What is Planetary motion: Definition and 71 Discussions
In physics, an orbit is the gravitationally curved trajectory of an object, such as the trajectory of a planet around a star or a natural satellite around a planet. Normally, orbit refers to a regularly repeating trajectory, although it may also refer to a non-repeating trajectory. To a close approximation, planets and satellites follow elliptic orbits, with the center of mass being orbited at a focal point of the ellipse, as described by Kepler's laws of planetary motion.
For most situations, orbital motion is adequately approximated by Newtonian mechanics, which explains gravity as a force obeying an inverse-square law. However, Albert Einstein's general theory of relativity, which accounts for gravity as due to curvature of spacetime, with orbits following geodesics, provides a more accurate calculation and understanding of the exact mechanics of orbital motion.
I was reading about the Tusi couple and read it "as a solution for the latitudinal motion of the inferior planets, and later used extensively as a substitute for the equant". Since the Tusi couple is related to plotting out an ellipse, did Nasir al-Din al-Tusi already discover the laws for...
HI!
I tried to solve this exercise, by assuming that it is an inelastic collision, the planet is spherical, and that the rotation axis is parallel to the z-axis, see the figure attached. (1) before the collision, (2) after the collision.I started by assuming angular momentum conservation, which...
https://www.feynmanlectures.caltech.edu/I_09.html
9-7
"From this figure we see that the horizontal component of the force is related to the complete force in the same manner as the horizontal distance x is to the complete hypotenuse r, because the two triangles are similar. Also, if x is...
Relevant formulae:-
Angular velocity in uniform circular motion ##=## ##\omega## ##=## ##\frac {2\pi} t##, where ##t## is the time taken to complete one revolution.
Centripetal acceleration in uniform circular motion ##=## ##a## ##=## ##\omega^2r##, where ##r## is the radius of the circular...
The answer to (c) is ##-2\pi AGMm##.
Answer to (d)
For sub-question d, I used a different approach and I don't know why the solution to (d) is an appropriate approximation.
What I did was that I use Newton's laws to obtain two differential equation in polar coordinate, as shown:
$$\text{Assume...
Homework Statement: The particle is moving in circular orbit such a way that the net force (F) is always towards the point p (point p is on the circumference of circle). Find the variation of force F with respect to r.
i.e find the value of n in the expression F=kr^n
Homework Equations: F=kr^n...
The thought of increasing a satellite's (for example) speed to allow it to transfer from a "higher energy" elliptical orbit to a "lower energy" circular orbit (in reference to the effective potential energy plot that arises after introducing the concept of an effective mass to simplify the...
Hey, this is how i tried solving the differential equation
The solution however does not match the general solution of the equation. Also differentiating it twice does not give me the previous equation. Please tell me if i did some mistake while solving.
I already know how to solve by finding...
Hello,
I am completing a research project for differential equations class. I am to derive Kepler's three laws and then compare the results of the derivation with real-world data. For Kepler's second law (a planet sweeps out an equal area in an equal time), I was hoping to find orbital data for...
Homework Statement
Consider a particle moving in the potential U (r)= -A/r^n, where A>0. What are the values of n which admit stable circular orbits?
Homework EquationsThe Attempt at a Solution
I tried to solve by putting dr/dt=0 in the total energy equation E= T + Ueff. But it didn't work...
Homework Statement
A space station is in orbit between the Earth and the moon. The force due to gravity on the space station from the moon is the same as the force due to gravity from the Earth. (FGmoon = FGearth). How far away from the Earth is the space station? How far from the moon is the...
You're the Galileo for a developing society on a remote archipelago on the far side of a tide-locked moon orbiting a gas giant. How do you figure out your place in that solar system? How do you convince others, who believe your world to be the center of the universe, of the truth? Will a road...
Homework Statement
A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 × 104 m/s, and the radius of the orbit is 5.25 × 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of...
Homework Statement
A planet orbiting a star experiences a force of magnitude 3x1022N due to gravitational attraction to the star. If the planet has a speed of 2x107 m/s to complete on orbit, calculate the mass of the planet and radius of the orbit? Assume the orbit to be a perfect circle...
