Time Period Of A Satellite

The satellites are the heavenly or artificial bodies that revolve around other heavier bodies in space. These satellites move on a path that is known as orbits. The time period taken by satellites to complete one revolution around the central body is said to be its time period. 

In this study material note, we will be discussing the time period of satellites and. The motion of satellites around the earth has the same characteristics as anybody in a circular motion. Let us learn about the topic with the time period of a satellite question. 

Time Period of a Satellite 

When a satellite revolves through the earth, it needs to orbit at a particular time period to maintain the orbit. By knowing the period of the satellite, we can determine its orbital radius as well. The time period of satellites is the total time to complete one revolution in orbit. 

We can determine the formula for the time period if we know the speed at which the velocity is orbiting, i.e., orbital velocity and radius of the orbit. 

We know vo the satellite’s orbital velocity, and its formula is GMR+h . As per the angular motion formula, we have a relation between linear velocity and angular velocity as:

vo=r

is the angular velocity of the satellite, determined by the formula: 2T

Here, T is the time period of the satellite. Substituting the value of is above equation, we get: 

vo=2rT 

T= 2rvo= 2r3GM

We have r = R + h and GM = gR2 we get: 

T=  2(R+h)3gR2

If the satellite is revolving too close to the earth, then, R+h R the time period will become: 

T=  2Rg

This expression is the formula of the time period of a satellite. For the satellite revolving around the earth, the time period will be: 

From the formula, we know that the time period is independent of the mass of the satellite, and it depends on the radius of the orbit and the mass of the body around which it is orbiting. 

Time Period of Satellite Questions 

• A satellite with an orbital radius has a time period as T. What will be the time period if the orbital radius becomes 4R?

Solution: Using the formula of the time period of satellite, the time period of the satellite is: 

T=  2Rg

If R = 4R, we have:

T’=  24Rg

T’=  22Rg

T’=  2T

• What would be the time period of the satellite at a distance of R from Earth’s surface?

Solution: We have the earth’s radius as R, and the satellite is at the height of R. We have the time period given as: 

T=  2(R+h)3gR2

Substituting h=R, we get:

T=  2(R+R)3gR2

T=  2(2R)3gR2

T=  28Rg

• Calculate the time period of a satellite in terms of the planet’s density, given as . 

Solution: We have the time period formula given as:

T= 2r3GM

We have volume of planet= 43r3

Density = Mass/volume

=M/43r3 

Substituting this value in the time period formula:

T= 2r3G43r3

T = 3G

• Calculate the time period of a satellite very close to earth? 

Solution: Using the time period formula:

T=  2Rg

Substituting the value of R = 6378 km and g =9.8, we get:

T=  263789.8 5075s=84 minutes

Conclusion

The satellite revolves around the earth and other heavenly bodies making circular or elliptical orbits. 

The time that these satellites take to complete one revolution is its time period. We can calculate the time period of a satellite by knowing the radius of the orbit, and the mass of the satellite does not influence its time period. 

The satellites have varieties of applications in technology and scientific research.