Nature of orbits of satellites for different speeds


'V' be velocity with which a body is projected from Earth.
Vs be minimum velocity of object to orbit around earth
Ve be escape velocity from surface of earth

then if,

i)  V < Vs ---  body falls to ground
ii) V = Vs --- body rotates round earth in circular orbit closer to surface of Earth
iii) Vs < V < Ve --- body revolves in elliptical orbit
iv)  V = Ve ----------body just  escapes from gravitational field
v)  V > Ve  --------- body moves in interstellar space with velocity equal to √V² -Ve²
vi)  V<Ve  ---------- Total energy of body is negative
vii)  V =Ve ---------- Total energy of body is zero

Satellites - Important points to be noted

1.  Orbital velocity of satellite is independent of mass of the satellite but depends on mass of planet and radius of orbit.

2. A satellite orbiting around a planet will have both Potential energy and Kinetic energy. Here Potential energy is negative and Kinetic energy is positive.

3. Total energy of satellite is negative.

4. With the increase of height of orbit from surface of planet, for a satellite

              a) Potential energy increases (from more negative to less negative)
              b) Kinetic energy decreases
              c) Orbital velocity decreases
              d) Total energy increases
              e) Period of revolution increases

5. A satellite orbiting very close to surface of Earth is known as its surface satellite. Orbital velocity for such a satellite is V = √gR = 8 Km.S⁻¹.

6. Relative velocity of parking satellite with respective to Earth is zero.

7. Orbital linear velocity is about 3 Km.Sec⁻¹.

8. A satellite cannot be coast in a stable orbit in a plane not passing through the Earth's center.

9. If two satellite move around the Earth in its equitorial plane such that one moves from West to East and other from East to West and other from East to West, the time period of revolution of first satellite will be more compared to other.

10. If a rocket launched in equitorial plane from West to East, advantage is up to 0.47 Km.Sec⁻¹  in the launching speed.  

11. If the Kinetic energy of an orbiting satellite is E, its Potential Energy will be -2E and total energy will be -E.

12. If a body is in a satellite which does not produce its own gravity, its true weight in that satellite W' is given by

W'/W =mg'/mg  ; W' = W/(1+[h/R])²

W - Weight of body on Earth
 h  - Height of orbit of satellite
 R - Radius of Earth

so true weight is lesser than its weight on Earth.  

13.  Apparent weight of a body in a satellite is zero and is independent of radius of orbit .


FRICTION - Important Points to be remembered

1. Friction is tangential force between the contact surfaces of two bodies.

2. Friction is due to Electromagnetic Forces between the surfaces in contact.

3. Friction is due to molecular interaction at the surfaces in contact.Friction is due to adhesive forces between molecules of two surfaces in contact.

4. Friction depends on nature of surfaces in contact and on the impurities present on these surfaces.

5. Normal Force: When two bodies are in contact or when one body is placed over another body, the contact force which either body exerts on other normal to contact surface is called Normal Force or Normal Reaction.

6. Limiting Friction is least force necessary to set a body into motion.

7. Static friction is a self adjusting force.

8. Kinetic Friction is not a self adjusting friction.

9. Generally coefficient of static friction is less than 1 but in some cases it may exceed 1.

10. Frictional force is a "Non-Conservative" force.

11. If a body of mass 'm' is on the floor of a lift which is moving with uniform acceleration 'a', Normal force on body or its apparent weight is

N = mg ±ma = m(g±a)

a) If the lift moves up, then N = m(g+a)
b) If the lift moves down, then N = m(g-a)
c) If the lift falls freely, then N=0
d) If the lift moves with uniform velocity, then  a =0, and N=mg

12. When a person falls on a rough road, the frictional force exerted by road on him is along his direction of motion.

13. The angle made by resultant of Normal force and Limiting friction with Normal force is called angle of friction. The tangent of this angle gives coefficient of static friction.

14. A good lubricant must be highly viscous and low volatile in nature.