# Physics

An earth satellite moves in a circular orbit with an orbital speed of 5800 m/s.

Find the time (expressed in seconds) of one revolution of the satellite.

Find the radial acceleration of the satellite in its orbit.

I think we need to know the radius of the earth and the satellite's average distance from the earth in order to answer the question. All we have right now is the angular velocity. If you have that information, then use
d=v*t where d is the diameter=pi*2*r and
a=v^2/r is the angular acceleration.

The length of time it takes for a satellite to orbit the earth, its orbital period, varies with the altitude of the satellite above the earth's surface. The lower the altitude, the shorter the period. The higher the altitude, the longer the period. For example, the orbital period for a 100 mile high satellite is ~88 minutes; 500 miles ~101 minutes; 1000 miles ~118 minutes; 10,000 miles 9hr-18min; 22,238 miles 23hr-56min-4.09sec. A satellite in an equatorial orbit of 22,238 miles altitude remains stationary over a point on the Earth's equator and the orbit is called a geostationary orbit. A satellite at the same 22,238 miles altitude, but with its orbit inclined to the equator, has the same orbital period and is referred to as a geosynchronous orbit as it is in sync with the earth's rotation.
Not surprisingly, the velocity of a satellite reduces as the altitude increases. The velocities at the same altitudes described above are 25,616 fps. (17,426 mph) for 100 miles, 24,441 fps. (16,660 mph.) for 500 miles, 23,177 fps. (15,800 mph.) for 1000 miles, 13,818 fps. (9419 mph) for 10,000 miles, and 10,088 fps. (6877 mph.) for 22,238 miles.

Depending on your math knowledge, you can calculate the orbital velocity and orbital period from two simple expressions. You might like to try them out if you have a calculator.
The time it takes a satellite to orbit the earth, its orbital period, can be calculated from

T = 2(Pi)sqrt[a^3/µ]

where T is the orbital period in seconds, Pi = 3.1416, a = the semi-major axis of an elliptical orbit = (rp+ra)/2 where rp = the perigee (closest) radius and ra = the apogee (farthest) radius from the center of the earth, µ = the earth's gravitational constant = 1.407974x10^16 ft.^3/sec.^2. In the case of a circular orbit, a = r, the radius of the orbit. Thus, for a 250 miles high circular orbit, a = r = (3963 + 250)5280 ft. and T = 2(3.1416)sqrt[[[(3963+250)5280]^3]/1.407974x10^16] = ~5555 seconds = ~92.6 minutes.

The velocity required to maintain a circular orbit around the Earth may be computed from the following:

Vc = sqrt(µ/r)

where Vc is the circular orbital velocity in feet per second, µ (pronounced meuw as opposed to meow) is the gravitational constant of the earth, ~1.40766x10^16 ft.^3/sec.^2, and r is the distance from the center of the earth to the altitude in question in feet. Using 3963 miles for the radius of the earth, the orbital velocity required for a 250 miles high circular orbit would be Vc = 1.40766x10^16/[(3963+250)x5280] = 1.40766x10^16/22,244,640 = 25,155 fps. (17,147 mph.) Since velocity is inversely proportional to r, the higher you go, the smaller the required orbital velocity.

The question here is circumspect: As TchrWill points out, orbital velocity depends on radius. The slower it goes, the higher it is.

Centripetal acceleration= V^2/r
setting these equal...

v^2/r= g re^2/r^2
or r= g re^2/v^2

So period= 2PI r/V= 2PI g re^2/v^3

T= 2*3.14g*(6.38E6)^2 /(5800)^3

You do it. I get over three hours, at a very high altitude.

1. 👍 0
2. 👎 0
3. 👁 473

## Similar Questions

1. ### Physics

A satellite moves in a circular orbit around the Earth at a speed of 6.3 km/s. Determine the satellite’s altitude above the surface of the Earth. Assume the Earth is a homogeneous sphere of radius 6370 km and mass 5.98 × 1024

2. ### Physics

An artificial satellite circles the Earth in a circular orbit at a location where the acceleration due to gravity is 8.26 m/s2. Determine the orbital period of the satellite.

3. ### trig

In a computer simulation, a satellite orbits around Earth at a distance from the Earth's surface of 2.1 X 104 miles. The orbit is circular, and one revolution around Earth takes 10.5 days. Assuming the radius of the Earth is 3960

4. ### physics

A satellite moves on a circular earth orbit that has a radius of 6.68E+6 m. A model airplane is flying on a 16.3 m guideline in a horizontal circle. The guideline is nearly parallel to the ground. Find the speed of the plane such

1. ### physics (sorry about all of these!)

A satellite moves in a stable circular orbit with speed Vo at a distance R from the center of a planet. For this satellite to move in a stable circular orbit a distance 2R from the center of the planet, the speed of the satellite

2. ### gravity

You are an astronaut in the space shuttle pursuing a satellite in need of repair. You are in a circular orbit of the same radius as the satellite (450 km above the Earth), but 24 km behind it. How long will it take to overtake the

3. ### Physics

A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.70 104 m/s, and the radius of the orbit is 5.30 106 m. A second satellite also has a circular orbit around this same planet. The orbit of

4. ### Physics

A communications satellite with a mass of 450 kg is in a circular orbit about the Earth. The radius of the orbit is 2.9×10^4 km as measured from the center of the Earth. Calculate the weight of the satellite on the surface of the

1. ### Physics

Find the orbital speed of a satellite in a circular orbit 3.70×107 m above the surface of the Earth. v = 3030 m/s So I've been trying to solve this problem for some time now and haven't figured it out. What I did is find orbital

2. ### physics

An earth satellite moves in a circular orbit with an orbital speed of 6200m/s. a) find the time of one revolution. b) find the radial acceleration of the satellite in its orbit.

3. ### Physics

An Earth satellite moves in a circular orbit at a speed of 5800 m/s. a)What is the radius of the satellite's orbit? b) What is the period of the satellites orbit in hours?

4. ### physics

A satellite of mass 205 kg is launched from a site on Earth's equator into an orbit at 200 km above the surface of Earth. (a) Assuming a circular orbit, what is the orbital period of this satellite? s (b) What is the satellite's