# Escaping Our Solar System

by Bashyboy
Tags: escaping, solar
 P: 946 1. The problem statement, all variables and given/known data (a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit? (a) What is the minimum speed, relative to the Sun, necessary for a spacecraft to escape the solar system if it starts at the Earth's orbit? 2. Relevant equations 3. The attempt at a solution I am not exactly sure how to solve this problem. Should I use an energy approach? Do I need to calculate the escape speed for each planet, because it will pass by each one, and then sum all of the velocities together?
 Thanks P: 5,794 What does "escape" really mean? Regarding your solution, consider, for example, a trajectory perpendicular to the plane of the ecliptic. Would it pass by each planet? Secondly, consider that your speed is that sufficient to escape Jupiter; would passing by Neptune need any more speed?
 PF Gold P: 6,329 The answer is posted online. I remember looking it up. Do you know how to use Google search?
P: 946
Escaping Our Solar System

 Quote by phinds The answer is posted online. I remember looking it up. Do you know how to use Google search?
I am quite capable to use Google's search engine; however, I'd like to figure out the answer without copying and pasting.
P: 946
 Quote by voko Regarding your solution, consider, for example, a trajectory perpendicular to the plane of the ecliptic. Would it pass by each planet?
I posted a picture of the two different trajectories. The line in red is the one I believe you are talking about. The line in blue is the one I was thinking about. Does the red line describe the trajectory you were speaking about?

 Would it pass by each planet? Secondly, consider that your speed is that sufficient to escape Jupiter; would passing by Neptune need any more speed?
Well, it would seem like it would. Wouldn't the gravity of Jupiter pull on the projectile as it passed but it, thus reducing its speed? It then being possible that the speed is reduced by Jupiter's gravitational pull, the reduced speed of the projectile might then be not enough to escape Neptune's gravitational pull, to a place where Neptune's gravitational pull is negligible.

EDIT: Forgot to post picture.
Attached Thumbnails

 Thanks P: 5,794 Yes, the red line would be one perpendicular to the plane of the ecliptic. You have not said what you think "escape" means. Let's get this clear before we talk about anything else.
 P: 946 From my understanding, escape speed is the speed necessary to reach a point away from the planet where the gravitational pull is so small it is assumed to be zero, implying that gravitational potential energy is also zero. It is at an "infinite" distance. Does that seem correct? Oh, so the red line is correct. So, that's why we only have to consider the escape speed of the sun and earth, because it doesn't have to pass by the other planets; and because the projectile is at an "infinite" distance from earth's adjacent planets, that their gravitational pulls are negligible?
Thanks
P: 5,794
 Quote by Bashyboy From my understanding, escape speed is the speed necessary to reach a point away from the planet where the gravitational pull is so small it is assumed to be zero, implying that gravitational potential energy is also zero. It is at an "infinite" distance. Does that seem correct?
I think you are slightly confused. Zero potential energy does not follow from zero force of gravity. Recall that the "zero" level of any potential energy is completely arbitrary. It just happens that the "zero" level of potential energy is usually set at the infinity, and the energy is negative elsewhere. What's the formula for it?

Anyway, "escape" means "get infinitely away" and "reach zero potential energy". What about the projectile's speed and the kinetic energy "at the infinity"?

 Oh, so the red line is correct. So, that's why we only have to consider the escape speed of the sun and earth, because it doesn't have to pass by the other planets; and because the projectile is at an "infinite" distance from earth's adjacent planets, that their gravitational pulls are negligible?
Being infinitely away does not free us from having to deal with the planet's gravity. In the end, we still have to deal with the Sun's gravity in the same situation.
 P: 946 Yes, but what happens to Newton's Law of Gravitation as you go "infinitely" far? It goes to zero. In fact, it goes to zero more quickly than the Gravitational Potential Energy Function.
Thanks
P: 5,794
 Quote by Bashyboy Yes, but what happens to Newton's Law of Gravitation as you go "infinitely" far? It goes to zero. In fact, it goes to zero more quickly than the Gravitational Potential Energy Function.
 P: 946 Well, you'd use the formula $v_e = \sqrt{\frac{2GM}{r}}$, where M is the mass of the object the projectile is trying to escape, and r is the radius of that object.