1.   A planet X has half the radius of a planet Y but the same density as planet Y. The ratio of (acceleration of free fall at surface of planet x): (acceleration of free fall at surface of planet Y) will be

A. 2:1 B. 1:2 C. 1:4 D. 1:1

2.    If the Earth's gravitational pull is centred at the core of the planet, is the force of gravity at the Poles greater than that at the Equator? (The Poles being nearer to the core due to the "flattening" of the Earth at those points).
Also, is the force of gravity at the Equator reduced to a greater degree than it is at the Poles by the opposing centrifugal force created by the Earth's spin? The latter force must range from maximum at the Equator to almost zero at the Poles?
In the event that our gravity is so effected; what is the residual difference between the Poles and Equator, how and by whom was the norm defined, and at what latitude will the norm be the exact reality?

3.    What does the gravitation force between two objects become when the distance between them is tripled?

4.    Do scientists know what causes gravity, or how it works? If so, how? If not, what are the theories?

5.   Consider two satellites, A and B, of equal mass m, moving in the same circular orbit of radius r around Earth, of mass M_E, but in OPPOSITE senses of rotation and therefore on a collision course.
    a. In terms of G, M_E, m, and r, find the total mechanical energy E_A + E_B of the two-satellite-plus-Earth system before collision.
    b. If the collision is completely inelastic so that the wreckage remains as one piece of tangled material (mass=2m), find the total mechanical energy immediately after collision.
    c. Describe the subsequent motion of the wreckage.

6.    What are
   (a) the speed and
   (b) the period of a 220 kg satellite in an approximately circular obit 640 km above the surface of Earth?
   Suppose the satellite loses mechanical energy at the average rate of 1.4x10⁵ J per orbital revolution. Adopting the reasonable approximation that the trajectory is a "circle of slowly diminishing radius," determine the satellite's
    c. altitude,
    d. speed, and
    e. period at the end of its 1500th revolution.
    f. What is the magnitude of the average retarding force?
    g. Is angular momentum around Earth's center conserved for the staellite or the satellite-Earth system?

Communication satellites are put into geostationary orbits. This means that the satellite orbits so that it stays above the same point on the Earth.

What is the period of a communication satellite? ( 1 mark)
Explain why it is useful for a communication satellite to stay above the same point on the Earth. ( 1 mark)
Show that the radius of a geostationary orbit is about 6.6 times the radius of the Earth. The following data is available:
Mass of the Earth = 6.0 x 10²⁴ kg; Radius of the Earth = 6.4 x 10⁶ m; Gravitation constant, G = 6.7 x 10^-11 Nm²kg^-2; Gravitation field at the surface of the Earth = 9.8 Nkg^-1. (5 marks)
Determine the magnitude and direction of the Earth's gravitational field at this distance. (3 marks)