Homework Statement
Deduce, from the equations employed in Q4 and Q5, the exponent n in the equation: T = k rn where k is a constant and T is the period of a satellite which orbits at a radius r from a massive object in space. Hence, how long is the “year” on Venus if its distance from the Sun...
Homework Statement
The period of a comet is 75.8 years. The perihelion distance is 0.596 AU (1 AU = 1.5 ⋅ 1011 m).
The velocity at perihelion is vp = 5.45 ⋅104 m/s.
a) Find the length of the major semi-axis of the elliptical orbit.
b) Find the aphelion distance and the velocity at aphelion...
Homework Statement
Homework Equations
I know that Fc = m * centripetal acceleration, where the Fc = the force of gravity
The Attempt at a Solution
[/B]
I was able to use process of elimination to get B for 25 correctly, but I am not able to understand how it is the right answer.
How can...
The graph I have made of Average Orbital Distance from the Sun vs. Average Orbital Velocity illustrates a decreasing exponential function. How, if it does, would this suggest that there is dark matter present in our solar system?
In planetary motion, the reduced mass of a system \mu is used in order to study the motion of the planet m in the non-inertial frame of the star M. Using \mu the trajectory of m turns out to be a conic. But this is the trajectory of the planet m as seen from the star M, correct?
I read that in...
I am disappointed by my graduate-level classical mechanics course, and especially the treatment of Lagrangian/Hamiltonian mechanics. Now, I scanned my notes and some crazy idea popped into my head, further fueling my discontent towards this course, because all the problems covered in class were...
Homework Statement
Using the equation
T = kr^p
I drew a loglog graph of orbital time period against orbit radius for the planets Mars to saturn.
lnT = plnr + lnk
My value for gradient was 5.25/0.48 = 10.94
Meaning p = 10.94
How do I compare this to the actual value? What is it?Homework...
Homework Statement
Hi there,
I wish to use Newton's Laws in conjunction with Euler's Method to model the motion of a planet around a star.Homework Equations
2nd Law
F = m*a
Law of Universal Gravitation
F = -G*M1*M2/r^2
The Attempt at a Solution
[/B]
First I combined the two laws above...
Homework Statement
Two stars of masses M and m, separated by a distance d, revolve in circular orbits around their center of mass.Show that each star has a period given by
T^2= (4π^2)(d^3)/ G(M+m)
Homework Equations
[/B]The Attempt at a Solution
I[/B] know the Kepler's Laws can be...
Could a planet orbiting around a sun be considered an example of perpetual motion? I know that the planet wouldn't be doing any work, since it goes back to the same spot every year, but does an object have to be performing for it to be considered perpetual motion? The two might have nothing to...
Homework Statement
The Attempt at a Solution
Honestly I'm completely lost, this is an assignment for my calc 3 class. I tried to do (a) but I think I'm completely off track so any helps appreciated.
r x a=0
|r x a|=0=|r||a|sin(theta)
r cannot be 0 since it's in the denominator
Assuming...
I was reading Planetary Motion (page 117) in Barry Spain's *Tensor calculus*, and stupidly enough, I didn't understand this. The equations are:
$$\frac{d^2\psi}{d\sigma^2} + \frac{2}{r}\frac{dr}{d\sigma}\frac{d\psi}{d\sigma} = 0,$$
$$\frac{d^2t}{d\sigma^2} +...
Homework Statement
A 20 kg satellite has a circular orbit with a period 2.4 h and radius 8.0×106m around a planet of unknown mass. If the magnitude of the gravitational
acceleration on the surface of the planet is 8.0 m/s2, what is the radius of the
planet?
Homework Equations
F =...
Suppose we have a planet of mass m orbiting a larger one of mass M along an elliptical path. If we use polar coordinates with the origin placed on the planet of mass M (focus of the ellipse) then at the instant when the smaller planet is at the point of closest approach we have:
\boldsymbol{v}...
Homework Statement
A planet with a mass of 8.99·1021 kg is in a circular orbit around a star with a mass of 1.33·1030 kg. The planet has an orbital radius of 1.21·1010 m.
a) What is the linear orbital velocity of the planet?
b) What is the period of the planets orbit?
c) What is the...
