{"product_id":"the-lyapunov-time-of-the-planets-plate-081-physics-poster","title":"The Lyapunov Time of the Planets – Plate 081 Physics Poster","description":"\u003cp\u003ePlate 81 speaks for itself: \u003cem\u003e“Beyond about 5 million years, even the planets can't be predicted.”\u003c\/em\u003e\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003eLaskar's integrations showed the inner Solar System is chaotic: tiny errors in the planets' positions grow exponentially with a Lyapunov time of about 5 million years.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eδ(t) ≈ δ₀ e^(t \/ t_L)\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eδ: separation between two nearby solutions, m\u003c\/li\u003e\n\u003cli\u003eδ₀: initial separation, m\u003c\/li\u003e\n\u003cli\u003et: time, s (quoted in Myr)\u003c\/li\u003e\n\u003cli\u003et_L: Lyapunov time ≈ 5 Myr, s\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eA 15 m error in Earth's position: ~150 m by 10 Myr, and ~150 million km by 100 Myr.\u003c\/p\u003e\u003ch3\u003eSources\u003c\/h3\u003e\u003cul\u003e\n\u003cli\u003eJ. Laskar, Nature 338, 237 (1989).\u003c\/li\u003e\n\u003cli\u003eJ. Laskar, Icarus 88, 266 (1990).\u003c\/li\u003e\n\u003c\/ul\u003e\u003ch3\u003eOn the poster\u003c\/h3\u003e\u003cp\u003ePlate 081, “The Lyapunov Time of the Planets”: the pixel-art plate with its slogan “Beyond about 5 million years, even the planets can't be predicted.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"9'' x 12\" (Vertical) \/ Matte","offer_id":50962683297895,"sku":"57765288572690159063","price":19.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Fine Art","offer_id":50962683330663,"sku":"51493246561402867585","price":29.99,"currency_code":"USD","in_stock":true},{"title":"9'' x 12\" (Vertical) \/ Semi Glossy","offer_id":50962683363431,"sku":"19219701948472287483","price":19.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Fine Art","offer_id":50962683396199,"sku":"27656142641195775635","price":44.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Semi Glossy","offer_id":50962683428967,"sku":"22648897333628224181","price":29.99,"currency_code":"USD","in_stock":true},{"title":"18″ x 24″ (Vertical) \/ Matte","offer_id":50962683461735,"sku":"16971356573772882172","price":29.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Matte","offer_id":50962683494503,"sku":"19543774570970218522","price":69.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Fine Art","offer_id":50962683527271,"sku":"77251575292459151961","price":119.99,"currency_code":"USD","in_stock":true},{"title":"36'' x 48\" (Vertical) \/ Semi Glossy","offer_id":50962683560039,"sku":"31275098517444979090","price":69.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/5828888376886763839_2048.jpg?v=1793636755","url":"https:\/\/pixelatedphysics.com\/zh-hans\/products\/the-lyapunov-time-of-the-planets-plate-081-physics-poster","provider":"Pixelated Physics","version":"1.0","type":"link"}