The Newtonian model of gravity in which the force between two objects is given by GMm/r^2.

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3answers
202 views

Can I make a rod in the vertical plane move with its one end on the ground in a slanting position?

Consider a rod kept vertically on the ground. I keeps the rod in a slanting position making some angle with the horizontal. Can I now move this rod along the horizontal plane by applying a force at ...
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3answers
135 views

Confused about Newton's 3rd law

I am confused about Newton's 3rd Law. If a person jumps off the ground a force is applied both to the person and to the ground. However, as $F=ma$ acceleration experienced by the Earth is much less ...
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3answers
206 views

Forces involved in a climbing jet aircraft

I have a problem with which I need help. The question is: A jet aircraft is climbing at an angle of 45° above the horizontal and is accelerating at 4.5m/s2. What is the total force that the cockpit ...
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2answers
55 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 ...
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2answers
90 views

Expression for Atmospheric Pressure with Altitude, including Tidal Forces

Is this simple to obtain? I've tried to modify the constant-gravity model to use the $GM/r^2$ form instead, but my result was shown to be wrong with some testing. Constant Gravity Model You can ...
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2answers
242 views

Signs in proof of gravitation potential energy (GPE)

Proof of gravitational potential energy. Work done by gravity in bringing mass from infinity to a distance of $r$ between masses. When we use the integration formula and arrive at the answer we ...
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2answers
116 views

How long will it take to fill a bath tub with oil compared to water?

As everyone knows, the oil is more viscous than water. But, I've been wondering how long it will take to fill a bath tub compared to water. It is quite obvious that oil will take longer. But, how much ...
4
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1answer
528 views

Gravitational attraction of triangles

Suppose I have two triangles relatively close together (so they probably shouldn't really be treated as point masses). I want to calculate the gravitational force (and potentially torque?) generated ...
3
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1answer
84 views

Pendulum in a Turning Airplane

My friend and I are having an argument over what happens with a pendulum hanging inside an airplane during a turn. Assuming that the airplane is making a standard 1 G coordinated turn, how does the ...
2
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1answer
48 views

Deceleration rate of objects of different mass but the same otherwise

Using a tennis ball as an example object, if one ball weighs 1 ounce and the other is 2 ounces, and both are struck at 100 mph on the same trajectory, would there be any difference in the deceleration ...
1
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1answer
72 views

Tangential and radial acceleration in projectile motion

I'm currently learing kinematics, specifically projectile motion and as an example in my textbook is a bullet fired at some angle. I understand the derivation of formulas to describe that motion and ...
0
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1answer
40 views

Follow up question regarding: Deceleration rate of objects of different mass but the same otherwise

My first question was answered here: Deceleration rate of objects of different mass but the same otherwise . But based on that, here is a follow-up question (I also edited my first post with the ...
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1answer
49 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, ...
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1answer
52 views

Tension in string and gravitational force on bob relative strength

When calculating time period of simple pendulum (an approximation of SHM at small amplitudes) we take gravitational force greater than tension in string and resolve gravitational force in two ...
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1answer
183 views

How is gravitational force is compared to flow of water?

I listened to a lecture. The professor said that the gravitational field around the particle (spherical in shape) can be compared to a pond having a constant height and depth and water is constantly ...
6
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0answers
135 views

Derivation of Universal Variables

Does anyone know of link to the derivation of the Universal Variables? This is in regards to Kepler's equations. The Wikipedia link didn't have enough information for me, and the Colorado page ...
4
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0answers
92 views

Victorian cosmology after the second law of thermodynamics but before relativity?

In the 19th century, most astronomers adopted an island universe model, in which our galaxy was the only object in an infinite space. They didn't know that the "spiral nebulae" were other galaxies. ...
3
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0answers
811 views

Gravity - What happens when two objects of unequal masses fall freely towards the ground? (Revisited)

The common perception regarding what happens when two objects of equal sizes but unequal mass are allowed to fall freely towards the ground is that - both the objects make contact with the ground at ...
3
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0answers
174 views

Calculation of a Gravity Resonance Keyhole

Can anyone describe the mathematics behind the calculation of a resonance keyhole (for a two-body model)? It seems like the size and position of the keyhole should be a function only of mass and ...
2
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0answers
49 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, ...
2
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0answers
85 views

Only gravitation and Newton's $2^{\mathrm{nd}}$ law needed to derive Kepler's laws?

