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How to Make an Orbit

Objects in orbit are falling toward the object they orbit, but moving fast enough laterally that they always miss the object toward which they are falling. Isaac Newton recognized this when he speculated that a cannon on a high mountain firing increasingly fast cannonballs would eventually send one into orbit, thus suggesting an equivalence between planetary motion and gravitational force (see diagram).

Things You'll Need

Lightweight, energy-dense fuel for propulsion
Launch site preferably close to the equator
Multi-stage rocket

Instructions

Determining the required velocity
- 1
  Decide on the period or the height of the orbit.
  
  The reason for the need for one or the other can be shown as follows. Using Newton's second law (F=ma), the gravitational force on the satellite is equal to the satellite's mass times its angular acceleration:
  
  GMm/r^2 = (m)(ω^2r), where G is the gravitational constant, M the Earth's mass, m the satellite mass, ω the angular velocity, and r the distance to the Earth's center.
  
  ω is 2π/T , where T is the period of the orbit.
  
  T and r are unknown, so one must be selected to determine the other.
- 2
  Calculate the speed.
  
  Once T and r are known, then the lateral velocity required to maintain orbit is 2πr / T.
  
  For a twice-daily period, the height is about 20,000 km above the Earth's surface at a lateral velocity of 3,900 km/sec.
- 3
  Use a higher speed initially, to account for drag and to gain altitude during launch.
  
  The velocity calculated above is not high enough to achieve orbit, just enough to maintain it. More speed would be required to overcome atmospheric drag and the higher gravitational pull of lower altitudes.
Entering orbit
- 4
  The satellite should be launched as close to the Earth's equator as possible.
  
  This takes advantage of the Earth's rotational velocity. The opposite extreme would be to launch from a pole, where there is no rotational velocity to exploit.
- 5
  Point the rocket vertically for most of the trip to the desired altitude.
  
  This strategy is efficient because it reduces the gravitational force that needs to be propelled against as fast as possible.
- 6
  Perform a gravity turn.
  
  This consists of pointing the rocket a few degrees from vertical, to initiate lateral motion. This strategy is the most efficient because it initiates lateral velocity while keeping aerodynamic velocity minimized. Because of the lack of resistance to lateral motion at higher altitudes, little lateral thrust is needed. Lateral thrust merely needs to be applied for an extended period to gradually accelerate the satellite to the desired lateral speed.
- 7
  A launch alternative is to use a Pegasus rocket.
  
  Pegasus rockets are used for small satellites, launched from airplanes at 40,000 feet to reduce the need for expensive, specialized fuel and fuel storage equipment for the part of the launch that experiences the most air resistance.

Astronomy