Download Mass of Jupiter

Mass of Jupiter
Jupiter’s moon Io has an orbital period of 1.77 Earth days and a mean orbital radius of
4.22 x 105 km. By combining Newton’s law of gravity and the expression for centripetal
force, you can determine the mass of Jupiter. Have fun “weighing” Jupiter!
When the Planets Align
Some authors seeking public attention have suggested that when many planets are “aligned” (i.e.,
are close together in the sky) their gravitational pull on the earth all acting together might
produce earthquakes and other disasters. To get an idea of whether this is plausible, set up the
following calculation.
a. Draw a sketch of the solar system and arrange the planets so that the earth, Mars, Jupiter,
Saturn are on the same side of the sun as the earth. Look up (there is a table in the back of
Understanding Physics) the radii of the planetary orbits and their masses.
b. Infer the distances these planets would be from earth in this arrangement.
c. Without doing all the calculations, decide which of the three planets would exert the
strongest gravitational force on the earth. (Hint: Use the dependence of Newton's
universal gravitation law on mass and distance to get a comparison.)
d. Calculate the gravitational force of the most important planet exerts on the earth.
e. Calculate how this compares to the gravitational force the moon exerts on the earth.
Note: In fact it is not the gravitational force itself that produces the possibly dangerous effects,
but the tidal forces — the derivative of the gravitational force. This reduces the effect by another
factor of the distance, i.e., the tidal force goes like 1/r3 instead of like 1/r2. This weakens the
planet's gravitational effect compared to the moon's by an additional factor of rearth-moon / rearthplanet, a number much less than 1.