Download Gravity and Orbital Motions

Gravity, Orbits, and Planets
How does gravity affect and define the orbits of satellites, comets, moons, and planets
in the solar system ?






The force due to gravity keeps the planets in orbit around the Sun, and Moon in
orbit around the Earth. Orbits are elliptical in general, with some orbits close to
circular.
According to Newton’s 1st Law, a planet would move in a straight line in the
absence of any external force. Turn off the Sun’s gravity and the Earth would move
off into interstellar space at 30 kilometers per second in a straight line.
To remain “in orbit” around another object, a satellite, moon or planet must
experience a force.
Objects orbiting at a constant speed around a more massive object still experience
a force, because the direction of their motion changes constantly, even if the
speed of their orbital motion remains constant.
Both objects in an orbiting system experience the same force, according to
Newton’s 3rd Law.
Each object (a planet or star) in a system actually orbits around their common
center-of-mass, a point lying along the line connecting the two objects.
 Mathematically, the center-of-mass for a system with two objects is expressed:
m1  d1 = m2  d2, where m1 refers to mass 1 and d1 refers to the distance
between mass 1 and the center-of-mass point.
 For the Earth – Sun system, the center-of-mass is located within the body of the
Sun, since the Sun is about 330,000 times more massive than Earth.
 For an equal mass system, the center-of-mass would be located at the mid
point of their mutual orbits.

The velocity required to reach (and remain) in orbit around a planet is defined by
the mass of the primary object AND the orbital radius.
 For Earth, this velocity is about 7 km per sec at low Earth orbit (100-500 km
above the surface). The Moon orbits Earth with a velocity of ~1 km per sec, due
to its much greater distance.
 The Earth orbits the Sun with a velocity of ~30 km per sec. The outer planets
have lower velocities.
 At larger distances from the primary object, orbital velocity decreases.

To escape from a massive object, the “escaping” object must achieve sufficient
velocity to overcome the force of gravity. That velocity would be provided by some
force, which accelerates the escaping object to the required velocity
 For Earth, escape velocity is ~10 km per sec. This speed is required to launch
spacecraft onto interplanetary trajectories.
 V(escape) = 2  V(circular)