Escape velocity of solar system

[purpleperson1717]

Homework Statement

Calculate the escape velocity of our solar system.

Relevant Equations

v=√(2GM/r)

I'm pretty confused by this but I have a few thoughts. Since the sun takes up most of the mass of the solar system, I was thinking maybe I'm really looking for the escape velocity of the sun? So I would use the mass of the sun for M and the radius of the sun for r. My other thought was to add up the masses of all the planets for M and use the radius of the solar system for r, but I'm not sure that makes as much sense because each planet has its own gravitational field. Any help would be appreciated!

 

[PeroK]

Homework Statement:: Calculate the escape velocity of our solar system.
Relevant Equations:: v=√(2GM/r)

I'm pretty confused by this but I have a few thoughts. Since the sun takes up most of the mass of the solar system, I was thinking maybe I'm really looking for the escape velocity of the sun? So I would use the mass of the sun for M and the radius of the sun for r. My other thought was to add up the masses of all the planets for M and use the radius of the solar system for r, but I'm not sure that makes as much sense because each planet has its own gravitational field. Any help would be appreciated!

In terms of mass, you could use the mass of the Sun as a first step. You need to decide on your starting point. The surface of the Sun doesn't seem like a suitable point from a practical perspective.

 

[Orodruin]

There is no such thing as the escape velocity of the solar system. Escape velocity is a velocity related to a celestial body that is required to escape to infinity from its surface. The solar system as such does not have a surface. How fast you need to go to escape depends on where you are.

 

[purpleperson1717]

There is no such thing as the escape velocity of the solar system. Escape velocity is a velocity related to a celestial body that is required to escape to infinity from its surface. The solar system as such does not have a surface. How fast you need to go to escape depends on where you are.

So you mean there is no answer?

 

[purpleperson1717]

In terms of mass, you could use the mass of the Sun as a first step. You need to decide on your starting point. The surface of the Sun doesn't seem like a suitable point from a practical perspective.

So if I pick a point within the Sun's gravitational field, then I could use that r and the mass of the Sun?

 

[PeroK]

So if I pick a point within the Sun's gravitational field, then I could use that r and the mass of the Sun?

Yes, why not?

 

[Orodruin]

Yes, why not?

That’s the escape velocity of the Sun. Not the solar system. The solar system has no surface and therefore no unique escape velocity. You can of course define an escape velocity from the solar system at some point, but that does not define the escape velocity.

 

[PeroK]

That’s the escape velocity of the Sun. Not the solar system. The solar system has no surface and therefore no unique escape velocity. You can of course define an escape velocity from the solar system at some point, but that does not define the escape velocity.

I'll bet you submitted some argumentative solutions when you were a student!

 

[Orodruin]

I'll bet you submitted some argumentative solutions when you were a student!

I did as a matter of fact. I particularly remember an exam in mechanics where the examiner asked for the angular frequency of small oscillatioms around an equilibrium. The equilibrium was unstable so everyone else got imaginary frequencies. I argued the equilibrium was unstable and explained how fast the system would move away, then found the (much less trivial) stable equilibrium and found the frequency for small oscillations around that one. It is the only exam I got higher than 100% score … :P

 

[purpleperson1717]

That’s the escape velocity of the Sun. Not the solar system. The solar system has no surface and therefore no unique escape velocity. You can of course define an escape velocity from the solar system at some point, but that does not define the escape velocity.

I agree with what you’re saying, which is why I was so confused about the question. I think I’ll include that reasoning in my solution along with my calculation of the escape velocity of the sun. Thanks!

 

[kuruman]

Homework Statement:: Calculate the escape velocity of our solar system.

Could this be a typo, "of" being incorrect and "from" being correct?

 

[purpleperson1717]

Could this be a typo, "of" being incorrect and "from" being correct?

I guess it could be. What I wrote is the exact wording of the question but I don't think it was a very good question.