I What does this description mean? (two bodies orbiting each other)

Hello, I'm reading a textbook named "Introduction to Rocket Science and Engineering" by Travis S. Taylor.

I'm now in a general cosepts about orbits. I have a question, what the book says in here?

From Equation 2.24, it is clear that as the distance, r, between the rocket and Earth gets larger and larger, the potential energy between them decreases. At a certain distance, the effect of the gravitational potential well of the Earth becomes neglible compared to other forces acting on it (such as gravitational pull of the Moon or the Sun) and the rocket is said to be out of the Earth's "sphere of influence". The term is only applicable for three or more body systems and can be dscribed as,

rSOI = αp(msmallerbody/Mlargerbody)2/5

Here, αp is the length of the semimajor axis of the smaller body's orbit relative to the larger body.
I can't understand the bold formatted sentence. What the author try to mean? If you can, can you describe this sentence by using images, datas or diagrams, please?

Thanks to everybody, have a good day!
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
30,484
4,363
This is my interpretation...
M is the mass of the body whose sphere of influence we are determining.
m is the mass of a smaller body orbiting the larger body, and which may serve to limit the larger's sphere of influence. I.e., when a third body is sufficiently far from M (>rSOI) its orbit may be significantly affected by m.
ap is the semimajor axis of m's orbit about M.
 

gleem

Science Advisor
1,196
623
I see it differently. Since the sphere of influence decreases as the mass of the larger body increases I am lead to believe that it refers to the distance from the smaller mass. Thus the larger the big mass gets the closer you have to get to the smaller mass for it to have a larger affect than the big mass.
 
This is my interpretation...
M is the mass of the body whose sphere of influence we are determining.
m is the mass of a smaller body orbiting the larger body, and which may serve to limit the larger's sphere of influence. I.e., when a third body is sufficiently far from M (>rSOI) its orbit may be significantly affected by m.
ap is the semimajor axis of m's orbit about M.
Well this description is good but, I can't image what is going on, sadly. Can you describe this with some paper & pen drawings or an paint image, please? My English and Google Translator's Turkish is not enough to describe three things' relations :P

I see it differently. Since the sphere of influence decreases as the mass of the larger body increases I am lead to believe that it refers to the distance from the smaller mass. Thus the larger the big mass gets the closer you have to get to the smaller mass for it to have a larger affect than the big mass.
Thanks for your reply, I got what you tried to mean, thanks!
 

haruspex

Science Advisor
Homework Helper
Insights Author
Gold Member
2018 Award
30,484
4,363
I see it differently. Since the sphere of influence decreases as the mass of the larger body increases I am lead to believe that it refers to the distance from the smaller mass. Thus the larger the big mass gets the closer you have to get to the smaller mass for it to have a larger affect than the big mass.
It specifically mentions the sphere of influence of the earth being constrained by the sun and the moon, but you are right that the form of equation only makes sense if the sphere of influence in question is that of the smaller body.
Thanks for the correction.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top