Asatellite of mass 190 kg is placed into earth orbit at a height of 850 km above the surface.
(a) assuming a circular orbit, how long does the satellite take to complete one orbit?
(b) what is the satellite's speed?
(c) starting from the satellite on the earth's surface, what is the minimum energy input necessary to place this satellite in orbit? ignore air resistance but include the effect of the planet's daily rotation.

Explanation:

Time period of satellite

a )T =

Where G is gravitational constant , M is mass of the earth , R is radius of the earth and h is height of satellite .

= 6273 s

= 104.5 minutes

b )

Orbital speed of satellite

v_o =

=

= 7.38 km /s

c )

Orbital energy

=

=

= - 2.6 x 10⁷ J

Potential energy on the surface

= - GM / R

=- 6.67 x 10⁻¹¹ x 5.67 x 10²⁴ / 6378 x 10³

- 5.93 x 10⁷

Energy required to place the satellite in orbit at height h

= 5.93 x 10⁷  - 2.6 x 10⁷

= 3.33 x 10⁷ J

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