PHYSICS'S PROBLEM

Gravitational Field Intensity and Universal Law of Gravity

G = 6.67 x 10^-11 Nm²/kg²

Problems

Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity Gravitation and Inertia

1. A mass of 20.0 kg is located 4.0 m to the right of a mass of 30.0 kg.
a. What is the force on the 20.0 kg mass?
b. What is the force on the 30.0 kg mass?

2. At what point between the Earth and the Moon is the gravitational pull of the Earth equal in magnitude to that of the moon?

3. Find the altitude above the Earth's surface where Earth's gravitational field strength would be two-thirds of its value at the surface.

4.

Four masses form the vertices of a 1 m X 1 m square as shown. What is the gravitational force on the 3 kg mass due to the other three masses?

5. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

7. An object projected at 127 m/s upward from a small moon reaches a height of 5.08 km. If the radius of the moon is 1820 km, calculate its mass.

8. Estimate the surface gravity on a star that has five times the mass of our sun, and a radius of 10 km.

9. If the mass of Titan is 1.35*10²³ kg and it's radius is 2570 km determine

a. the force at the surface on a 500 kg boulder.

b. the acceleration due to gravity.

10. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?

11. What is the acceleration due to gravity at an altitude of 2*10⁶ m above the earth\'s surface? Earth's mass is 5.98*10²⁴ kg and of Earth's radius is 6.37*10⁶ m .

12. A 492kg uniform solid sphere has a radius of .405m. Find the magnitude of the gravitational force (in N) exerted by the sphere on a 50.4g particle located 0.197m from the center of the sphere.

13. A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?

 Problems

(See below for answers)

1. satellite altitude

The period of Earth's moon is 27.3 d and has a mean orbital radius of 3.8 x 10⁵ km. The Earth's radius is 6380 km. What is the altitude of a satellite orbiting the Earth once every 14.0 days? (search term: satellite altitude)

2. A satellite has a mass of 5850 kg and is in a circular orbit 4.1 * 10⁵ m above the surface of a planet.

The period of the orbit is two hours. The radius of the planet is 4.15 * 10⁶ m. What is the true weight of

the satellite when it is at rest on the planet's surface?

3. The orbit of the earth about the sun is almost circular. The closest and farthest distance are 1.47*10⁸ and 1.52*10⁸ km, respectively. Find the maximum variation in each of the following that result from the changing earth-sun distance in the course of 1 year.
a. kinetic energy
b. potential energy
c. total energy
d. orbital speed

4. At what horizontal velocity would a satellite have to be launched from the top of Mt. Everest to be placed in a circular orbit around the Earth?

5. The rings of a Saturn-like planet are composed of chunks of ice that orbit the planet. The inner radius of the rings is 78,000 km, while the outer radius is 190,000 km.The mass of this planet is 6.14*10²⁶ kg. Find the period of an orbiting chunk of ice at the inner radius.

6. Calculate the kinetic energy of a 1249 kg Earth satellite in a circular orbit with a radius of 13740 miles.

7. Neptune is an average distance of 4.5*10⁹ km from the sun. Estimate the length of the Neptunian year gives that the Earth is 1.50 * 10⁸ km from the sun on the average?

8. What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 169km?

(a) in m/s
(b) What is the period of revolution?

9. Use the known period 27.3 days for the moon’s orbital motion around the earth. Given the radius of the orbit as 3.84x10⁸m, calculate
a) the radius of the orbit of an earth satellite in a geosynchronous orbit with a period of 24 hours.
b)the mass of the earth.

10. Assume that you are agile enough to run across a horizontal surface at 8.5 m/s, independently of the value of the gravitational field. What would be the radius and the mass of an airless spherical asteroid of uniform density 1.1 x 10³ kg/m³ on which you could launch yourself into orbit by running? What would be your period?

11. For a certain satellite with an apogee distance of r_a=1.81*10⁷m, the ratio of the orbital speed at perigee to the orbital speed at apogee is 1.11. Find the perigee distance r_p, in meters.

12. Acceleration for a satellite is greater at its

a. same at both places b. perigee c. apogee

13. A satellite of mass 200 kg is launched from a site on Earth's equator into an orbit 200 km above the surface of Earth. Assuming a circular orbit and no air friction,

a. what is the orbital period of this satellite

b. what is the speed of the satellite in its orbit

c. what is the minimum energy necessary to place the satellite in orbit?