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The time period of a geostationary satellite is

Question

The time period of a geostationary satellite is

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Solution

The time period of a geostationary satellite can be determined using the formula:

T = 2π√(r³/GM)

where: T is the time period of the satellite, π is a mathematical constant approximately equal to 3.14159, r is the radius of the satellite's orbit, G is the gravitational constant, and M is the mass of the Earth.

To calculate the time period, follow these steps:

  1. Determine the radius of the satellite's orbit. This is the distance between the satellite and the center of the Earth. It is usually given in kilometers or meters.

  2. Determine the mass of the Earth. This is a constant value and is approximately 5.972 × 10^24 kilograms.

  3. Substitute the values of r and M into the formula.

  4. Calculate the square of r by multiplying it by itself.

  5. Multiply the square of r by the gravitational constant G.

  6. Multiply the result by 2π.

  7. Take the square root of the previous result.

The final value obtained will be the time period of the geostationary satellite.

This problem has been solved

Similar Questions

The time period of a geostationary satellite is(A) 24 hours (B) 12 hours(C) 365 days (D) One month

Geostationary satellites have the same period as the Earth.a.FALSEb.TRUE

Assume that the Moon is at a distance of3,00,000 km from the Earth, and that ittakes 28 days for it to orbit the Earth once.Geostationary satellites are those which areat a rest relative to the Earth. Using thesetwo facts, derive the altitude of thegeostationary satellite from the centre ofthe Earth.

A satellite follows a circular geostationary orbit, where its position can be described as x(t)=(Rsin(kt))i+(Rcos(kt))j𝑥(𝑡)=(𝑅𝑠𝑖𝑛(𝑘𝑡))i+(𝑅𝑐𝑜𝑠(𝑘𝑡))j, where R=40,000𝑅=40,000 is the radius of the orbital path in kilometres, t𝑡 is measured in hours, and k=π/12𝑘=𝜋/12.

The approximate height of a geostationary satellite is

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