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Abstract
Although the sun is seen to move across the sky each day, we believe that this is due to the earth’s really rotating on its axis rather than to the sun’s really revolving around the earth.
The stars are scattered across the sky in patterns that imaginative minds have seen as all manner of objects and creatures- the Big Dipper, the flying horse, Pegasus.......etc.
It is easily seen, the North Star appears motionless; the others all appear to move around it in arcs of circles during the course of the night.
As a matter of fact the planets revolve in elliptical orbits about the sun which is at one focus of the ellipse, satellites (natural or man-made) may revolve around planets in elliptical orbits.
The motion of an object in an inverse square field (Newton’s universal law of gravitational) need not always be elliptical but may be parabolic or hyperbolic; according to the total energy E.
(i) If E < 0 the path is an ellipse
(ii) If E = 0 the path is a parabola
(iii) If E > 0 the path is a hyperbola
The speed v of a particle moving in an elliptical path is
where G is the universal gravitation constant ,M is the mass of the earth, a is the semi major axis
Finally we calculate the Astronomical speeds
(i) First Astronomical speed the minimum speed needed to move the object in an elliptical orbit about the earth 7.905 km/s
(ii) Second Astronomical speed the minimum speed needed to escape the object from the gravity of the earth and is equal to 11.1862 km/s
(iii) Third Astronomical speed the minimum speed needed to escape the object from the gravity of the solar system and equal to 16.66 km/s