Homework Statement
a planet with radius of 12km spins at 520revs/s
find:
a) avg speed of a point on the planets equator over 2.5 of a revolution
b)find avg acceleration on stars circumfrance over 3/4 of a rev
c)find distance covered by point on the equator in 1 second
d) find displaement...
Homework Statement
At a ertain point between Earth and the moon the total gravitation force exted on an object by both planets is 0. The Earth - moon distance is 3.84 x 10^5 and the moon has 1.2% of the mass of earth. Where is this point located.
Homework Equations
Fg=GmM/R^2
The...
Hello,
The inverse square law of Newton's gravitational force, is it somehow related to each other?
I mean to say P^2 is directly prop.a^3. Is it from the third law that the derivation of inverse sq.law of G=M.m/R2 is derived?
Thanks.
Homework Statement
Two spheres of mass m and radius r, are released from rest in empty space. The centers of the spheres are separated by a distance R. They end up colliding due to gravitation attraction. Find the magnitude of the impulse just before they collide.Homework Equations
Eg= -Gmm/r...
Gyroscopic effect on planetary motion!
Hi PFians
This is my first ever post in astrophysics since I've got very interested in it from last 2 days...
I was wondering when Earth rotates about it's axis and at the same time changes it's direction due to revolution about sun...won't it have...
I'm reviewing my old calculus textbook and I stumbled upon a proof of Kepler's First Law of Planetary Motion which uses vector valued functions along with all of the operations to demonstrate the material. I understand the math and how to to DO it but what I am struggling with is why.
It goes...
Why is it that for instance the Earth and the moon orbit their common center of mass? I mean surely the moon feels a gravitational force as though the mass of the Earth were concentrated at its center? If yes, what is that then makes it orbit around their center of mass rather than this point. I...
Homework Statement
Kepler's third law of planetary motion relates P, the period of a planet's orbit, to R, the planet's mean distance from the sun, through the equation log P = \frac{1}{2} (log K + 3log R), where K is a constant.
Rewrite the formula as a single logarithm.
Homework...
Hi,
I know that centripetal force for planetary motion is the same as the force of gravity between that satellite and planet. For example (I know these numbers may be completely unrealistic but just for the sake of easy calculation...) if the mass of the Earth is 1x10^30 kg and the mass of...
Homework Statement
A meteor is moving at a speed of 20000mi/hr reltiave to the centre of the Earth when it is 350 mi from the surface of the earth. At that time, the meteor has a radial velocity component of 4000 mi/hr toward the center of the earth. How close does it come to the Earth's...
Homework Statement
You are one of the first astronomers in a civilization on Planet B in another solar system. With your unaided eye, you follow planet A in the same solar system and note that it never gets further away than 16 degrees from the star (around which both planets orbit).
What...
Homework Statement
An explorer plans a mission to place a satellite into a circular orbit around Jupiter, the radius of the planned orbit would be R.
a)The explorer wants the satellite to be sychronized w/ Jupiter's rotation. Determine the required orbital radius in meters.
b) What must...
Homework Statement
Planet X rotates in the same manner as the earth, around an axis through its north and south poles, and is perfectly spherical. An astronaut who weighs 950.0 N on the Earth weighs 917.0 N at the north pole of Planet X and only 860.0 N at its equator. The distance from the...
Hi
I'm a bit confused, I hope you can help.
The question is -
In the course of their orbits, the distance between the Earth and Venus changes. The radii of the orbits of the two planets are 1.5 x 10e8 km and 1.1 x 10e8 km. If a radio pulse is transmitted from Earth towards Venus, calculate...
Hi everyone,
I'm really confused with a particular question:
Homework Statement
A space shuttle orbits the Earth at 6720 km from its centre. The gravitational field strength is 8.9N/kg. Calculate the shuttle's orbital period in minutes...
Homework Equations
g=4pi^2...
Homework Statement
If a planet were suddenly stopped in it's orbit, supposed circular, Show that it would fall into the sun in a time which is\frac{\sqrt{2}}{8} times it's time period.Homework Equations
Kepler's Third lawThe Attempt at a Solution