Gravitational PE for a certain distance from the Sun

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Homework Help Overview

The discussion revolves around understanding gravitational potential energy and escape velocity in the context of a problem involving the Sun and Earth's distance from it. The original poster expresses confusion regarding the assumptions made in calculating escape velocity from a specific distance rather than from the Sun's surface.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the concept of escape velocity, questioning the initial conditions and the relevance of distances involved, particularly the distinction between escaping from the Sun's surface versus a distance of 1 AU.

Discussion Status

Participants are actively clarifying the problem's requirements and the meaning of escape velocity in this context. Some have provided explanations that help frame the question more clearly, while others continue to seek further understanding of the underlying concepts.

Contextual Notes

There is a noted lack of familiarity with Kepler's laws among some participants, which may affect their understanding of the problem. The discussion also highlights the importance of distinguishing between different gravitational contexts, such as the Earth's influence versus the Sun's.

simphys
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Homework Statement
Determine the escape velocity from the Sun for an
object (a) at the Sun’s surface (##r=7E5km, M=2E30kg##)
and (b) at the average distance of the
Earth(##1.5E8km##) Compare to the speed of the Earth
in its orbit.
Relevant Equations
##U = -GM_Sm/r_S##
hello guys, sims back again with another question..

I don't understand what is up with question (b)
cuz like.. to get ##v_esc## we assume that at ##r_0=\inf## ##v=0## but now if I assume at ##r=1.5E8## that ##v=0##.
And then find ##v_esc## from the following:
##\frac12*mv_{esc}^2 - \frac{GM_Sm}{r_S} = GM_Sm/r_0## is not correct?

HOWEVER IN THE STUPID SOLUTIONS IT SAYS THAT IT'S FOUND AS IF IT'S THE Escape velocity as is written for the sun but with ##r_0## instead of ##r_S##
i.e. ##v_{esc} = \sqrt{2GM_S/r_0}##
What I don't understand is... why?

Note: I am not acquainted with kepler's laws, not covered at univ (engineering) but I'll look into it myself a bit later.
I only know the ##U_grav## and ##F_grav## and that's about it.Thanks in advance
 
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(b) is about finding the velocity required to reach infinity from Earth’s distance to the Sun, not about reaching the Earth’s distance from the Sun’s surface.
 
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Orodruin said:
(b) is about finding the velocity required to reach infinity from Earth’s distance to the Sun, not about reaching the Earth’s distance from the Sun’s surface.
wow, can you elaborate on that please? 😬
 
do you mean it's like the initial velocity needed to get FROM the sun TO the earth?
 
if so, nope doesn't make sense to me in line with the eq. ##\frac12*mv_{esc}^2 - \frac{GM_Sm}{r_S} = \frac{GM_Sm}{r_0}##
 
simphys said:
do you mean it's like the initial velocity needed to get FROM the sun TO the earth?
No, that is essentially what you did. You are being asked about the escape velocity from 1 AU to infinity.
 
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Orodruin said:
No, that is essentially what you did. You are being asked about the escape velocity from 1 AU to infinity.
arghh, unfortunately, I don't get it.. but really thank you for your help!
edit: oh wait so you are saying that the initial velocity is at the 1AU (which is I presume the distance at the Earth's surface? And then what to escape what exactly?

f.e. for the Earth the escape velocity is to escape the Earth to not return so to say. but for this idk??
 
simphys said:
arghh, unfortunately, I don't get it.. but really thank you for your help!
edit: oh wait so you are saying that the initial velocity is at the 1AU (which is I presume the distance at the Earth's surface? And then what to escape what exactly?

f.e. for the Earth the escape velocity is to escape the Earth to not return so to say. but for this idk??
No, you are still misrepresenting the problem. The Earth is irrelevant apart from giving the relevant distance. The question is: ”You are 1 AU from the Sun. How fast do you need to move to escape to infinity?”

In other terms, how fast would the Earth need to move to escape Sun’s gravity?
 
okaaay, amazing, thanks a lot! that explains it!
I'll need to go through the gravity(+Newton's synthesis) chapter to understand it better then.

But thanks a lot for explaining this one, very much appreciated!