A satellite orbits the sun with a period of 1day.What is the radius of its orbit?

Short Answer

Expert verified

The radius of the orbit of the satellite is2.9×109m.

Step by step solution

01

Given information

Time period of the satellite =1day=8.64×104s.

02

Calculation

According to the Kepler's third law, the time period is given by : T2=4Ï€2R3GM.

Where, T is time period, R is the required radius of the orbit, G is the universal gravitational constant and M is mass.

We know, mass of the sun = 1.989×1030kg.

Solving we get,

T2=4π2R3GMR3=T2×GM4π2R=T2×GM4π21/3R=8.64×104s2×(6.67×10-11Nm2/kg2)(1.989×1030kg)4π21/3R=2.9×109m

03

Final answer

The radius of the orbit of the satellite is2.9×109m.

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