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The Impossible Task of Solving a 2nd Order DE for r(t)
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[QUOTE="Repainted, post: 2367242, member: 198919"] Suppose an object is moving toward the Earth(with a direction perpendicular to the Earth's surface) at an initial speed [B]v[SUB]0[/SUB][/B], starting from a distance [B]r[SUB]0[/SUB][/B]. The object also experiences gravitational acceleration. Is it possible to obtain an expression of [B]r[/B] as a function of t? In other words, what's the distance from the Earth at a time t? I tried solving this second order differential equation: d[SUP]2[/SUP][B]r[/B]/dt[SUP]2[/SUP] = GM/[B]r[/B][SUP]2[/SUP] I ended up with a mess of stuff. And it seems impossible to make [B]r[/B] the subject of the equation. [/QUOTE]
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The Impossible Task of Solving a 2nd Order DE for r(t)
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