Jupiter\'s moon lo has an orbital period of 1.77 Earth days and a mean orbital r
ID: 1359581 • Letter: J
Question
Jupiter's moon lo has an orbital period of 1.77 Earth days and a mean orbital radius of 4.22 Three 10^5 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. 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. Infer the distances these planets would be from earth in this arrangement. Without doing all the calculations, decide which of the three planets would exert the strongest gravitational force on the earth. Calculate the gravitational force of the most important planet exerts on the earth. Calculate how this compares to the gravitational force the moon exerts on the earth.Explanation / Answer
You can find the mass of a planet if you know certain quantities about
a satellite in orbit around it.
The formula is T = 2*pi*SQR( R^3/G*M)
where:-
T = the time it takes the satellite to make 1 orbit - in Seconds
= 1.77 x 24 x 3600 = 1.529 10^5 sec.
R = radius of satellite orbit in metres
= 4.22 10^5 x 1000 = 4.22 10^8 metres
G = Gravitational constant
= 6.7 10^-11
M = mass of Jupiter, in Kg
It is better to rearrange the formula first.
T^2 = 4*pi^2 * R^3 / G*M
So M = 4 * pi^2 * R^3 / G * T^2
Substituting values:-
M = 4 * 9.87 * (4.22 10^8)^3 / 6.7 10^-11 * (1.529 10^5)^2
= 1.89 10^27 Kg.
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