Gravity assists: the free slingshot

ក្នុង 1977 យានអវកាស Voyager ពីរបានចាកចេញពីផែនដីនៅលើផ្លូវដែលប្រើការតម្រឹមកម្រនៃភពព្រហស្បតិ៍, ភពសៅរ៍, Uranus និង Neptune ដែលកើតឡើងម្តងក្នុងមួយ 175 ឆ្នាំឬដូច្នេះ. Each planet bent their path and flung them onward faster. Without those free boosts, Voyager 2 could never have reached Neptune in twelve years.

The planet does not give energy away. It lends you its motion.

មើល

Picture a tennis ball thrown at the front of a moving train. It bounces back faster than it was thrown, because the train was moving towards it. A gravity assist is the same idea, with gravity instead of a collision:

1. Seen from the planet, the spacecraft falls in, swings round and climbs out at exactly the same speed it came in with. Only the direction changes.
2. Seen from the Sun, the planet itself is moving at many km/s. Add that motion to the spacecraft’s before and after the flyby: because the direction changed, the total speed can be much larger after.

Passing behind the planet, in the planet’s wake, adds speed. ឆ្លងកាត់ in front យកវាចេញ;that is how Messenger slowed down to reach Mercury.

យល់

In the example, the spacecraft approaches Jupiter at v∞ = 7.5 km/s and passes 5 Jupiter radii from the centre. អ៊ីពែបូល​កោង​ទិស​របស់​វា​តាម

δ =2arcsin( 1/ e),   e = 1 + r_ p v∞² / μ

ជាមួយ μ_Jupiter = 1.267 × 10⁸ km³/s², e = 1.16 និងការវិលគឺប្រហែល 119 ដឺក្រេ ។ Adding Jupiter’s orbital velocity (13.1 km/s):

• Before: about 7.6 km/s relative to the Sun.
• After: about 19.9 km/s relative to the Sun.

យានអវកាសបានទទួលលើសពី 12 km / s ដោយមិនចាំបាច់ប្រើម៉ាស៊ីន។ ភព​ព្រះច័ន្ទ, 10²⁴ ដងធ្ងន់ជាង, បានបាត់បង់ចលនាដូចគ្នានិងបានថយចុះដោយចំនួនតិចតួចណាស់ដែលមិនធ្លាប់មានដើម្បីវាស់វែង។

មេ

ការផ្លាស់ប្តូរ​ដែល​អាច​ធ្វើ​បាន​ធំ​បំផុត​នៃ​ល្បឿន heliocentric គឺ 2 v∞ sin(δ/2) ដែល​ត្រូវ​បាន​សម្រេច​នៅពេល​ដែល​ល្បឿន​ទាក់ទង​ចូល និង ចេញ ត្រូវ​បាន​ដាក់​នៅ​ក្នុង​ភាព​ស៊ីម៉ងត៍​អំពី​ល្បឿន​របស់​ភព ។ The closer the pass (smaller r_p) and the more massive the planet, the larger δ can be, down to the limit set by the planet’s atmosphere or radius.

Gravity assists are a transfer of orbital energy in the three-body problem: in the planet’s frame energy is conserved;in the Sun’s frame the spacecraft’s energy changes by Δε = v_planet · Δv_rel. Mission designers chain them (Cassini: Venus, Venus, Earth, Jupiter) and add small powered flybys where a burn at closest approach profits from the Oberth effect.