Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about...

Question:

Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 7460 km. Satellite B is to orbit at an altitude of 20500 km. The radius of Earth is 6370 km.

(a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit?

(b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit?

(c) Which satellite (answer A or B) has the greater total energy if each has a mass of 11.4 kg?

(d) By how much?

The Orbital speed of a satellite about Earth:

A satellite that is orbiting the Earth at its orbit has an orbital speed.

The orbital speed of the satellite is given by;

{eq}v = \sqrt{\dfrac{GM}{r}} {/eq}

where,

  • {eq}M {/eq} is the mass of the Earth.
  • {eq}r {/eq} is orbiting radius of the satellite.
  • {eq}G = 6.67 \times 10^{-11} \ Nm^2/kg^2 {/eq} is the gravitational constant.

Answer and Explanation:

Given:

  • The mass of the satellite A and the satellite B is {MathJax fullWidth='false'

m_A= m_B = m = 11.4\ kg


Learn more about this topic:

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Stable Orbital Motion of a Satellite: Physics Lab

from Physics: High School

Chapter 8 / Lesson 16
627

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