Contents Motivation Initial Setup Methodology Analysis Conclusion

Slides:



Advertisements
Similar presentations
Monday October 20. Motion of a rigid body Body can translate only. In this case we can replace the body by a point located at the center of mass. Body.
Advertisements

Gravitation Newton’s Law of Gravitation Superposition Gravitation Near the Surface of Earth Gravitation Inside the Earth Gravitational Potential Energy.
“Concern for man himself and his fate must always form the chief interest of all technical endeavors… Never forget this in the midst of your diagrams and.
Lecture 18 Circular Orbits Newton’s Law of Gravity.
Module on Computational Astrophysics Professor Jim Stone Department of Astrophysical Sciences and PACM.
CHAPTER-13 Gravitation.
Chapter 13: Gravitation. Newton’s Law of Gravitation A uniform spherical shell shell of matter attracts a particles that is outside the shell as if all.
Physics 218 Lecture 21 Dr. David Toback Physics 218, Lecture XXI.
The Properties of Stars Masses. Using Newton’s Law of Gravity to Determine the Mass of a Celestial Body Newton’s law of gravity, combined with his laws.
Physics 111: Elementary Mechanics – Lecture 12 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research.
SMDEP Physics Gravity: Orbits, energy. Ch 6, #27 (b) only: mass of stars? 1.9x10 28 kg 2.9x10 26 kg 3.5x10 26 kg 4.5x10 24 kg 5.Other 6.Didn’t finish.
Chapter 13 Gravitation.
6. Centripetal force F = ma 1. Example: A stone of mass m sits at the bottom of a bucket. A string is attached to the bucket and the whole thing is made.
Chapter-5: Circular Motion, the Planets, and Gravity Circular Motion: Centripetal acceleration Centripetal force Newton’s law of universal gravitation.
Circular Motion Tangential & Angular Acceleration
Newton and Kepler. Newton’s Law of Gravitation The Law of Gravity Isaac Newton deduced that two particles of masses m 1 and m 2, separated by a distance.
5 Gravitation. The Milky Way galaxy and the black hole.
Newton’s Law of Gravitation. Newton concluded that gravity was a force that acts through even great distances Newton did calculations on the a r of the.
Kepler’s first law of planetary motion says that the paths of the planets are A. Parabolas B. Hyperbolas C. Ellipses D. Circles Ans: C.
航天动力学与控制 Lecture 年 2 月 4 General Rigid Body Motion –The concept of Rigid Body A rigid body can be defined as a system of particles whose relative.
In order to stay in a closed orbit, an object has to be within a certain range of velocities: Too slow  Object falls back down to Earth Too fast  Object.
Essential Idea:  The Newtonian idea of gravitational force acting between two spherical bodies and the laws of mechanics create a model that can be.
Chapter 13 Outline Gravitation Newton’s law of gravitation Weight Gravitational potential energy Circular orbits Kepler’s laws Black holes.
1) What is a satellite? 2) What does orbit mean? 3) What does Period mean? 4) What does angular velocity mean? 5) If the angular velocity is to remain.
Proportionality between the velocity V and radius r
Gravity and Orbits   Newton’s Law of Gravitation   The attractive force of gravity between two particles   G = 6.67 x Nm 2 /kg 2 Why is this.
 This version has no answers.. Which is stronger, Earth’s pull on the Moon, or the Moon’s pull on Earth? 1) the Earth pulls harder on the Moon 2) the.
Dynamics of Uniform Circular Motion Uniform Circular Motion Centripetal Acceleration Centripetal Force Satellites in Circular Orbits Vertical Circular.
Chapter 13 Gravitation Newton’s Law of Gravitation Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the.
Chapter 13 Gravitation.
Newton’s Second Law Pages Describe your acceleration if you are in a circular motion. What is the net force of your motion? You are constantly.
Gravitation. Chronology Nicolaus Copernicus (1543): First to propose a system of planetary orbits. He argued that planets were in circular orbit around.
