Help physic to calculate btw satellite and earth

[lovelycecila]

the angular velocity of the satellite to be equal to the rotation rate of the earth.given that the radius of the Earth is 6380km and the mass Earth 5.98 * 10^24.how high the surface of Earth should satellite be placed

 

[Gib Z]

Hello lovelycecila!

It seems from the date you provided, and what result you want, that what you meant was "Orbital Velocity" rather than "angular velocity" .

On PF it is required that you show us some working and a reasonable attempt before we can offer any real help. We don't do the homework for you, after all. Think perhaps of some relevant equations, that should definitely help.

 

[baba89]

To calculate the height at which a satellite should be placed above the surface of the Earth, we need to use the formula for centripetal force:

F = (mv^2)/r

Where F is the centripetal force, m is the mass of the satellite, v is the velocity of the satellite, and r is the distance between the satellite and the center of the Earth.

First, we need to find the velocity of the satellite. We know that the angular velocity of the satellite is equal to the rotation rate of the Earth, which is 1 revolution per day or 2π radians per day. We can convert this to radians per second by dividing by the number of seconds in a day (24 hours * 60 minutes * 60 seconds), giving us a value of 7.27 * 10^-5 radians per second.

Next, we need to find the mass of the satellite. This information is not provided in the question, so we will assume a standard satellite mass of 1000 kg.

Now, we can plug in these values into the formula:

F = (mv^2)/r

F = (1000 kg)(7.27 * 10^-5 radians/second)^2 / (6380 km)

F = 0.111 N

This is the force required to keep the satellite in orbit around the Earth. To find the height at which the satellite should be placed, we can use the equation for gravitational force:

F = (GmM)/r^2

Where F is the force of gravity, G is the gravitational constant, m is the mass of the satellite, M is the mass of the Earth, and r is the distance between the satellite and the center of the Earth.

We can rearrange this equation to solve for r:

r = √(GmM/F)

Plugging in the values, we get:

r = √(6.67 * 10^-11 N m^2/kg^2 * 1000 kg * 5.98 * 10^24 kg / 0.111 N)

r = 4.2 * 10^7 meters

This is the distance from the center of the Earth to the satellite, so we need to subtract the radius of the Earth (6.38 * 10^6 meters) to get the height above the surface:

Height = 4.2 * 10^7 meters - 6