere of influence of each body in a 3 body system. What is the best way to find such a boundary? My understanding is at the edge an SoI is the ...
2
votes
3answers
161 views

How do scientists place satellites into orbit?

How do scientists place satellites into orbit? How do they calculate the gravity acting on the spacecraft in order to generate exact opposite force by means of Kinetic energy to keep the satellite ...
2
votes
2answers
217 views

Two suns, one moon, and one planet?

I have a question about how would seasons and the moon cycle be affected in a system where one planet orbits Sun #1, and Sun #1 orbits a second sun. Online I found this description: "Type II: ...
0
votes
1answer
101 views

Where does the potential energy go when mass is lifted out of Earth's gravitational field?

There is a finite amount of energy needed to be spent on a rocket or a rock that is taken out of the Earth's gravitational field. Lets suppose the rock is taken far enough to have no effect of Earth's ...
2
votes
1answer
90 views

What is the constant $K_1$ in these orbital equations?

I want to compute the derivatives of argument of periapsis and longitude of the ascending node of the orbit of a GPS satellite from the following formula. $$\frac{d\Omega}{dt} = -K \cos{i} \\ ...
2
votes
0answers
72 views

Travel time in elliptical orbit around the sun

Hi I'm calculating a problem, and I think it ought to be correct - but the result I get isn't. The problem is described as follow: A spacecraft is traveling from Earth to Venus in an elliptical, ...
0
votes
2answers
42 views

Why turning velocity of star towards point “A” makes it's satelites, change their apoapsis to side opposite of velocity vector?

Why turning velocity of star towards point "A" makes it's satelites, change their apoapsis to side opposite of velocity vector? Sentence above turned a bit crazy or not understandable (possible ...
1
vote
1answer
126 views

Determine orbital position after change in velocity

I am working on a satellite simulator for a project/game and I am stuck on this one bit of physics. So far I have a satellite that revolves around earth on a 2D plane following Keplerian motion using ...
2
votes
1answer
275 views

How do I convert tangential speed to angular speed in an elliptic orbit?

I am running an animation of a satellite in an elliptic orbit (defined by a parametric equation for $x$ and $y$ as a function of $t$) and want to make sure the spacecraft is traveling at the right ...
2
votes
2answers
582 views

Angular speed of the planets

Do all the planets in our solar system have the same angular speed? Physics teacher says yes, my research is not crystal clear. I want to make sure I have the right information for future reference. ...
1
vote
1answer
198 views

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 ...