The physics of gravity and satellite motion around Jupiter.

A satellite of mass 2.00 x 104 kg is placed in orbit around Jupiter. The mass of Jupiter is 1.90 x 1027 kg. The distance between the satellite and the centre of Jupiter is 7.24 x 107 m.
a) Determine the force of gravitational attraction (Fg) between the satellite and Jupiter.
b) One of the moons of Jupiter is Io. The distance between the centre of Jupiter and the centre of Io is 4.22 x 108 m. If the force of gravitational attraction between Io and Jupiter is 6.35 x 1022 N, what must be the mass of Io?
c) If the mass of Io were to suddenly double, by what amount would the force of gravitational attraction change?
(Do not actually calculate the force of attraction; just determine how much more or less the force of gravity would change.)
d) One of the other moons that orbit Jupiter is Callisto. Its mass, mC, is 1.08 x 1023 kg. If the force of gravity between Jupiter and Callisto is 3.87 x 1021 N, then what must be the distance between the centre of Jupiter and the centre of Callisto? (This represents the radius of orbit Ro)
e) If the distance between (Ro) Jupiter and Callisto doubles, by what amount would the force of gravitational attraction (Fg) change?

i need the answer please

a) To determine the force of gravitational attraction (Fg) between the satellite and Jupiter, we can use Newton's Law of Universal Gravitation. The formula is given as:

Fg = (G * Msatellite * Mjupiter) / r^2

Where:
Fg is the force of gravitational attraction
G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2)
Msatellite is the mass of the satellite (2.00 x 10^4 kg)
Mjupiter is the mass of Jupiter (1.90 x 10^27 kg)
r is the distance between the satellite and the center of Jupiter (7.24 x 10^7 m)

Plugging in the values into the formula, we get:

Fg = (6.674 x 10^-11 N*m^2/kg^2 * 2.00 x 10^4 kg * 1.90 x 10^27 kg) / (7.24 x 10^7 m)^2

Calculating this expression will give you the force of gravitational attraction between the satellite and Jupiter.

b) To determine the mass of Io, we can rearrange the formula from part a) as follows:

Mio = (Fg * r^2) / (G * Mjupiter)

Where:
Mio is the mass of Io (what we want to find)
Fg is the force of gravitational attraction between Io and Jupiter (6.35 x 10^22 N)
r is the distance between the center of Jupiter and the center of Io (4.22 x 10^8 m)
G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2)
Mjupiter is the mass of Jupiter (1.90 x 10^27 kg)

Plugging in the given values into the formula, we can solve for Mio, which will determine the mass of Io.

c) To determine how much the force of gravitational attraction would change if the mass of Io were to double, we can use the formula from part b) and compare the calculated values for Fg with the new mass of Io (2*Mio). The change in force can be expressed as:

ΔFg = Fg_new - Fg_old

Where:
ΔFg is the change in force of gravitational attraction
Fg_new is the force of gravitational attraction with the new mass of Io (2*Mio)
Fg_old is the original force of gravitational attraction calculated in part b) (6.35 x 10^22 N)

Substituting the values into the formula and calculating the expression will give us the change in force.

d) To determine the distance between the center of Jupiter and the center of Callisto (Ro), we can rearrange the formula from part a) as follows:

Ro = sqrt(G * Mjupiter * mC / Fg)

Where:
Ro is the distance between the center of Jupiter and the center of Callisto (what we want to find)
G is the gravitational constant (approximately 6.674 x 10^-11 N*m^2/kg^2)
Mjupiter is the mass of Jupiter (1.90 x 10^27 kg)
mC is the mass of Callisto (1.08 x 10^23 kg)
Fg is the force of gravity between Jupiter and Callisto (3.87 x 10^21 N)

Plugging in the given values into the formula and solving for Ro will give us the distance between the center of Jupiter and the center of Callisto.

e) To determine how much the force of gravitational attraction would change if the distance between Jupiter and Callisto doubles, we can use the formula from part a) and compare the calculated values for Fg with the new distance (2*Ro). The change in force can be expressed as:

ΔFg = Fg_new - Fg_old

Where:
ΔFg is the change in force of gravitational attraction
Fg_new is the force of gravitational attraction with the new distance (2*Ro)
Fg_old is the original force of gravitational attraction calculated in part d) (3.87 x 10^21 N)

Substituting the values into the formula and calculating the expression will give us the change in force.