Summary From Before:

• All orbits can be understood by Newtons Gravitational Force Law
• Orbital characteristics depend only on the distance from the sun, not the mass of the object
• Relation between orbital Period and Distance from The Sun
  • Mercury: A = 0.39 AU P = 0.24 yr
  • Venus: A = 0.72 P = 0.61
  • Mars: A = 1.52 P = 1.88
  • Jupiter: A = 5.2 P = 11.87
  • Saturn: A = 9.55 P = 29.48

• Verification: Multiply A by itself 3 times (e.g. Jupiter: 5.2 x 5.2 x 5.2 = 140.61; take the square root of this quantity and it should be very close to P; square root of 140.61 = 11.86)

Overview of Solar System Orbits:

• All planetary orbits lie very nearly in the same plane. The two biggest exceptions (apart from Mercury which orbits in curved spacetime) are Pluto with an inclination of 17 degrees and Venus with an inclination of 3.4 degrees.

• All planets revolve around the sun in the same direction (appear to move eastward with respect to the stars)

• In general, planets rotate in the same direction they are revolving around the sun (exceptions are Venus and Uranus)

• Most orbits are very nearly circular. Pluto has a large departure from circularity of 25% and Mars has a departure of 9%.

The problem of the orbit of Mercury Einstein to the rescue:

Moving Towards General Relativity

In the late 19th century, precision observations of the position of Mercury showed that it did not agree with the predictions from Newtonian theory

This is similar to the case of Mars, where Kepler used positional discrepancies to show that planetary orbits had to be elliptical in shape.

The resolution of the positional discrepancy of Mercury requires that space be "curved" in the vicinity of Mercury so that Mercury orbits inside this curvature. Such an orbit will differ slightly from an orbit in purely flat space.

Newton had implicitly assumed that space was flat.

General Theory of Relativity

Space communicates with matter and instructs it how to move and, in turn, matter communicates with space and instructs it how to curve.

Mercury orbits in Curved Space because it is a near a very large mass (the Sun).

The Visibility of the Planets:

Depends on the the planet-earth-sun angle. For the Outer Planets:

When this angle is 180 degrees , planet is overhead at midnight

When this angle is 0 degrees , the planet is up in the day time

When this angle is 90 degrees the planet is overhead at sunset

When this angle is 270 degrees the planet is overhead at sunrise

For the Inner Planets the situation is much different as they are always relatively near the Sun. There is a time in the orbit of Mercury and Venus called greatest elongation in which Venus appears at its maximum angular separation from the Sun. This is illustrated below. Note that since there are 15 degrees in one hour of time, then the angle of 46 degrees shown below corresponds to about 3 hours of time. When Venus is at the position in its orbit shown below, it will appear in the sky either 3 hours before or after sunrise. At any other position in its orbit, Venus will appear closer in time and angular separation to the sun.

For further experimentation please us Real Examples from the System Orbital Simulator