Page 93 - Fisika Terapan for Engineers and Scientists

Summary 293

QUESTION 3: Suppose that we launch a body horizontally from the surface of the
Earth, with a velocity exactly equal to the escape velocity of 11.2 km/s. What kind of
orbit will this body have? Ignore atmospheric friction.
QUESTION 4: Uranus has a smaller gravitational acceleration at its surface than the
Earth. Can you conclude that the escape velocity from its surface is smaller than from
the Earth’s surface?
QUESTION 5: Suppose that three comets, I, II, and III, approach the Sun. At the
instant they cross the Earth’s orbit, comet I has a speed of 42 km/s, comet II has a
larger speed, and comet III a smaller speed. Given that the orbit of comet I is parabolic,
what are the kinds of orbit for comets II and III, respectively?
(A) Elliptical; hyperbolic (B) Elliptical; parabolic (C) Hyperbolic; elliptical
(D) Hyperbolic; parabolic (E) Parabolic; elliptical

SUMMARY

PHYSICS IN PRACTICE Communication Satellites (page 281)
and Weather Satellites

MATH HELP Ellipses (page 283)

LAW OF UNIVERSAL GRAVITATION (9.1)
GMm The force on each
Magnitude: F 2 particle is directed m
r toward the other
particle.
Direction: The force on each mass is directed
r
toward the other mass. M
2
GRAVITATIONAL CONSTANT G 6.67 10 11 N m /kg 2 (9.2)

ACCELERATION OF FREE FALL ON EARTH GM E (9.6)
g 2
R E

SPEED FOR CIRCULAR ORBIT AROUND SUN GM (9.10)
v S
B r

PERIOD OF ORBIT AROUND SUN 4p 2
2
T r 3
GM
S
KEPLER’S FIRST LAW The orbits of the planets are
ellipses with the Sun at one focus.

KEPLER’S SECOND LAW The radial line segment S
from the Sun to a planet sweeps out equal areas in
equal times. Radial line sweeps out
equal areas in equal times.
KEPLER’S THIRD LAW The square of the period is
proportional to the cube of the semimajor axis of a
planetary orbit.