Gravity pulls a satellite toward Earth's center. So why doesn't the satellite actually fall to Earth?

Imagine you're holding a ball attached to a string and spinning it around you. That's akin to how satellites orbit Earth; only instead of a string, there's gravitational pull from Earth keeping satellites in a consistent path. Every object with mass exerts a force of attraction towards other masses, a fundamental aspect of gravitational pull.

When a satellite is launched into space, Earth's gravity pulls it towards the planet's center. But why doesn't it simply fall back to Earth? That's because gravity isn’t the sole force at play. Gravitational pull serves as the 'string' pulling the satellite inward, which is counteracted by the satellite's tangential velocity - the speed at which it moves across space - ensuring it doesn’t crash into Earth but instead circles around it.

Centripetal acceleration is crucial to understanding how satellites remain in orbit. It's the acceleration that acts on any object moving along a circular path, directed towards the center of the circle or orbit. In our satellite's case, this acceleration is provided by the gravitational pull of the Earth.

Even though the satellite is moving rapidly in space, this acceleration doesn't increase the satellite's speed but rather constantly changes its direction, keeping it on a circular (or nearly circular) orbit. The balance between the satellite's velocity and Earth's gravitational pull creates a stable centripetal force that allows the satellite to 'fall' around Earth, rather than straight down into it.

Orbital mechanics, also known as celestial mechanics, is the field of study that explains the motion of objects in space. It's based on Isaac Newton's laws of motion and universal gravitation. The interplay between a satellite's velocity and Earth's gravity means the satellite is in freefall, but it has enough forward velocity to keep missing the Earth.

The path it takes is a result of these forces balancing out. Think of it like throwing a stone forward; if thrown with enough speed, it keeps falling towards the ground but also moves forwards. If able to throw it fast enough, it would fall towards the horizon perpetually, effectively orbiting the Earth. That's essentially what satellites do, facilitated by the mathematics and physics of orbital mechanics.

Tangential velocity is the velocity of an object moving along a circular path that is directed at a tangent to that path. In the context of a satellite orbiting Earth, this is the speed the satellite must maintain to stay in orbit without spiraling into Earth or drifting off into space.

A delicate balance is required here: too little speed and the satellite would plummet to Earth; too much, and it could break free of Earth's gravitational pull and escape into space. The 'just right' speed for maintaining orbit depends on the satellite's altitude; the higher the orbit, the slower the required tangential velocity. Understanding this balance is critical for keeping satellites on track and functional within their designated orbits.