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Physics

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    $\begingroup$ I don't think there is a "ds" in the expression of acceleration. $\endgroup$
    – Y Z
    Commented Jun 20 at 8:30
  • 1
    $\begingroup$ Use conservation of energy i.e. KE + PE = constant $\endgroup$
    – John Rennie
    Commented Jun 20 at 8:52
  • $\begingroup$ This may be helpful: en.wikipedia.org/wiki/Hyperbolic_trajectory $\endgroup$
    – PM 2Ring
    Commented Jun 20 at 9:22
  • $\begingroup$ Your object can escape Earth, but it doesn't have enough orbital energy to escape the Sun. $\endgroup$
    – PM 2Ring
    Commented Jun 20 at 9:31