Planetary orbits

3.2 Planetary orbits

Figure 1.13 shows the terms that are given to the orbital properties of the planets. They orbit the Sun in elliptical orbits with the Sun at one focus. A key parameter is the semi-major axis, a, which is half the major axis of the ellipse. For a circular

orbit, a will be the radius of the orbit. Due to the eccentricity, e, of their orbits their

In our Solar System Venus, whose orbit has an eccentricity of 0.007, is in a vir- tually circular orbit. Neptune and the Earth have near circular orbits with eccen- tricities of 0.01 and 0.17, respectively. Mercury and the dwarf planets Pluto and Eris have the most eccentric orbits with eccentricities of 0.205, 0.249 and 0.441, respectively. It is worth noting that, for part of its orbit, Pluto can come closer to the Sun than Neptune.

An interesting consequence of the eccentricity of the orbit of Mars is that when Mars comes closest to us (every 2 years and 2 months) its distance from us can vary signifi cantly. As a result, its angular size at closest approach will vary signifi cantly and so determine the amount of surface detail that we can see from Earth. Mars is closest to us within a few days of opposition – that is, when it is on the opposite side of the sky to the Sun – and will thus be seen approxi- mately south at midnight. Mars will be seen with the smallest angular size at opposition when Mars is furthest from the Sun (at aphelion) and the Earth is closest from the Sun (at perihelion) as shown in Figure 3.2a. Figure 3.2b shows the inverse situation when Mars will be seen with the largest angular diameter during opposition.

The Earth is at aphelion, furthest from the Sun, on July 4 each year, so the very closest approaches of Mars will occur in the summer months. The closest approach for nearly 60 000 years occurred on August 27, 2003, when Mars was

55 758 006 km from Earth and had an angular diameter of just over 25 arcsec (Figure 3.3). In contrast, if Mars is at aphelion and the Earth at perihelion at the time of closest approach, as shown in Figure 3.2b, then the angular size is just less than 14 arcsec – a very signifi cant difference!

The angular sizes observed at opposition are currently reducing and reach a

78 Introduction to Astronomy and Cosmology

Figure 3.2 The situations when Mars is seen with the smallest (a) and largest (b) angular sizes when at opposition.

Figure 3.3 Mars as observed by the Hubble Space Telescope at the time of its closest approach for 60 000 years. Image: J. Bell (Cornell U.), M. Wolff (SSI) et al., STScI, NASA.

on July 27, 2018, the angular diameter will be 24.31 arcsec – only just less than the absolute maximum.

3.2.1 Orbital inclination

The orbital inclination of a planet’s orbit is the angle at which the orbital plane of

a planet is inclined to the plane of the Solar System. The plane of the Solar System

Our Solar System 2 – The Planets

zero. The inclination angles tend to be small except in the case of Mercury, at 7°, and the dwarf planets, Pluto and Eris, at 17 and 44.2°, respectively.