how to better understand how dawn dusk orbits work?

Question

I am starting to study orbital mechanics and I have some doubts about the sun-synchronous orbits and particularly about dawn-dusk orbits. I often read phrases like: Often, satellites in SSO are synchronised so that they are in constant dawn or dusk – this is because by constantly riding a sunset or sunrise, they will never have the Sun at an angle where the Earth shadows them.

However, I can't figure it out, perhaps due to the absence of images or animations that make me understand in what sense the satellite rides the terminator and why it never appears to be in shadow.

I also take this opportunity to ask, if the LTAN is 6.00 am but the orbital period is 90 minutes, will the next LTAN be at 7.30 am? If the LTAN is at 6 a.m. and the orbital period is 90 minutes, how it is possible that the LTDN is at 6 p.m.? Thanks in advance for your explanations.

Answer 1

If the Earth had a spherically distributed gravitational field, a satellite's right ascension of ascending node would be constant. Right ascension of ascending node (RAAN) is expressed in Earth-centered inertial. This means the local time of the ascending node (LTAN) would be changing.

Fortunately, the Earth's gravitational field is not spherical. The Earth's rotation results in an equatorial bulge. This equatorial bulge causes RAAN to precess (or recess). The precession rate is approximately

$$\dot\Omega = -\frac32 \frac{Re^2}{a^2} J_2 n \cos i$$

where

• $\dot\Omega$ is the precession rate of the satellite's right ascension of ascending node,
• $R_e$ is the Earth's equatorial radius,
• $a$ is the semi-major axis length of the satellite's orbit,
• $J_2$ is the Earth's "second dynamic form factor", a unitless number that reflects the size of the equatorial bulge,
• $n$ is the satellite's mean motion (average orbital angular velocity), and
• $i$ is the inclination of the satellite's orbit.

Sun synchronous orbits are chosen so that RAAN precesses by 360 degrees per year, or a bit less than one degree per day. This specially-selected precession rate makes LTAN constant. Note that the inclination needs to be a bit greater than 90° to yield a sun synchronous orbit, the amount varying with orbital altitude. For a satellite orbiting at 600 km altitude, the required inclination is about 97.8°.

A dawn-dusk satellite is a special case of a sun synchronous orbit. The local time of ascending node is either 6 AM or 6 PM. This makes the local time of descending node 6 PM or 6 AM. A dawn-dusk orbit typically does not quite follow the terminator. Following the terminator would require a rather high orbit.

Most sun synchronous satellites are not dawn-dusk satellites. China launched the world's first dawn-dusk meteorological satellite a bit over a year ago. Most Earth observation satellites have a local time of ascending node sometime in the morning (e.g., 10 AM) or sometime in the afternoon (e.g., 2 PM). This makes the solar illumination angle nice in the sense of good illumination and some (but not too long) shadows.