v = 29,000 m/s. (Wow, fast ... that converts to about 14 miles every second—much faster than, say, a
school bus.)
Along with the equation for gravitational force, you need to know the equation for gravitational
potential energy.
Why negative? Objects tend get pushed toward the lowest available potential energy. A long way away
from the sun, the r term gets big, so the potential energy gets close to zero. But, since a mass is attracted
to the sun by gravity, the potential energy of the mass must get lower and lower as r gets smaller.
We bet you’re thinking something like, “Now hold on a minute! You said a while back that an object’s
gravitational potential energy equals mgh . What’s going on?”
Good point. An object’s gravitational PE equals mgh when that object is near the surface of the Earth.
But it equals no matter where that object is.
Similarly, the force of gravity acting on an object equals mg (the object’s weight) only when that
object is near the surface of the Earth.
The force of gravity on an object, however, always equals regardless of location.Kepler’s Laws
Johannes Kepler, the late 1500s theorist, developed three laws of planetary motion based on the detailed
observations of Tycho Brahe. You need to understand each law and its consequences.
- Planetary orbits are ellipses, with the sun at one focus . Of course, we can apply this law to a
satellite orbiting Earth, in which case the orbit is an ellipse, with Earth at one focus. (We mean the
center of the Earth—for the sake of Kepler’s laws, we consider the orbiting bodies to be point
particles.) In the simple case of a circular orbit, this law still applies because a circle is just an
ellipse with both foci at the center. - An orbit sweeps out equal areas in equal times . If you draw a line from a planet to the sun, this line
crosses an equal amount of area every minute (or hour, or month, or whatever)—see Figure 15.2 . The
consequence here is that when a planet is close to the sun, it must speed up, and when a planet is far