A satellite orbits around the earth. The mass of the satellite is 1170 kg, and its altitude is 220 km. The mass of the earth is 5.98×1024 kg. The radius of the earth is 6.38×106 m.

1)What is the gravitational force on the satellite?
2)What is the orbital velocity of the satellite?
3)What is the period of the satellites motion?
4)What is the gravitational potential energy of the satellite?
5)What is the total mechanical energy of the satellite in orbit?

Part 1

Fg = m1m2g/d^2

force of gravity = (mass 1)(mass 2)(gravitational constant)/distance^2

Fg =(1170kg)(5.98 x 10^24kg)(g)/(220km + 6.38 x10^6)

I don't remember what the exact value for g (gravitational constant) is, but you can probably get that from your text. It might be
6.67 x 10^-11 N m^2/kg^2

Miss X meant G, not g.

Fg=GMeMs/(re+alt)^2 watch units.

Orbital velocity: Fg=Fcent
Fg= Ms*v^2/(re+alt)

solve for v
Period:
Period= 2PI*(re+alt)/velocity

GPE= -GMeMs/(re+alt)

total: GPE+ KE

Step 1: Find the gravitational force on the satellite.

The gravitational force between two objects can be calculated using the formula F = (G * m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant (6.67430 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.

Given:
Mass of satellite (m1) = 1170 kg
Mass of Earth (m2) = 5.98 × 10^24 kg
Radius of Earth (r) = 6.38 × 10^6 m

Using the formula, we can calculate the gravitational force:

F = ( G * m1 * m2 ) / r^2
F = ( 6.67430 × 10^-11 N m^2/kg^2 * 1170 kg * 5.98 × 10^24 kg ) / ( 6.38 × 10^6 m )^2

Calculating the gravitational force will give you the answer to the first question.

Step 2: Find the orbital velocity of the satellite.

The formula for orbital velocity is v = √(G * M / r), where v is the orbital velocity, G is the gravitational constant, M is the mass of the object being orbited (in this case, Earth), and r is the distance between the center of Earth and the satellite.

Using the given values:

Mass of Earth (M) = 5.98 × 10^24 kg
Radius of Earth (r) + Altitude = 6.38 × 10^6 m + 220 km = (6.38 × 10^6 m) + (220,000 m)

Calculating the orbital velocity will give you the answer to the second question.

Step 3: Find the period of the satellite's motion.

The formula for the period of an object in circular motion is T = (2π * r) / v, where T is the period, r is the radius (distance between the center of Earth and the satellite), and v is the orbital velocity.

Using the values of r and v calculated in the previous steps:

Period (T) = (2π * r) / v

Calculating the period will give you the answer to the third question.

Step 4: Find the gravitational potential energy of the satellite.

The gravitational potential energy can be calculated using the formula PE = - (G * m1 * m2) / r, where PE is the gravitational potential energy.

Using the values for G, m1, m2, and r:

PE = - ( G * m1 * m2) / r

Calculating the gravitational potential energy will give you the answer to the fourth question.

Step 5: Find the total mechanical energy of the satellite in orbit.

The total mechanical energy of an object in orbit is the sum of its kinetic energy and gravitational potential energy. Since the satellite is in orbit, its potential energy is negative.

Total Mechanical Energy = Kinetic Energy + Gravitational Potential Energy

Calculating the total mechanical energy will give you the answer to the fifth question.

1) To calculate the gravitational force on the satellite, we can use the formula for gravitational force:

F = (G * m1 * m2) / r^2

where F is the gravitational force, G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2), m1 and m2 are the masses of the objects (in this case, the mass of the satellite and mass of the Earth), and r is the distance between the centers of the objects (in this case, the altitude of the satellite plus the radius of the Earth).

Plugging in the values:
Mass of the satellite (m1) = 1170 kg
Mass of the Earth (m2) = 5.98 × 10^24 kg
Distance (r) = altitude of the satellite (220 km) + radius of the Earth (6.38 × 10^6 m)

Calculate F = (6.67 × 10^-11 * 1170 * 5.98 × 10^24) / (220000 + 6.38 × 10^6) ^ 2

2) To find the orbital velocity of the satellite, we can use the formula for orbital velocity:

v = sqrt((G * m2) / r)

where v is the orbital velocity, G is the gravitational constant, m2 is the mass of the Earth, and r is the distance between the center of the Earth and the satellite (the altitude plus the radius of the Earth).

Plug in the values:
Mass of the Earth (m2) = 5.98 × 10^24 kg
Distance (r) = altitude of the satellite (220 km) + radius of the Earth (6.38 × 10^6 m)

Calculate v = sqrt((6.67 × 10^-11 * 5.98 × 10^24) / (220000 + 6.38 × 10^6))

3) To find the period of the satellite's motion, which is the time it takes to complete one orbit, we can use the formula for period:

T = 2π * sqrt((r^3) / (G * m2))

where T is the period, G is the gravitational constant, m2 is the mass of the Earth, and r is the distance between the center of the Earth and the satellite (the altitude plus the radius of the Earth).

Plug in the values:
Mass of the Earth (m2) = 5.98 × 10^24 kg
Distance (r) = altitude of the satellite (220 km) + radius of the Earth (6.38 × 10^6 m)

Calculate T = 2π * sqrt(((220000 + 6.38 × 10^6)^3) / (6.67 × 10^-11 * 5.98 × 10^24))

4) To find the gravitational potential energy of the satellite, we can use the formula:

U = (-G * m1 * m2) / r

where U is the gravitational potential energy, G is the gravitational constant, m1 and m2 are the masses of the objects (the mass of the satellite and the mass of the Earth), and r is the distance between the centers of the objects (altitude of the satellite plus the radius of the Earth).

Plug in the values:
Mass of the satellite (m1) = 1170 kg
Mass of the Earth (m2) = 5.98 × 10^24 kg
Distance (r) = altitude of the satellite (220 km) + radius of the Earth (6.38 × 10^6 m)

Calculate U = (-6.67 × 10^-11 * 1170 * 5.98 × 10^24) / (220000 + 6.38 × 10^6)

5) The total mechanical energy of the satellite in orbit is the sum of its kinetic energy and gravitational potential energy. Assuming there is no other form of energy, we can find the total mechanical energy by adding the kinetic energy and gravitational potential energy together.