It is known that Kepler's laws of planetary motion can be derived from Newton's laws of motion and his law of universal gravitation. However, are all of Newton's laws of motion necessary? According ...
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0answers
34 views

How strong can tidal forces get?

I am imagining a planet the size of Earth being in close proximity to something of high mass such as a gas giant or a star, but ultimately I'd be more interested in how to figure this out myself. So ...
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0answers
88 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: ...
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0answers
37 views

Where are the L3, L4, and L5 of a hyperbolic orbit?

Do the L3, L4, L5 points exist in hyperbolic orbits? If yes, then where do they lie?
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0answers
33 views

The magnitude of spacecraft anomalous velocities?

That Voyager and several other spacecraft have had anomalous changes in speed is known. According to the news reports, the differences are unsettling. But just how large are these anomalies really? ...
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0answers
82 views

Formulation of the Three-Body Newtonian problem

I am trying to understand three body problem in Newtonian space. I want to make formulation of differential equations for known initial conditions for the case with: Identical three masses ...
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0answers
659 views

Calculating semi-major axis of binary stars from velocity, position and mass

I'm trying to calculate the 'instantaneous' semi-major axis of a binary system with two equal (known) mass stars for an $N$-body simulation. I know their velocities and positions at a given time, but ...
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0answers
23 views

Effect of small variable transverse force on satellite orbital precession

Consider a small satellite which moves in a 2D elliptical orbit around a much larger body (e.g. the Sun) under the influence of Newtonian gravitational acceleration $$Ar = G.M/d^2 $$ Next imagine ...
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78 views

Has this approach to Coulomb force/Newton gravity unification ever been published?

Introduction: When toying with gravitational and electromagnetic equations in my undergrad days I stumbled upon this interesting relationship. With the very childish hopes of unifying gravitation ...
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0answers
24 views

Any way to Find the Position Function of a body under gravitational force?

Here's the problem I am trying to find a solution to: Consider a heavy point particle of mass $m_2$ fixed at a point (preferably the origin) and another light point particle of mass $m_1$ at an ...
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0answers
32 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 ...
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0answers
76 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 ...
0
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0answers
88 views

Simulating orbits using Newton's Law of Universal Gravitation

I've been having a go at programming an orbital simulator from scratch (without using any existing libraries) using the formula below to find the acceleration first for particle A and then for ...
0
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0answers
289 views

Gravitational potential inside a solid sphere

To calculate the gravitational potential at any point inside a solid sphere, why do we need to separately integrate gravitational field from infinity to radius and then from radius to the point? Why ...
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0answers
53 views

How to derive “Anti-Lagrangian” $L_4$ and $L_5$ points

In this paper on co-orbital dynamics the authors discover, numerically, "Anti-Lagrangian" solutions to the restricted 3 body problem. These Anti-Lagrange $L_4$ and $L_5$ points are 120 degrees ahead ...
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0answers
60 views

origin of cusps in simulated dark matter halos

I keep reading that cusps are one of the most "robust" predictions of N-body simulations of dark matter halos. But any paper I've found on the topic makes it sound like these simulations are ...
0
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0answers
65 views

Gravitational Behavior of Rotating Body

Consider a stick with a (ball-shaped) weight at the end of it. Let's say this stick is in a state of rotation (it's floating in vacuum) and is also in a state of translational motion. Consider a ...
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0answers
58 views

What is the equation for Lin-Shu density wave theory?

Lin-Shu density wave theory is a (very good) theory to explain the spiral arm structure of spiral galaxies. Where can I find the equations that underlie this theory? I've seen its computer ...