A community for students.
Here's the question you clicked on:
 0 viewing
chris215
 one year ago
Va is the orbital speed of a satellite at a distance x from the centre of the Earth. If the satellite is at a distance 2x from the centre of the Earth and with the speed of Vb, which of the following statements is correct?
chris215
 one year ago
Va is the orbital speed of a satellite at a distance x from the centre of the Earth. If the satellite is at a distance 2x from the centre of the Earth and with the speed of Vb, which of the following statements is correct?

This Question is Closed

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435735326495:dw we need to use the following formula \[\huge v_{escape}^2 = \frac{ 2GM }{ r }\] so we have \[\large v_a^2 = \frac{ 2GM }{ x }\] and \[\large v_b^2 = \frac{ 2GM }{ 2x } = \frac{ GM }{ x }\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0So now we have \[\large v_a = \sqrt{\frac{ 2GM }{ x }} \implies \sqrt{2}\sqrt{\frac{ GM }{ x }}\] and we have \[\large v_b = \sqrt{\frac{ GM }{ x }}\] therefore we can say \[\huge v_a = \sqrt{2}v_b\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1for mechanical stability, we can write: \[\Large \begin{gathered} m\frac{{v_a^2}}{x} = \frac{{GMm}}{{{x^2}}} \hfill \\ \hfill \\ m\frac{{v_b^2}}{{2x}} = \frac{{GMm}}{{{{\left( {2x} \right)}^2}}} \hfill \\ \end{gathered} \] where m is the mass of our satellite, and M is the mass of Earth. Now simplifying both equations, I get: \[\Large {v_a} = \sqrt {\frac{{GM}}{x}} ,\quad {v_b} = \frac{1}{{\sqrt 2 }}\sqrt {\frac{{GM}}{x}} \] So, what can you conclude?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.0Why did you do that @Michele_Laino ?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1It is another way to solve that question @Astrophysics
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.