One of the moons of Jupiter is Io. The distance between the centre of Jupiter and the centre of Io is 4.22 x 10^8 m. If the force of gravitational attraction between Io and Jupiter is 6.35 x 10^22 N, what must be the mass of Io?
You need to know the mass of Jupiter to do this problem.
Jupiter has a total mass of 1.9 x 10^27 kg.
Now use Newton's universal law of gravity to get the mass of Io.
Force = G*M(jupiter)*M(io)/R^2
G is the universal gravty cnstant.
To find the mass of Io, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for gravitational force is:
F = (G * M1 * M2) / r^2
Where:
F = gravitational force
G = gravitational constant (approximately 6.67430 × 10^-11 N m^2 kg^-2)
M1 = mass of object 1 (Jupiter)
M2 = mass of object 2 (Io)
r = distance between the centers of the two objects (4.22 x 10^8 m)
In this case, we have the value for the gravitational force between Io and Jupiter (6.35 x 10^22 N). We know the value for G, and we have the value for r. We need to solve for the mass of Io (M2).
Let's rearrange the formula to solve for M2:
M2 = (F * r^2) / (G * M1)
Substituting the given values:
M2 = (6.35 x 10^22 N * (4.22 x 10^8 m)^2) / (6.67430 × 10^-11 N m^2 kg^-2 * M1)
We still need to know the mass of Jupiter (M1) to calculate the mass of Io. Unfortunately, the mass of Jupiter is not provided in the given information. The mass of Jupiter is approximately 1.898 x 10^27 kg.
Using this value, we can substitute it into the equation to calculate the mass of Io:
M2 = (6.35 x 10^22 N * (4.22 x 10^8 m)^2) / (6.67430 × 10^-11 N m^2 kg^-2 * 1.898 x 10^27 kg)