Calculate the mass of Jupiter knowing that a person who weighs 490 N on the earth's surface would weight 1293 N on the surface of that planet. Jupiter has a radius of 7.15 × 107 m.
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To calculate the mass of Jupiter, we can use the concept of gravitational force and the formula for weight.
The weight of an object can be calculated using the formula: Weight = mass * acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.81 m/s^2.
Given that a person who weighs 490 N on Earth weighs 1293 N on Jupiter, we can set up the following equation:
490 N = mass * 9.81 m/s^2 (for Earth)
1293 N = mass * acceleration on Jupiter
To find the mass of Jupiter, we need to compare the acceleration on Jupiter with that on Earth.
The acceleration due to gravity on a planet can be calculated using the formula: acceleration = gravitational constant * (mass of planet / radius of planet^2)
The gravitational constant (G) is approximately 6.674 × 10^-11 m^3/(kg*s^2).
Let's solve for the acceleration on Jupiter:
acceleration on Jupiter = (6.674 × 10^-11 m^3/(kg*s^2)) * (mass of Jupiter / (7.15 × 10^7 m)^2)
Now we equate the weight on Earth to the weight on Jupiter:
mass * 9.81 m/s^2 = mass * acceleration on Jupiter
490 N = (mass * 9.81 m/s^2) / [(6.674 × 10^-11 m^3/(kg*s^2)) * (mass of Jupiter / (7.15 × 10^7 m)^2)]
By rearranging the equation and solving for the mass of Jupiter, we can find the answer.