This document provides 5 practice problems related to gravitation, gravitational force, gravitational field, satellite motion, and Kepler's Laws. The problems cover calculating gravitational force between objects of different masses on a pool table, determining gravitational acceleration and mass of a planet based on satellite motion data, calculating orbital parameters of satellites around Earth and Jupiter, and using orbital period and radius to determine the mass of Jupiter. Consultation is available for any difficulties solving the problems.

1. Problem Exercises
GRAVITATION
Here are some additional problems that you can work out. These are about gravitational force, gravitational
field, satellite motion,and Kepler’sLaws.
If you haveconcernsand difficultyin solving problems,do nothesitateto consult.
01. A coordinate system (in meters) is constructed on the surface of a pool table, the three objects are
placed on the table as follows: a 2.0-kg object at the origin of the coordinate system, a 3.0-kg object
at (-2.0, 0), and a 4.0-kg object at (4.0, 0). (a) What is the force (magnitude and direction) by the
3.0-kg object on the 2.0-kg object? (b) What is the force (magnitude and direction) by the 4.0-kg
object on the 2.0-kg object? (c) What is the net force (magnitude and direction) by the two objects
on the 2.0-kg object?
02. A man is standing on the surface of a hypothetical X-planet with a radius of 𝑅 𝑥 = 7.12 𝑥 103 km. He
drops a rock from a height of 9.0 m. It takes 5.09 s to hit the ground. (a) Calculate the acceleration
due to gravity (gravitational field) of the planet? (b) Find the mass of the X-planet given the said
data. (c) Calculate the acceleration due to gravity 50.0 km from the surface of the X-planet.
03. A certain satellite is launched and moves in a circular orbit around the Earth. The speed of the
satellite is 5000 m/s. (a) What is the orbital radius of the satellite? (b) What is the satellites
altitude above the Earth’s surface? (c) What are the period and frequency of the satellite’s orbit?
The mass of the Earth is 5.98 𝑥 1024 kg.
04. The mean distances of Venus from Sun and Mars from Sun are 𝑟𝑉𝑆 = 1.08 𝑥 1011 m and 𝑟 𝑀𝑆 =
2.28 𝑥 1011 m, respectively. If Mars has 687.5 days to complete one revolution around the Sun, what
is the period of Venus’ orbit?
05. Io, a satellite of Jupiter, has an orbital period of 1.77 days and an orbital radius of 4.22 x 105
km.
From these data, determine the mass of the Jupiter.
-Sir Bernard L.
-Sir Darwin Q.
For 3RD
Years… 