A satellite in a circular orbit of radiusrhas time period of 4hrs. A satellite with orbital radius of 4raround the same planet will have a time period of inhours.Correct answer is '32'. Can you explain this answer?

Question

Answer

Explanation:

1. Introduction:
In this problem, we are given that a satellite is in a circular orbit of radius r with a time period of 4 hours. We need to determine the time period of a satellite with an orbital radius of 4r around the same planet.

2. Orbital Period and Radius:
The time period of an object in circular orbit can be calculated using the formula:

T = 2π√(r³/GM)

Where T is the time period, r is the radius of the orbit, G is the gravitational constant, and M is the mass of the planet.

3. Relationship between Orbital Radius and Time Period:
We can observe that the time period is dependent on the radius of the orbit. As the radius increases, the time period also increases.

4. Relationship between Orbital Radius and Time Period:
In this problem, we are given that the original satellite has a time period of 4 hours and an orbital radius of r. We need to find the time period of a satellite with an orbital radius of 4r.

5. Applying the Formula:
Let's calculate the time period of the original satellite using the given values:

T₁ = 2π√(r³/GM)

Now, let's calculate the time period of the satellite with an orbital radius of 4r:

T₂ = 2π√((4r)³/GM)

Simplifying the equation:

T₂ = 2π√(64r³/GM)

We can see that the orbital radius has increased by a factor of 4, which means the time period will also increase by a factor of √(64) = 8.

Therefore, the time period of the satellite with an orbital radius of 4r is 4 * 8 = 32 hours.

6. Conclusion:
The time period of a satellite with an orbital radius of 4r around the same planet is 32 hours.

Answer

Radius of orbit of the first satellite

R₁ = R

Time period of the first satellite T = 4 hrs. and radius of orbit of second satellite = 4r
The time period of satellite is given by

The correct answer is: 32

Similar Physics Doubts

A satellite revolves around a planet in circular orbit of radiusR(much larger than the radius of the planet) with a time period of revolutionT. If the satellite is stopped and then released in its orbits (Assume that the satellite experiences gravitational force due to the planet only).

A planet is moving around a star of mass M_{o} in a circular orbit of radius R. The star starts to lose its mass very slowly (adiabatically), and after some time, it reaches a mass M (M

A planet is moving around a star of mass M_{0} in a circular orbit of radius R. The star starts to lose its mass very slowly (adiabatically), and after some time, it reaches a mass M (M

A satellite is placed in a circular orbit about the earth whose radius is 1/50 th thedistance between the earth and the moon.If the lunar period around the earth is 28 days, the period of revolution of the satellite is approximately.

Top Courses for Physics

Suggested Free Tests

Related Content

Schools

Competitive Examinations

Quick Access Links

Technical Exams