Study Guide

Forces and Motion In the Real World

  • Orbits in Space


    Sir Isaac Newton verified and explained Kepler’s elliptical planetary orbits by the development of his law of universal gravitation.

    Elliptical orbits are the most common orbits in the universe. They’re characterized by bodies which move faster when closer to what they’re orbiting, and slower when further away, with the orbited body at one of the two foci of the ellipse.

    The difference in speeds is because the force of gravity is stronger when nearer the orbited mass, which we’ll call stars from here on out. The law of universal gravity says that so if the distance is smaller, the force is larger. Planets with elliptical orbits (a.k.a. all of them) have smaller gravitational forces when they’re furthest from their star, so they travel faster when they’re nearest the star.

    The same effect is visible between orbits of different planets: Mercury is the fastest planet solely because being so close to the sun, it experiences the largest force of gravity. The slow planets are on the fringes of the solar system, where the force of gravity is small.

    The orbits in our own solar system are nearly circular, such that Isaac Newton treated the placement of the Sun at the center of a circular orbit and found enough agreement to produce the law of universal gravitation .

    Where do elliptical orbits come from? First, let’s investigate where circular orbits come from, which is when . This simplifies to . In other words, the radius and velocity have to be just right to be a circular orbit. If a body travels too fast or slow for the distance it is from the sun or star (or planet, in the case of a moon), then the orbit becomes elliptical.

    That, in a nutshell, is why elliptical orbits are the most common kind in our universe. It’s impossible for us to speed up or slow down a planet to force it into a circular orbit.

    Elliptical and circular orbits aren’t the only kind out there, though we grant that parabolic and hyperbolic paths can’t be termed orbits: they’re the paths a celestial body takes when passing through a gravitational field without being orbital material: they escape. Check out the relationships between the paths and velocities in the diagram below.

    “C” is for circle, not cookie. “E” is for ellipse, in the sense of the longest elliptical orbit possible before the orbit changes to a parabolic path.

  • Physics in the Ocean

    Surfing on Lunar Tides

    Surfing requires a lot of skills and involves a lot of physics to boot: equilibrium, friction, conservation of momentum, and buoyancy, just to name a few.

    Fortunately, surfers don’t have to know how these rules work. They just need to know how to use them well.

    Surfing on Lunar Tides sounds like a sporting event in a sci-fi trilogy of some kind, but it’s usually just called surfing.

    The Moon orbits the Earth, thanks to their mutual gravitational attraction. It’s a slightly elliptical orbit, as orbits tend to be. The force of gravity on the Moon from the Earth keeps it there. The equal-and-opposite reaction force of gravity from the Moon on the Earth does something noticeable too.

    The ocean tides are caused by the gravitational pull of the Moon on the Earth. Depending on where Earth’s natural satellite is located, a beach will have a tide that is either low or high, or somewhere in between.

    There are three separate force diagrams up there: one for the center of the earth, one for the side by the moon, and one on the opposite side of the moon. The sum of the forces on the sides contributes to the action of the tides.

    This diagram shows how the tides are dependent on the position of the Moon as it passes over the surface of the water. The Moon “pulls” the water closest to it towards it, creating a tidal bulge; consequently, the ocean on the opposite side of that tidal bulge doesn’t feel the gravitational pull as much, but the Earth-Moon center of mass orbiting the Sun is constant, so the water on the opposite side of the moon essentially “pulls back” to keep the center of mass where it belongs.

    In reality the tides are complicated by the motion of the Sun as noted by the diagram, but its position relative to Earth doesn’t affect the tides half as much as the Moon. When the Sun pulls with the Moon, the tides are higher than usual. Against it, they’re smaller.

    When the Moon is closer to Earth with its elliptical orbit, then the height difference between low and high tide is greater as well. Naturally, the converse is also true.

    A surfer scientist could determine when the maximum tides occur to his advantage. The rest of us just use a tide table.

    By the way, surfers unfortunately look like seals—a.k.a shark food—as they paddle on their boards. You never know what’s hiding underneath the surf!