Gravitational Acceleration to calculate radius of Jupiter

In summary, the conversation discusses the calculation of the radius of Jupiter based on the orbital period and distance of its moon Europa, as well as the gravitational acceleration on Jupiter compared to that on Earth. The final calculated radius is approximately 74,038 km, close to the actual value of 71,492 km. There is a slight discrepancy due to assumptions made in the calculations.
  • #1
mlostrac
83
0

Homework Statement


The moon Europa, of the planet Jupiter, has an orbital period of 3.55 days and
an average distance from the center of the planet equal to 671,000 km. If the
magnitude of the gravitational acceleration at the surface of Jupiter is 2.36 times greater than that on the surface of the Earth, what is the radius of Jupiter?
(Hint: begin by calculating the rotation speed.)

radius of orbit of Europa, rm = 671000km
rotational period of Europa, T = 3.55 days
Acceleration due to gravity on Jupiter = GM/r² = 2.36g
radius of Jupiter, r = ?

Homework Equations


Rotational velocity of Europa, ω = 2π/(3.55*86400) radians/second
Centripetal acceleration, a =rmω²

The Attempt at a Solution



Gravitational acceleration on Europa
=GM/(rm)²
=(GM/r²)*r²/(rm)²
=(2.36g)(r/rm)²

Equating gravitational acceleration with centripetal acceleration,
(2.36g)(r/rm)² = rmω²
r=(rm)³ω²/(2.36g)
=74,038 km

According to Google, r(Jupiter) = 71,492 km. Did I miss something?
 
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  • #2
I don't think so, that's pretty close. You can't expect your calculation to be perfectly exact because, for example, you're implicitly assuming that Europa has a circular orbit.
 
  • #3
Ok. So I did all my calculations correctly? Do you get the same answer?

Thanks for your help
 

1. What is gravitational acceleration?

Gravitational acceleration is the acceleration experienced by an object due to the force of gravity.

2. How is gravitational acceleration calculated?

Gravitational acceleration can be calculated by dividing the force of gravity acting on an object by its mass.

3. How is gravitational acceleration related to the radius of Jupiter?

Gravitational acceleration is directly proportional to the mass of an object and inversely proportional to the square of its radius. So, as the radius of Jupiter increases, the gravitational acceleration on its surface decreases.

4. What is the formula for calculating gravitational acceleration on Jupiter?

The formula for calculating gravitational acceleration on Jupiter is g = G * M / R^2, where g is the acceleration, G is the universal gravitational constant, M is the mass of Jupiter, and R is the radius of Jupiter.

5. Why is it important to calculate the gravitational acceleration on Jupiter?

Calculating the gravitational acceleration on Jupiter is important for understanding the planet's surface conditions and its impact on objects that may land or orbit on it. It also helps in studying the planet's formation and evolution.

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