PHYSICS 103: Lecture 11 Circular Motion (continued) Gravity and orbital motion Example Problems Agenda for Today:
Section 7-1 Circular Motion Acceleration can be produced by a change in magnitude of the velocity and/or by a change in ____________________ of the velocity.
1 The law of gravitation can be written in a vector notation (9.1) Although this law applies strictly to particles, it can be also used to real bodies.
Physics Section 7.3 Apply Kepler’s Laws of Planetary Motion The Polish astronomer Nicolas Copernicus was the first to correctly place the sun at the center.
Summer 2012 PHYS 172: Modern Mechanics Lecture 19 – Angular momentum Read 11.4 – 11.7.
More Examples About Gravity Stuff Answers 1. Find the value of g at an altitude of m above Earth’s surface. ReRe r g = G M e r2r m r =
Chapter 13 Gravitation In this chapter we will explore the following topics: -Newton’s law of gravitation, which describes the attractive force between.
Newtonian Physics – 10 Mr. Jean
3. The Restricted Three-Body Problem
Astronomy 340 Fall 2005 Class #3 13 September 2005.
Circular Motion Chapter 12.
Chi Yung Chim, Jaehyeok Yoo, Xiang Zhai, Yaojun Zhang
Universal Law of Gravitation
Michael Wong EPS 109 Multiple-Star Systems.
WHAT IS….. DARK MATTER??.
Ch6: Gravitational Fields
Example 7-12 A group of extended bodies, each with a known CM. Find the CM of the group.
The Fate of Intergalactic Gas Clouds
Chapter-5: Circular Motion, the Planets, and Gravity
Find the velocity of a particle with the given position function
The Martian: Hermes Spacecraft Trajectories
ORBITAL Trajectories!!! Made by Karol Sanchez
Rigid Body Dynamics (unconstrained)
Gravity and Orbits – Not Free Fall
Chapter 13 Gravitation In this chapter we will explore the following topics: -Newton’s law of gravitation that describes the attractive.
Just for Kicks: a Molecular Dynamics Simulation by Dino B.
9. Gravitation 9.1. Newton’s law of gravitation
Chapter 13 Gravitation In this chapter we will explore the following topics: -Newton’s law of gravitation, which describes the attractive force between.
Example 5.2 Astronomical measurements show that the orbital speed of
Chapter 2 Astronomy.
Uniform circular motion
Numerical solution of first-order ordinary differential equations
Space And Gravity Ben Kendall 9B.
Rotational Motion and the Law of Gravity
1. What is the force of gravity between a 3
Chapter 2 - Part 1 The two body problem
3. a. What is the force of gravity between a 2
Numerical solution of first-order ordinary differential equations 1. First order Runge-Kutta method (Euler’s method) Let’s start with the Taylor series.
Presentation transcript:

Contents Motivation Initial Setup Methodology Analysis Conclusion PH241 Midterm The Antennae Group

Toomre and Toomre 1972 – T&T set out to model galaxies NGC-4038/9 (i.e. the antennae) and were able to successfully produce an accurate rendering using a fourth order Runge-Kutta integration method. PH241 Midterm The Antennae Group

1972  2006 PH241 Midterm The Antennae Group

Kepler problem PH241 Midterm The Antennae Group

Geometry PH241 Midterm The Antennae Group

Galaxy Setup We filled 12 concentric rings of radii 0.2Rmin to 0.75Rmin with a step of 0.05Rmin, with each ring having 3 more particles than the previous Particles given initial velocity to maintain a circular orbit. Softening: ε = 0.2 PH241 Midterm The Antennae Group

Restricted 3-Body Send satellite masses to 1.0 E-9 as compared to M = 1 for the center of mass. PH241 Midterm The Antennae Group

Our Results PH241 Midterm The Antennae Group

Comparison PH241 Midterm The Antennae Group

Orbit Plane φ = 0 φ = 2π/3 PH241 Midterm The Antennae Group

Tidal Forces PH241 Midterm The Antennae Group

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2025 SlidePlayer.com. Inc. All rights reserved.