9.1. Kepler’s Laws http://www.ck12.org
FIGURE 9.3
Kepler’s First Law: Planet P follows an
elliptical path as it orbits the sun at focal
point F 2.FIGURE 9.4
Kepler’s Second LawCheck Your Understanding
- Show, given the information above, thatkmust have a value equal to 1.
Answer:Since the period of the Earth about the sun is one year and by definition it is a distance of one AU from the
sun, we have:
T^2 =kr^3 →( 1 )^3 =k( 1 )^2 →k= 1
- Mars is 1.52 AU from the sun. How long, in years, does it take Mars to complete one orbit about the sun? In other
words, how long is a Martian year?
Answer:
Using Kepler’s Third Law:T^2 =r^3 →T^2 = ( 1. 52 )^3 →T=
√
( 1. 52 )^3 → 1. 874 → 1. 87 years- It takes Pluto 248 years to make one orbit about the sun. What is Pluto’s average distance from the sun in AU?
Answer:r^3 =T^2 →r^3 = ( 248 )^2 →r=^3
√
( 2482 ) = 39. 47 → 39. 5 AU.
Kepler’s Third Law, in the form that we have presented it, is valid as long as the central body (the object that is being
orbited) is much more massive than the orbiting object. For example, we could time the period for a moon of Jupiter
and then use Kepler’s Third Law to find the average distance that the moon is from Jupiter (Jupiter would then be
the central body). Or we can use Kepler’s Third Law to determine the period of a satellite in orbit about the earth if
we knew its distance from the Earth (the Earth would now be the central body). Later we will learn thatrrepresents
the distance between the center of the orbiting body and the center of the central body. For the time being, though,
we will simply accept this as true without explanation.