Vis-viva equation (Orbital Velocity) with massive satellite?

AI Thread Summary
The vis-viva equation assumes the orbiting body's mass is negligible compared to the central body's mass, which raises questions about its accuracy in systems with comparable masses, like binary stars. In such cases, the relative speed of the two bodies must be considered, as it differs from the individual speeds around their common center of mass. The discussion clarifies that the combined speed of both bodies can be calculated using their masses, leading to a better understanding of their dynamics. It emphasizes the importance of correctly interpreting the variables involved, particularly distinguishing between relative speed and individual speeds. Ultimately, the conversation highlights the complexities of applying the vis-viva equation in scenarios with significant mass ratios.
taylorules
Messages
5
Reaction score
0
Wikipedia states that "In the vis-viva equation the mass m of the orbiting body (e.g., a spacecraft ) is taken to be negligible in comparison to the mass M of the central body."
I'm wondering how the velocity is determined if the satellite's mass is non-negligible. For example, in a binary star system where both stars have comparable masses, would the vis-viva equation be accurate?
Thanks.
 
Physics news on Phys.org
Have you found an answer to your question yet? I was waiting for someone to reply to you because I found the vis-viva equation interesting. So don't take my post as an authoritative answer.

v is defined as the relative speed of the two bodies. If the difference in mass of the two bodies is not significant then simply adding the two masses should work.

gif.latex?v_o=\sqrt{G(M_1+M_2)\left(\frac{2}{r}-\frac{1}{a}&space;\right&space;)}.gif


But since I could not find a reference of the equation being used this way, I am not sure that it is correct.

Keep in mind that the relative speed of the two bodies is not the same thing as the speed of one body about the common center of mass of the two bodies. In the latter case, the speed of one body will be different from the speed of the other body if there masses are different.
 
TurtleMeister said:
v is defined as the relative speed of the two bodies.
Thank you! That was the problem.
Because Body1's speed = Body2's speed * (Mass2/Mass1), and v = Body1's speed + Body2's speed, I found Body2's speed = (Mass1 * v) / (Mass1 + Mass2).
The problem was that I thought v represented Body2's speed, not the combined speed of both.
Thanks
 
Glad I could help. If you write out the equation using your method, you will find that the (M1+M2) cancels out:

gif.latex?v_1=\sqrt{GM_2\left(\frac{2}{r}-\frac{1}{a}&space;\right&space;)}.gif


gif.latex?v_2=\sqrt{GM_1\left(\frac{2}{r}-\frac{1}{a}&space;\right&space;)}.gif


This is the speed of each body relative to the barycentre of the two bodies.
 

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

Orbital Mechanics Vis Viva Equation Question
Replies
1
Views
2K
Why do we need the hyperbolic excess velocity?
Replies
1
Views
12K
Calculate elliptical orbit using attitude and velocity
Replies
7
Views
3K
Orbital and spin angular velocity?
Replies
17
Views
3K
Orbital Mechanics: Find Eqns of Motion w/ Initial Conditions
Replies
3
Views
1K
A Orbit velocity in Schwarzschild metric?
Replies
13
Views
4K
Escape Velocity and the Motion of Two Massive Bodies
Replies
4
Views
2K
What happens when the velocity of a revolving satellite/body changes?
Replies
7
Views
6K
Interplanetary Trajectory Calculation
Replies
1
Views
5K
Change in mechanical energy (gravitation)
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top