\sqrt{r^2 + (vt)^2} = r \sqrt{1 + (vt/r)^2} = r + (1/2) (vt)^2 / r + o(t^2), так что вторая производная равна
v^2/r = (vr)^2 / r^3.
Числитель — (vr)^2 — это квадрат углового момента. Так что он вдоль орбиты всегда один и тот же! А знаменатель r^3 — как раз и соответствует закону всемирного тяготения: куб, как и раньше. Так что, если взять константу l = (vr)^2/ (GM), то для разницы (r-l) будет (r-l)’’ = r’’ = hr + (vr)^2 / r^3 = - GM r / r^3 + (vr)^2 / r^3 = - GM / r^3 * (r- l) = h (r-l).
Так что трёхмерный вектор R = (x,y,r-l) подчиняется центральному закону R’’ = h R, h = -GM/r^3.
\sqrt{r^2 + (vt)^2} = r \sqrt{1 + (vt/r)^2} = r + (1/2) (vt)^2 / r + o(t^2), так что вторая производная равна
v^2/r = (vr)^2 / r^3.
Числитель — (vr)^2 — это квадрат углового момента. Так что он вдоль орбиты всегда один и тот же! А знаменатель r^3 — как раз и соответствует закону всемирного тяготения: куб, как и раньше. Так что, если взять константу l = (vr)^2/ (GM), то для разницы (r-l) будет (r-l)’’ = r’’ = hr + (vr)^2 / r^3 = - GM r / r^3 + (vr)^2 / r^3 = - GM / r^3 * (r- l) = h (r-l).
Так что трёхмерный вектор R = (x,y,r-l) подчиняется центральному закону R’’ = h R, h = -GM/r^3.
Ура — теорема доказана!
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Telegram does offer end-to-end encrypted communications through Secret Chats, but this is not the default setting. Standard conversations use the MTProto method, enabling server-client encryption but with them stored on the server for ease-of-access. This makes using Telegram across multiple devices simple, but also means that the regular Telegram chats you’re having with folks are not as secure as you may believe. Channels are not fully encrypted, end-to-end. All communications on a Telegram channel can be seen by anyone on the channel and are also visible to Telegram. Telegram may be asked by a government to hand over the communications from a channel. Telegram has a history of standing up to Russian government requests for data, but how comfortable you are relying on that history to predict future behavior is up to you. Because Telegram has this data, it may also be stolen by hackers or leaked by an internal employee. Stocks dropped on Friday afternoon, as gains made earlier in the day on hopes for diplomatic progress between Russia and Ukraine turned to losses. Technology stocks were hit particularly hard by higher bond yields. Either way, Durov says that he withdrew his resignation but that he was ousted from his company anyway. Subsequently, control of the company was reportedly handed to oligarchs Alisher Usmanov and Igor Sechin, both allegedly close associates of Russian leader Vladimir Putin. This provided opportunity to their linked entities to offload their shares at higher prices and make significant profits at the cost of unsuspecting retail investors.
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