Physics, 25.06.2019 12:00 orianabrown15

In 1610 galileo made a telescope and used it to study the planet jupiter. he discovered four moons. one of them was ganymede. the mean radius of the orbit of ganymede around jupiter is 10.7 × 108m and the period of the orbit is 7.16 days. i) determine the mass of jupiter.

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Answer from: JamesDelia

$1.893(10)^{27}kg$

Explanation:

This problem can be solved by the Third Kepler’s Law of Planetary motion, which states:

“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.

In other words, this law stablishes a relation between the orbital period of a body (moon, planet, satellite) orbiting a greater body in space with the size of its orbit.

This Law is originally expressed as follows:

$T^{2}=\frac{4\pi^{2}}{GM}a^{3}$ (1)

Where;

T=7.16days=618624s is the period of the orbit Ganymede describes around Jupiter

is the Gravitational Constant and its value is $6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}$

is the mass of Jupiter (the value we need to find)

$a=10.7(10)^{8}m$ is the semimajor axis of the orbit Ganymede describes around Jupiter (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit)

If we want to find , we have to express equation (1) as written below and substitute all the values:

$M=\frac{4\pi^{2}}{GT^{2}}a^{3}$ (2)

$M=\frac{4\pi^{2}}{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(618624s)^{2}}(10.7(10)^{8}m)^{3}$ (3)

Finally:

$M=1.8934(10)^{27}kg$ This is the mass of Jupiter

Answer from: Quest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

Answer from: Quest

The next element is345640

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In 1610 galileo made a telescope and used it to study the planet jupiter. he discovered four moons....

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