May 12, 2018 is a red-letter day in the history of Bangladesh. On this day, “Bangladesh started a glorious chapter in the history with the launching of Bangabandhu-1 satellite,” President Abdul Hamid said in a message to the nation. Indeed, Bangabandhu-1 added a new milestone to the path of continued advancement of the country. Proudly displaying the flag of Bangladesh on its solar panels, the satellite is orbiting the Earth in a geostationary orbit located at 119.1 degrees east longitude.
The physics of a satellite’s orbit is remarkable. For our current knowledge of orbital motion, we owe tons of gratitude to Johannes Kepler who, in the early 17th century, relentlessly pursued the planetary orbits by putting the Sun at the centre of ‘his’ Universe. In this pursuit, he gave us three laws of planetary motion that endure to this day. Of particular interest to the motion of satellites is his third law, which states that the square of a planet’s orbital period (in years) is equal to the cube of the planet’s average distance (in astronomical unit) from the Sun. One astronomical unit is the average distance of Earth from the Sun, which is approximately 150 million km.
By working with his laws of motion and the universal law of gravitation, Isaac Newton found that Kepler’s third law is a special case of a more general law. He showed that in addition to the cube of the average distance of a planet from the Sun, square of the orbital period is also inversely proportional to the mass of the Sun. Moreover, according to Newton, the orbital speed of a small object orbiting a much more massive object depends only on its orbital radius, not on its mass. Accordingly, if satellites are closer to Earth, the pull of gravity gets stronger, and they move more quickly in their orbit.
The speed, however, depends on the mass of the massive object. That is why an astronaut does not need a tether to stay close to the International Space Station during a space walk. Even though the space station is much bigger than the astronaut, both are much smaller than Earth and thus stay together because they have the same orbital speed.
Satellites can be placed in different kinds of orbit – geosynchronous, geostationary, Sun-synchronous, semi-synchronous, orbit at Lagrange points.When a satellite is placed in a ‘sweet spot’ where, irrespective of its inclination, it orbits the Earth in the same amount of time the Earth rotates with respect to the stars, which is 23 hours 56 minutes and 4 seconds, it would appear stationary over a single longitude in the sky as seen from the Earth. This kind of orbit, where communication satellites are placed, is called geosynchronous orbit.
A special case of geosynchronous orbit is the geostationary orbit, which has a circular, geosynchronous orbit directly above the Earth’s equator. Besides communications, both orbits are also extremely useful for monitoring the weather because satellites in these orbits provide a constant view of the same surface. Using the rotational time and known mass of the Earth, we find that the orbital radius of a geostationary orbit is about 42,220 km from the centre of the Earth, which is about 35,850 km above the Earth’s surface.
Just as geosynchronous satellites have a sweet spot, satellites in a near polar orbit have a sweet spot too. If the orbits of these satellites are tilted by about eight degrees from the pole, a perturbing force produced by Earth’s oblateness would cause the orbit to precess 360 degrees during the course of the year. Satellites in such an orbit, known as Sun-synchronous or Helio-synchronous orbit, would pass over any given point on the Earth’s surface at the same local time each day. Additionally, they would be constantly illuminated by the Sun, which would allow their solar panels to work round the clock. Orbiting at an altitude between 700 and 800 km with an orbital period of roughly 100 minutes, satellites in a Sun-synchronous orbit are used for reconnaissance, mapping the Earth’s surface and as weather satellites, especially for measuring the concentration of ozone in the stratosphere and monitoring atmospheric temperature.
Many Global Positioning System (GPS) satellites are in another sweet spot known as semi-synchronous orbit. While geosynchronous orbit matches Earth’s rotational period, satellites in semi-synchronous orbit, at an altitude of approximately 20,000 kilometres, are in a 12-hour near-circular orbit. With a smaller orbital radius, a satellite would have a larger coverage of ground area on the Earth’s surface.
Other orbital sweet spots are five points located on the Earth’s orbital plane. The combined gravitational force of the Earth and the Sun acting on a satellite placed at these points, known as Lagrange points, would ensure that its orbital period is equal to that of Earth’s. Hence, the satellite will maintain its position relative to the Earth and the Sun.
The two nearest Lagrange points, one between the Earth and the Sun and the other in the opposite direction of the Sun, each 1.5 million km away from the Earth, are home to many space-based observatories. Some of them are the Solar and Heliospheric Observatory designed to study the internal structure of the Sun, the Deep Space Climate Observatory producing accurate forecasts and providing warning by monitoring dangerous space-weather conditions, and the Wilkinson Microwave Anisotropy Probe measuring the cosmic background radiation left over from the Big Bang.
The writer is a Professor of Physics at Fordham University, New York.