It's almost impossible to think of something that's made without the help of mathematics, buildings, transport, technology, medicine, even clothes and food.

如果沒有數學、建築、交通、科技、醫藥，甚至衣食住行的幫助，幾乎是想都不敢想的事情。

All rely on numbers, measurements and sums.

都是靠數字、測量和求和。

Since man first looked to the stars, we have dreamed of exploring worlds beyond our own.

自從人類第一次仰望星空，我們就夢想著探索我們自己以外的世界。

In the last century, the space age began as first satellites were launched into space, followed by animals, humans and now entire space stations.

在上個世紀，隨著第一顆衛星被髮射到太空，接著是動物、人類，現在是整個空間站，太空時代開始了。

But it's extremely difficult to leave our planet and enter space, requiring complex math to calculate the massive amount of opposing force to escape the earth's gravity.

但要離開我們的星球，進入太空是非常困難的，需要複雜的數學計算出巨大的反作用力來擺脫地球引力。

Just try to jump upwards.

就試著往上跳。

That force pushing you back to Earth is gravity.

把你推回地球的力量就是引力。

One projectile that can create enough energy to beat gravity is the rocket.

有一種彈丸可以產生足夠的能量來戰勝地心引力，那就是火箭。

Early rockets were wild, inaccurate and almost impossible to control.

早期的火箭很狂野，不準確，幾乎無法控制。

Modern rockets, however, rely on complex maths to reach space.

然而，現代火箭依靠複雜的數學來到達太空。

Rockets gain speed.

火箭獲得速度。

No Nas thrust by igniting backfiring gasses from the rocket engine, creating a huge explosion.

沒有納斯的推力，通過點燃火箭發動機的反燃氣體，產生巨大的爆炸。

This force generates more kinetic energy than Earth's.

這種力量產生的動能比地球的還要大。

Gravity Thrust propels the rocket into the air fast enough to escape the speed required to do.

重力推力將火箭推進到空中，足夠快的速度來逃避所需的速度。

This is around 11 kilometers per second or over 40 0 kilometers per hour.

這大約是每秒11公里或每小時40多公里。

That's around 120 times the takeoff speed of a jumbo jet.

那是巨型噴氣機起飛速度的120倍左右。

Using mats, scientists can calculate the amount of fuel that's needed to create enough thrust to escape Earth's gravity.

利用墊子，科學家們可以計算出產生足夠的推力以擺脫地球引力所需的燃料量。

The quantity of fuel needed depends on both the weight of the rocket on the cargo or payload that it carries.

所需燃料的數量既取決於火箭對所載貨物或有效載荷的重量。

But these calculations are dependent on gravity and the bigger the planet, the greater the force.

但這些計算是依賴於重力的，星球越大，力越大。

A rocket launching from Saturn, for example, would need to reach 35.6 kilometers per second, while in zero gravity, the tiniest amount of thrust would propel the rocket a very long way as there would be no force to stop it.

例如，從土星發射的火箭需要達到每秒35.6公里的速度，而在零重力的情況下，最微小的推力也會將火箭推進很遠，因為沒有任何力量可以阻止它。

Precise mathematics is also needed in order to steer the rocket in the right direction.

為了引導火箭向正確的方向發展，還需要精確的數學。

With such high speed travel, even the smallest error could result in a rocket straying thousands of kilometers off course.

在如此高速的飛行中，即使是最小的誤差也會導致火箭偏離航線數千公里。

Nowadays, computers calculate and control space travel, but the Apollo 11 mission in 1969 relied on less powerful technology than the average modern smartphone.

如今，計算機計算和控制太空旅行，但1969年的阿波羅11號任務所依賴的技術不如一般現代智能手機強大。

Imagine what clever mathematics was used to get those first astronauts to land safely on the moon.

想象一下，那些第一批太空人是用什麼巧妙的數學方法，讓他們安全登陸月球的。

Maths has conquered our planet and made space travel a reality.

數學已經征服了我們的星球，使太空旅行成為現實。

Who knows what the future holds?

誰知道未來會怎樣？

There's almost no limit to the ways that maths benefits humanity.

數學造福人類的方式幾乎沒有限制。