# Math WORD PROBLEM

The time in hours it takes a satellite to complete an orbit around the earth varies directly as the radius of the orbit (from the center of the earth) and inversely as the orbital velocity. If a satellite completes an orbit 860 miles above the earth in 12 hours at a velocity of 34,000 mph, how long would it take a satellite to complete an orbit if it is at 1700 miles above the earth at a velocity of 27,000 mph? (Use 3960 miles as the radius of the earth.)

1. 👍
2. 👎
3. 👁
1. T1= r1/r2 * V2/V1

T1= (1700+3960)/(860+3960) * 34000/27000

1. 👍
2. 👎
👤
bobpursley
2. The actual velocity of a satellite orbiting at 860 miles altitude is 24,113 fps.

The period derives from
T = 2(Pi)sqrt(r^3/µ) = 113.3 minutes.

The actual velocity of a satellite orbiting at 1700 miles altitude is 21,705 fps.

The period derives from
T = 2(Pi)sqrt(r^3/µ) = 144.18 minutes.

Alternatively,
T2/T1 = sqrt[(r2)^3/(r1)^3]
or T2/T1 =sqrt[5660^3/4820)^3]=1.272489

T2 = 113.3(1.272489) = 144.18

1. 👍
2. 👎

## Similar Questions

1. ### Physics

An Earth satellite moves in a circular orbit 765 km above the Earth's surface. The period of the motion is 99.9 min. (a) What is the speed of the satellite? ______ m/s (b) What is the magnitude of the centripetal acceleration of

2. ### 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

3. ### 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.

4. ### physics

An Earth satellite moves in a circular orbit 775 km above the Earth's surface. The period of the motion is 100.1 min. (a) What is the speed of the satellite? m/s (b) What is the magnitude of the centripetal acceleration of the

1. ### 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

2. ### physics

Scientists want to place a 3100 kg satellite in orbit around Mars. They plan to have the satellite orbit a distance equal to 1.9 times the radius of Mars above the surface of the planet. Here is some information that will help

3. ### Physics

Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 511 km above the earth's surface, while that for satellite B is at a height of 895 km. Find the orbital speed for satellite A and

4. ### Math

A satellite is launched into orbit 200 kilometers above the Earth.The orbital velocity of a satellite is given by the formula v=√GmE/r, where v is the velocity in meters per second, G is a given constant, mE is the mass of

1. ### physics

A satellite orbits at a distance from the Earth's center of about 4.40 Earth radii and takes 13.0 hours to go around once. What distance (in meters) does the satellite travel in one day?

2. ### geometry

A satellite in a nearly circular orbit is 2000 km above Earth's surface. The radius of Earth is approximately 6400 km. If the satellite completes its orbit in 12 hours, calculate the speed of the satellite in kilometers per

3. ### 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

4. ### physics

On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 {\rm km} above the earth's surface, and we shall assume a circular orbit. How many