Flag. Change velocity, hit flag again At this distance, and at 2,280 mph, the apple orbits (it's inertia and force of gravity are balanced) What happens when forward velocity is less than orbital velocity? Greater than orbital velocity? Did Newton just wonder why apple falls down? Or did he also see an object could "fall" into orbit?
Newton realized apple could "fall" around earth, if shot forward. Without that forward speed, it falls to ground. His breakthrough idea: gravity applies to falling and orbits. He made this great connection about "falling." Newton imagined a giant cannon. With this thought experiment, he realized that orbiting objects also fall, but have enough forward velocity to continuously "fall around" earth. This threshold orbital velocity is the minimum velocity an object must achieve to maintain a stable, circular orbit around a celestial body at a specific altitude. If the initial velocity is higher, the object would be lost to space. If less, it will fall to earth eventually. If you threw an apple horizontally, from a great height, it would travel some distance before hitting the ground. With enough speed, the apple travels so far sideways that by the time gravity pulls it down, the Earth's surface would have curved away, and the apple would be falling "around" the Earth rather than toward it. So, orbital velocity is the forward velocity (horizontal speed) allowing the "satellite" to continuously fall, but miss the Earth because the planet curves away beneath it at the same rate the satellite falls. Orbital velocity is when apple's inertia and force of gravity are balanced. This balance is captured by equating the gravitational force with the centripetal force (the mass of the satellite cancels out, so that it doesn't matter), leading to: Orbital velocity v = sqrt(GM/r) where M is earth's mass So then r = GM/v*v Note: Newton's thought experiment involved a cannonball from cannon rather than apple. When initial speed out of cannon is the orbital velocity, it should keep in orbit. We assume the apple is orbiting 238,900 miles from the Earth's surface (that's about how far the moon is from earth), so it would take about 27.3 days to complete one orbit, close to the Moon's orbital period. The Moon orbits Earth at about 2,170 to 2,420 miles per hour (not constant because the orbit is elliptical). Orbital velocity v = sqrt(GM/r) Escape velocity is v = sqrt(2GM/r)
