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Question: What is the mass of Jupiter ?...

What is the mass of Jupiter ?

Explanation

Solution

If a planet has an observable moon (or moons), its mass can be found out. We can compute Jupiter’s mass, relative to the mass of Earth, with Jupiter’s moon Callisto. Researchers can utilize information about how something orbits another planet, or how that planet orbits a star, to estimate a planet's mass. We can find Jupiter’s mass, relative to the mass of Earth, with Jupiter’s moon Callisto.

Complete step by step answer:
Scientists must investigate the tug of war between a planet and another object, such as a moon or star, in order to ascertain the mass of planets other than Earth.
To find Mass of a planet ⇒ a3p2 \Rightarrow {\text{ }}\dfrac{{{a^3}}}{{{p^2}}}
One Lunar Distance \left( {LD} \right){\text{ }} = {\text{ }}384,400{\text{ }}kilometers$$$$\left( {238,855{\text{ }}miles} \right)
Moon’s orbital period = 27.322 days. = {\text{ }}27.322{\text{ }}days.
Callisto’s mean distance from Jupiter is 1,882,700{\text{ }}kilometers$$$$\left( {1,169,856{\text{ }}miles} \right) and its orbital period is 16.689 days.16.689{\text{ }}days. putting these values in above we will find the mass of Jupiter.
Callisto’s mean distance from Jupiter is 1,882,700{\text{ }}kilometers$$$$\left( {1,169,856{\text{ }}miles} \right) and its orbital period is 16.689 days.16.689{\text{ }}days.

Converting Callisto’s mean distance and orbital period into lunar figures:
Callisto’s mean distance a= 4.898 lunara = {\text{ }}4.898{\text{ }}lunar
Callisto’s orbital period p= 0.611 lunarp = {\text{ }}0.611{\text{ }}lunar
We know, the mass of Jupiter ⇒ a3p2 \Rightarrow {\text{ }}\dfrac{{{a^3}}}{{{p^2}}}
Putting values from above we get
Mass of Jupiter ⇒314.756 Earth−masses{\text{ }} \Rightarrow 314.756{\text{ }}Earth - masses
We figured Jupiter’s mass relative to the Earth-moon system since the Earth comprises about 98.78%98.78\% (0.9878)\left( {0.9878} \right)of the mass in the Earth-moon system.
Therefore 10.9878×314.75=318 Earth−masses\dfrac{1}{{0.9878}} \times 314.75 = 318\,Earth - masses

Hence, Jupiter is the Solar System's largest planet and the fifth planet from the Sun.

Note: Jupiter is the largest and heaviest planet in our solar system. The mass of Jupiter is as twice as the mass of all the planets combined. Sending a spacecraft to a planet and measuring the acceleration due to gravity as the spacecraft passes by is the most accurate technique of determining its mass. If the planet has a moon, the mass can be determined using the orbit of the moon.