A particular satellite with a mass of 5x10^8 kg is put into orbit around Ganymede (the largest moon of Jupiter) at a distance 300 km from the surface. What is the gravitational force of attraction between the satellite and the moon? (Ganymede has a mass of 1.48x1023 kg and a radius of 2631 km.) b) What is the satellite's centripetal acceleration? c) What is the satellite's period of rotation?
To solve these questions, we can use Newton's law of universal gravitation, as well as centripetal acceleration and the formula for the period of rotation.
a) Gravitational force of attraction between the satellite and the moon:
The formula for gravitational force is F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the two objects.
Let's plug in the given values:
G = 6.67 × 10^(-11) N m^2/kg^2 (gravitational constant)
m1 = 5 × 10^8 kg (mass of the satellite)
m2 = 1.48 × 10^23 kg (mass of Ganymede)
r = 300 km + radius of Ganymede = 300,000 m + 2,631,000 m (since the distance is given from the surface)
Calculating the gravitational force:
F = (6.67 × 10^(-11) N m^2/kg^2 * 5 × 10^8 kg * 1.48 × 10^23 kg) / (300,000 m + 2,631,000 m)^2
Simplifying the equation will give us the value for the gravitational force.
b) Satellite's centripetal acceleration:
The formula for centripetal acceleration is a = v^2 / r, where v is the velocity of the satellite and r is the distance between the satellite and Ganymede's center.
Given that the satellite is in orbit, we know that the gravitational force and the centripetal force are equal. Therefore, we can set the gravitational force equal to the centripetal force, which can then be used to calculate the centripetal acceleration.
c) Satellite's period of rotation:
The formula for the period of rotation is T = 2π * √(r^3 / GM), where r is the distance between the satellite and Ganymede's center, G is the gravitational constant, and M is the mass of Ganymede. By using this formula, we can calculate the satellite's period of rotation.
With these formulas and the given values, you can now calculate the answers to these questions.