1. Effects of Gravitation

2. The Gravitational Field Region surrounding a mass or body where another body experiences a force of attraction due to the first body There is a gravitational field around the earth, and it affects a body by giving it an acceleration due to gravity g, as determined by Newton’s Law of Gravitation.

3. Using Newton’s Law of Gravitation, the force of attraction between the earth and an object is given by, F = G (m e m a / r e 2 )

4. The weight of a body, w, is the total gravitational force exerted on it by the earth equivalent to m x g. So the acceleration due to gravity of a planet of mass M and radius r is given by g = G (M/r 2 )

5. Pendulum Motion Another way of deriving g is by using pendulums. A simple pendulum is just a mass suspended by a “mass less” or a string with negligible mass. Starting from a certain height an allowed to swing freely, it will move along a curved path, moving back and forth.

6. A Simple Pendulum

7. This could be assumed as uniform circular motion with a period τ, so we can use the equation for the centripetal acceleration a c. The radius of curvature will just be the length L, so a c = (4π 2 r/τ 2 ) = (4π 2 L/τ 2 )

8. At the lowest point, a c is just equal to the acceleration due to gravity g, so g = (4π 2 L/τ 2 )

9. Satellite Motion

10. Simplifying, we assume the satellite of mass m follows a uniform circular motion of radius r around a large body, like earth. We can then use this equation for centripetal acceleration, a c = (v 2 /r) directed towards the center of the larger body, like earth.

11. The centripetal acceleration is also equal to g, the acceleration due to gravity, given by g= G(m e /r 2 ) Since F = mg and from Newton’s Second Law, F = ma c, we can equate the two, so F = mg = m s a c

12. Substituting G(m e /r 2 ) for g and (v 2 /r) for a c, mG (mₑ/r 2 ) = m(v 2 /r) G (mₑ/r 2 ) = (v 2 /r) Solving for v, v=

13. To solve for period τ, τ= (2 r/v)π τ = 2 πr

14. Human Beings in Space

15. Satellites and spacecraft are said to be weightless when they are in orbit around the earth because of the influence of gravity. Aerodynamic forces on the lifting surfaces of an aircraft keep it up against the force of gravity, but a space vehicle cannot stay aloft in this way because of the absence of air in space. Spacecraft must orbit if it is to remain in space.

16. Aircraft flying in the earth’s atmosphere can cause propellers and wings for propulsion and maneuvering, but spacecraft cannot do so because of the lack of air. When spacecraft fires a rocket blast in one direction, the reaction imparts momentum to the spacecraft in the opposite direction. Space – hostile environment for human beings The vacuum of space can destroy an unprotected human body in a few seconds by explosive decompression.

17. Temperatures can become fatally high under direct solar radiation. Energetic solar and cosmic radiations – fatal to an unshielded person who is not protected by the Earth’s atmosphere. Hermitically sealed cabin or space suit, with a supply of pressurized air or oxygen to approximate conditions on Earth. Absorbing and reflecting surfaces – regulate the amount of heat radiation affecting the craft.

18. Heavy shielding – protect against solar radiation storms Crews might be sheltered in a central position within the spacecraft with supplies and equipment to surround and shield them. Spacecraft might be shaped like a large wheel that spins slowly around its own axis, or like a dumbbell, rotating end over end.