កម្លាំង​ទាក់​ទាញ​របស់​នីវ៉ូត

The force that pulls an apple to the ground is the same force that holds the Moon in its orbit and the planets around the Sun. Isaac Newton’s great idea was that one law explains them all. Here you will fire his cannon and find out why.

The Moon is falling towards Earth all the time. It just keeps missing.

មើល

Drop a ball and it falls. Throw it sideways and it still falls, but it lands farther away. Isaac Newton បានសួរសំណួរសាមញ្ញមួយ: តើធ្វើដូចម្តេចប្រសិនបើអ្នកបានបោះវា * ពិតប្រាកដ * រហ័ស?

Imagine a cannon on top of an impossibly tall mountain, above the air. Fire a cannonball slowly and it curves down and hits the ground. Fire it faster and it lands farther away. Because Earth is round, the ground curves away beneath the ball. At just the right speed, the ground curves away exactly as fast as the ball falls. The ball keeps falling, but never lands. វា​គឺ ស្ថិត​ក្នុង​អ័ក្ស.

Try it with the cannon above. Start slow, then go faster:

• Too slow: it falls back (red).
• Just right: it goes all the way around (green).
• Much faster: it escapes and never comes back (yellow).

នេះ​ក៏​ជា​មូលហេតុ​ដែល​អ្នក​បាញ់​អវកាស​ហោះ​ឡើង​លើ​ខ្យល់​ផង​ដែរ ។ They are not beyond gravity. They, and their spacecraft, are falling around Earth together.

យល់

Newton’s law of universal gravitation says every mass pulls on every other mass:

F = G · M · m / r²

• F is the force, M and m the two masses, r the distance between their centres.
• G គឺជាអថេររបស់ធរណីមាត្រ: 6.674 × 10⁻¹¹ N m² kg⁻² ។

Two ideas are packed into it:

1. រឿងធ្ងន់ធ្ងរទាញកាន់តែខ្លាំង។ ទ្វេដងនៃម៉ាស, កម្លាំងទ្វេដង។
2. Distance weakens it fast. Double the distance and the force drops to a quarter. នោះ​គឺ​ជា ច្បាប់​ការេ​ផ្ទុយ ។

Near a planet, the acceleration of anything falling is g = GM / r². សម្រាប់ផែនដីដែលផ្តល់នូវអំពី 9.8 ម៉ែត្រ / s² នៅផ្ទៃ. នៅកំពស់នៃស្ថានីយ៍អវកាសអន្តរជាតិ (ប្រហែល 420 គីឡូម៉ែត្រ) r គឺមានតែ7% ធំជាងនេះ, ដូច្នេះកម្លាំងធ្ងន់នៅតែជា 88% ខ្លាំង។

For a circular orbit, gravity must supply exactly the pull needed to keep turning the path:

v_circular = √(GM / r)

គ្រាន់តែនៅខាងលើផ្ទៃផែនដីនេះគឺប្រហែល 7.9 គីឡូម៉ែត្រ / វិនាទី។ រហ័សជាងគ្រាប់កាំភ្លើង: ប្រហែល 28,000 km / h ។

មេ

In practice we almost never use G and M separately. ផលិតផលរបស់ពួកគេ μ = GM, the gravitational parameter, ត្រូវបានវាស់ដោយផ្ទាល់និងច្បាស់លាស់ជាងមុនពីចលនានៃផ្កាយរណបនិងយានអវកាស។ សម្រាប់ផែនដី μ = 398,600.4355 km³ s⁻², ដែលត្រូវបានគេស្គាល់ថាជាផ្នែកមួយក្នុងចំណោមភាគរយរាប់ពាន់លានខណៈពេលដែល G ផ្ទាល់ត្រូវបានស្គាល់តែទៅលើ 22 ភាគរយក្នុងមួយលាន (CODATA 2018) ។ The mass of Earth quoted in tables is really μ divided by G, and it inherits G’s uncertainty.

The cannon tool solves the motion exactly for a two-body problem. A horizontal launch from radius r₀ with speed v gives angular momentum h = r₀v and a conic orbit:

r( ν) = p / (1 + ecos ν),   p = h² / μ,   e = |p / r₀ − 1|

where ν is the angle from periapsis. If v is below the circular speed, the launch point is the apoapsis and the path dips inward;if it also dips below the surface, the ball hits the ground. នៅ √( μ/ r₀) អ័ក្ស​គឺ​ជា​រង្វង់ (e =0) ។ នៅ √(2μ/r₀) វា​ក្លាយ​ជា​ប៉ារ៉ាបូឡា (e = 1) ហើយ​បាល់​រត់​ចេញ ។

Newton’s law also explains why the tool’s mountain is drawn so absurdly tall: in reality the air would slow any cannonball long before orbital speed, which is why rockets climb above most of the atmosphere before accelerating sideways.