Can the distance between two bodies be calculated to prove they are gravitationally bound?

In summary, the distance between two bodies can be calculated to determine if they are gravitationally bound, but this requires knowledge of their masses, velocities, and positions. This method has been used to estimate the motion of the Milky Way and its relationship with the Great Attractor.
  • #1
wolram
Gold Member
Dearly Missed
4,446
558
Can the distance between two bodies be calculated to prove they are gravitationally bound?

Use two bodies with known mass.
 
Astronomy news on Phys.org
  • #2
You need to know velocity as well as distance in order to know this. If you took a snapshot of the Earth and the Moon you wouldn't know whether the Moon was in orbit, moving away from the Earth at sufficient velocity to escape or indeed plunging straight towards it!

Edit: you would also need to know that masses, since that will tell you what velocities would indicate stable orbits. So that's three things, position, velocity and mass.
 
  • #3
Thankyou Wallace.

From that i guess there is no way the milky way and its motion towards the great attractor could be proven by calculation to be cause by gravity?
 
  • #4
No, since we can get an estimate of the masses of the bodies involved and measure velocities via redshift, hence we have (to some level of precision) the three things I mentioned.
 

1. How is the distance between two bodies calculated to determine if they are gravitationally bound?

The distance between two bodies can be calculated by using the gravitational force equation, F = G * (m1 * m2 / r^2), where G is the gravitational constant, m1 and m2 are the masses of the two bodies, and r is the distance between them. By rearranging the equation to solve for r, the distance between the two bodies can be determined.

2. What is the significance of determining if two bodies are gravitationally bound?

Determining if two bodies are gravitationally bound is important because it can provide insight into the dynamics of the system and how the bodies interact with each other. It can also help predict the future behavior of the system and its stability.

3. Can the distance between two bodies change over time, and how does this affect their gravitational binding?

Yes, the distance between two bodies can change over time due to various factors such as gravitational forces from other bodies or external forces. This can affect their gravitational binding as the strength of the gravitational force between them is inversely proportional to the square of the distance. As the distance increases, the gravitational force decreases and the bodies may eventually become unbound.

4. Is the distance between two gravitationally bound bodies always constant?

No, the distance between two gravitationally bound bodies can vary depending on their orbits and other factors. For example, in a binary star system, the distance between the stars may vary as they orbit each other. However, the overall gravitational binding between the two bodies remains constant as long as their masses and positions relative to each other do not change significantly.

5. Can the distance between two bodies be used to determine their mass?

Yes, the distance between two bodies can be used to determine their mass if the gravitational force between them is known. This is because the gravitational force is directly proportional to the masses of the two bodies. By measuring the distance and the gravitational force, the masses of the bodies can be calculated using the gravitational force equation.

Similar threads

  • Astronomy and Astrophysics
Replies
5
Views
1K
  • Astronomy and Astrophysics
Replies
10
Views
2K
  • Astronomy and Astrophysics
Replies
0
Views
219
  • Astronomy and Astrophysics
Replies
4
Views
2K
  • Astronomy and Astrophysics
Replies
13
Views
2K
Replies
3
Views
1K
  • Astronomy and Astrophysics
Replies
3
Views
1K
  • Astronomy and Astrophysics
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
745
Back
Top