Question

What is the mass of Jupiter ?

Answer 1

Hint: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 \[ \Rightarrow {\text{ }}\dfrac{{{a^3}}}{{{p^2}}}\]
 One Lunar Distance \[\left( {LD} \right){\text{ }} = {\text{ }}384,400{\text{ }}kilometers\]\[\left( {238,855{\text{ }}miles} \right)\]
Moon’s orbital period \[ = {\text{ }}27.322{\text{ }}days.\]
Callisto’s mean distance from Jupiter is \[1,882,700{\text{ }}kilometers\]\[\left( {1,169,856{\text{ }}miles} \right)\] and its orbital period is \[16.689{\text{ }}days.\] 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 \[16.689{\text{ }}days.\]

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

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.