The planet Jupiter is more than 300 times more massive than Earth. However, an object scarcely weighs 3 times as much on the surface of Jupiter as it does on the surface of the Earth. How can that be? determine the radius of Jupiter in terms of Earth radii.

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To understand why an object weighs less on the surface of Jupiter compared to Earth, we need to consider the concept of surface gravity. The weight of an object depends on both its mass and the force of gravity acting upon it.

The force of gravity can be calculated using the equation F = (G * m1 * m2) / r^2, where F represents the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r stands for the distance between the two objects (in this case, the radius of the planet).

Since we are comparing the weight of an object on Jupiter's surface to Earth's surface, we can equate the force of gravity on each planet:

(Fjupiter) = (Fearth)

(Mass of the object * Gravity of Jupiter) = (Mass of the object * Gravity of Earth)

By canceling out the mass of the object on both sides, we get:

(Gravity of Jupiter) = (Gravity of Earth)

Now let's substitute the equations for gravity:

((G * Mjupiter) / r_jupiter^2) = ((G * Mearth) / r_earth^2)

We can rearrange the equation to find the ratio of the radii:

(r_jupiter^2 / r_earth^2) = (Mjupiter / Mearth)

Given that Mjupiter is more than 300 times the mass of Mearth, we replace Mjupiter with 300Mearth:

(r_jupiter^2 / r_earth^2) = (300Mearth / Mearth)

Simplifying further:

(r_jupiter^2 / r_earth^2) = 300

Taking the square root of both sides:

(r_jupiter / r_earth) = sqrt(300)

Therefore, the radius of Jupiter in terms of Earth radii is:

r_jupiter = r_earth * sqrt(300)

It's important to note that this equation assumes that Jupiter's density is constant throughout, which is not entirely accurate. However, for basic calculations, this approximation is adequate.