Is Orbital period related to the mass of a body?

[juvilado]

Hi, i have the physics quite oxidized, and i was wondering if an orbital period, and therefore the average orbital speed of any celestial body is related to its mass. Im quite sure it is not, but i dont know what are the factors that determine an orbit of a planet and its orbital velocity.

A) For example, is venus and mars orbits were switched, would their orbits tend to vary in any direction?

B) Every celestial body (in the same star system) with 24.000 mts/sec will have quite similar orbits. Is this always true?

C) Is the distance to the center of mass (the sun) what determines orbital period and speed? Only that?

Thanks!

 

[Shpaget]

In systems where the satellite has small mass compared to the parent body, usually the mass of the smaller body is discarded as irrelevant, but if you start to significantly increase mass, than yes, orbital period goes down.

This is a great little tool to play around with orbits. Change mass and other parameters as you please.

https://phet.colorado.edu/sims/my-solar-system/my-solar-system_en.html

[PB666]

u = M_{central body} * G (6.67 E-11), assume the satellites mass is negligible, if its not you need to use a binary formula (u = (m1 + m2) *G) you cant use planet or star as systems center.

v = SQRT(u/r) 

w²r = u/r²   w = SQRT(u/r^3)

period = 2*pi/w  = 2 * pi SQRT(r³/u)

if a = r then period = 2 * pi SQRT(a³/u)

This is the kepler law of planetary motion the period is an 3/2 function of the semimajor axis and an inverse sqrt function of M_{central body}

Now lets see how close I got without using a textbook or wikik

https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Third_law

But then if this is in wikipedia why do you need to ask here?

 

[juvilado]

8 hours ago, PB666 said:

u = M_{central body} * G (6.67 E-11), assume the satellites mass is negligible, if its not you need to use a binary formula (u = (m1 + m2) *G) you cant use planet or star as systems center.

v = SQRT(u/r) 

w²r = u/r²   w = SQRT(u/r^3)

period = 2*pi/w  = 2 * pi SQRT(r³/u)

if a = r then period = 2 * pi SQRT(a³/u)

This is the kepler law of planetary motion the period is an 3/2 function of the semimajor axis and an inverse sqrt function of M_{central body}

Now lets see how close I got without using a textbook or wikik

https://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion#Third_law

But then if this is in wikipedia why do you need to ask here?

 

Well, i didn't know how exactly search on wikipedia, so that i asked here ^^