Nozomi’s Swingby of Earth

On June 19, the Mars explorer NOZOMI came close to Earth at a distance of
approx. 11,000 km and implemented the earth swingby. This means that the
“2nd swingby” in the NOZOMI’s new orbit (see Fig. 1) was accomplished and,
accordingly, we succeeded in putting NOZOMI into the orbit that enables to
arrive at Mars in mid-December of this year.

The technology called "Swingby" has been often used for solar system
explores such as Voyager and Galileo. The purpose of this article is to
give an explanation to answer the question, "What is really swingby", that
readers must have. I am not an orbital design specialist, so, conversely
taking advantage of my non-expertise, I try to explain as plain as
possible.

Usually, making change of spacecraft’s direction or velocity in space
requires much onboard propellant. The swingby is a technology to enable
large change of spacecraft’s orbit by making use of gravity of celestial
bodies such as Earth without consuming propellant. Gravity of a celestial
body is in proportion to its mass and in inverse proportion to square of
distance from it. Spacecraft cruising interplanetary space in the solar
system is under the influence of the gravity of Sun, the biggest and exceptionally huge celestial body in the system. But, when the spacecraft
comes very close to a planet (or its satellite), gravity of the planet
exceeds that of Sun. The spacecraft, which is naturally to fly straight
near by the planet, is pulled by the force of the planet and, accordingly,
its orbit is curved.

When the spacecraft passes through the field that the
gravity of the planet works, its trajectory describes a hyperbolic curve
centering the planet (see Fig. 2 (a)). Relative velocity of the spacecraft
to the planet is the same at both entering into its gravitational field and
escaping from it. However, since the planet goes around the sun, velocity
of the spacecraft to the absolute coordinate system is changed. In case
that the spacecraft passes by the opposite face of the direction of the
planet’s revolution, it is accelerated (see Fig. 2 (b)). In case that the
spacecraft passes by the face of the direction of the planet’s revolution,
it is slowed down (see Fig. 2 (c)).

To conduct swingby, precise orbital control in advance is essential. In
preparation for the swingby in June, position of NOZOMI was accurately
determined by operations prioritizing ranging and VLBI and its orbit was
precisely adjusted. Following the orbital determination efforts conducted
for one week after the swingby, we could confirm that NOZOMI entered into
the planned orbit.