**Energy Required to Launch a Satellite into Orbit**Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass \( m \) into circular orbit at altitude \( h \) above Earth's surface is:\[\left( \frac{G M_E m}{R_E} \right) \left( \frac{R_E + 2h}{2(R_E + h)} \right)\]**Problem:**How much energy is required to launch a 10,000 kg satellite into a 200 km altitude circular orbit around the Earth?

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Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass m into circular orbit at altitude h above Earth's surface is: GMEM RE + 2h RE 2(RE +h) How much energy is required to launch a 10,000 kg satellite into a 200 km altitude circular orbit around the Earth?

Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass m into circular orbit at altitude h above Earth's surface is: GMEM RE + 2h RE 2(RE +h) How much energy is required to launch a 10,000 kg satellite into a 200 km altitude circular orbit around the Earth?

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

**Energy Required to Launch a Satellite into Orbit**

Neglecting Earth's rotation, show that the energy needed to launch a satellite of mass \( m \) into circular orbit at altitude \( h \) above Earth's surface is:

\[
\left( \frac{G M_E m}{R_E} \right) \left( \frac{R_E + 2h}{2(R_E + h)} \right)
\]

**Problem:**

How much energy is required to launch a 10,000 kg satellite into a 200 km altitude circular orbit around the Earth?

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