Math WORD PROBLEM
posted by Ty .
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.)

T1= r1/r2 * V2/V1
T1= (1700+3960)/(860+3960) * 34000/27000 
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
Respond to this Question
Similar Questions

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 … 
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 Earth, … 
physics
Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 7460 km. Satellite B is to orbit at an altitude of 20500 km. The radius of Earth … 
Physics
A communications satellite with a mass of 400 is in a circular orbit about the Earth. The radius of the orbit is 3.7×104 as measured from the center of the Earth. Calculate the gravitational force exerted on the satellite by the Earth … 
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 … 
physics
What is the radius of a communications satellite’s orbital path that is in a uniform circular orbit around Earth and has a period of exactly 24.0 hours (86,400 seconds). (Measurement is from the center of Earth.) G = 6.67 × 1011 … 
physics
A satellite is in a circular orbit around the Earth at an altitude of 3.30 106 m. (a) Find the period of the orbit. (Hint: Modify Kepler's third law so it is suitable for objects orbiting the Earth rather than the Sun. The radius of … 
Physics
The radius of the earth's orbit around the sun (assumed to be circular) is 1.50 X 108 km, and the earth travels around this orbit in 365 days. (a) What is the magnitude of the orbital velocity of the earth, in m/s? 
maths
A satellite travels around the earth in a circulsr orbit 700 kilometres above the earth's surface. Find the radius of the satellite's orbit if the radius of the earth is 6400 kilometres. Also find the distance traveled by the satellite … 
Physics 20
Astronomers launch a satellite to explore a nearby asteroid that has come dangerously close to the earth.The satellite begins orbit around the earth,with an orbital radius 6.85 X 10^3 Km, before being moved to an orbit about the asteroid …