A satellite is in a 7000-km -radius circular orbit around Earth. If the satellite moves to a new

Name: Problem 21, Chapter 9: Essential College Physics
Uploaded: 2021-05-28T06:59:33-08:00
Duration: 1 min 15 s
Channel: Narayan Hari
Description: A satellite is in a 7000-km -radius circular orbit around Earth. If the satellite moves to a new orbit with period twice that of the original, the new radius is (a) 10,000 km (b) 11,100 km; (c) 14,000 km (d) 19,800 km

step 1 From Kepler's third law, I can write the expression as r cubed by t square is equal to constant

Question

A satellite is in a $7000-\mathrm{km}$ -radius circular orbit around Earth. If the satellite moves to a new orbit with period twice that of the original, the new radius is (a) $10,000 \mathrm{~km}$ (b) $11,100 \mathrm{~km}$; (c) $14,000 \mathrm{~km}$ (d) $19,800 \mathrm{~km}$

   A satellite is in a $7000-\mathrm{km}$ -radius circular orbit around Earth. If the satellite moves to a new orbit with period twice that of the original, the new radius is
(a) $10,000 \mathrm{~km}$
(b) $11,100 \mathrm{~km}$;
(c) $14,000 \mathrm{~km}$
(d) $19,800 \mathrm{~km}$

Essential College Physics

Andrew F. Rex,… 1st Edition

Chapter 9, Problem 21

Instant Answer

Solved by Expert Narayan Hari

05/28/2021

Step 1

Mathematically, this can be written as: \[T^2 = kR^3\] where $T$ is the period of the orbit, $R$ is the radius of the orbit, and $k$ is a constant of proportionality. Show more…

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A satellite is in a $7000-\mathrm{km}$ -radius circular orbit around Earth. If the satellite moves to a new orbit with period twice that of the original, the new radius is (a) $10,000 \mathrm{~km}$ (b) $11,100 \mathrm{~km}$; (c) $14,000 \mathrm{~km}$ (d) $19,800 \mathrm{~km}$

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Key Concepts

Kepler's Third Law

Kepler's Third Law relates the orbital period of an object to its orbital radius, stating that the square of the period is proportional to the cube of the radius (T^2 ? r^3). This law is crucial for determining how the size of an orbit changes when the orbital period is altered, such as doubling the period.

Circular Orbits

Circular orbits are orbits where the distance between the orbiting body and the central body remains constant. In these orbits, the centripetal force required for motion is provided by gravity, simplifying the analysis of orbital mechanics problems by avoiding the complexities of elliptical orbits.

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