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CENTRIPETAL FORCE=
<=
/span>Unit 14Dr. Joh=
n P.
Cise, Professor of Physics, Austin Com.College, 1212 Rio Grande St., AustinTx.78701jpcise@austincc.edu& New York TimesDec. 17,2009byDennis Overbye
Hints=
=
(continued):
0.62 miles =3D=
1 km,
Fcis supplied from
the gravitation=
al
force =3D G MpMs/r2,
G =3D 6.67 X 10=
–11
Solve using mks=
units.
ANSWER:~ 3 X 1029 kg<=
/o:p>
Quest=
ion:(=
b) Verify the density of this planet is
1/3 the densit=
y of the
earth.? Dearth =3D5515 kg/m3, rearth=
=3D6378
km.
Astronomers said Wedn=
esday
that they had discovered a planet composed mostly of wat=
er.
You would not want to live there. Besides the heat
— 400 degrees Fahrenheit on the ocean surface — the planet is
probably cloaked in a dark fog of superheated steam and other gases. But its
discovery has encouraged a growing feeling among astronomers that they are =
on
the verge of a breakthrough and getting closer to finding a planet that
something could live on. Only 2.7 times the size of Earth and 6.6 times=
as
massive, the new pla=
net
takes 38 hours to circle a dim red star, GJ 1214,<=
/i>
in the constellation Ophiuchus — about 40 light-years from here. It is
one of the lightest and smallest so-called extrasolar planets yet found, pa=
rt
of a growing class of planets that are less than 10 times the mass of Earth=
. In the 15 years since the first extrasolar planet was=
found,
more than 400 have been detected.The field is getting more
intense as dedicated planet-hunting instruments like the Kepler satellite f=
rom
the National Aeronautics and Space Administration,
due to report a new batch of such planets next month, get into the gameR=
21; Dr.
Charbonneau’s planet, only 1.3 million miles from its home star, is distinguished by its re=
lative
coolness — a consequence of the dimness of GJ 1214, wh=
ich
puts out one three-hundredth of the Sun’s energy. In May, Z=
achory
Berta, a first-year graduate student of Dr. Charbonneau, called the
group’s attention to blips in the Ophiuchus star that seemed to be
happening every 1.6 days. If he was right, Mr. Berta said, the next transit
would occur at 6 a.m. on May 13.
From the drop in starlight, the astronomers could calculate the diameter of the Ophiuchus planet=
,
known now as GJ 1214b. Then they used a sensitive spectrograph on a 3.6-met=
er
telescope in Chile to measure its gravitational tug on the star, thus deriving the planet’s mass. Using
those two numbers, Dr. Charbonneau and his colleagues could calculate the density of the planet, about one-third that of Earth<=
/span>.