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Chapter 8: Problem 9

How should a satellite be launched so that its orbit takes it over every point on the (rotating) Earth?

Short Answer

Expert verified
To have a satellite pass over every point on the rotating Earth, it should be launched into a polar orbit, which allows it to cover every longitudinal point as the Earth rotates on its axis.

Step by step solution

01

Understanding a Polar Orbit

A polar orbit is an orbit in which a satellite passes above or nearly above both poles of the body being orbited on each revolution. It has an inclination of about 90 degrees to the body's equator.
02

Applying the Polar Orbit to Satellites

For a satellite to cover every point on Earth, it needs to be put in a polar orbit. This way, as the Earth rotates on its axis, the satellite would be able to pass over every point on Earth.
03

Conceptualizing the Rotating Earth

Imagine the rotating Earth underneath the orbital path of the satellite. With every rotation (approximately every 24 hours), the satellite has an opportunity to cover every longitudes on Earth, given that it is in a polar orbit.

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Most popular questions from this chapter

Determine escape speeds from (a) Jupiter's moon Callisto and (b) a neutron star, with the Sun's mass crammed into a sphere of radius \(6.0 \mathrm{km} .\) See Appendix E for relevant data.

Tidal effects in the Earth-Moon system cause the Moon's orbital period to increase at a current rate of about 35 ms per century. Assuming the Moon's orbit is circular, to what rate of change in the Earth-Moon distance does this correspond? (Hint: Differentiate Kepler's third law, Equation 8.4, and consult Appendix E.)

To what radius would Earth have to shrink, with no change in mass, for escape speed at its surface to be \(30 \mathrm{km} / \mathrm{s} ?\)

What do Newton's apple and the Moon have in common?

Given the Moon's orbital radius of \(384,400 \mathrm{km}\) and period of 27.3 days, calculate its acceleration in its circular orbit, and compare with the acceleration of gravity at Earth's surface. Show that the Moon's acceleration is lower by the ratio of the square of Earth's radius to the square of the Moon's orbital radius, thus confirming the inverse-square law for the gravitational force.
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