IGCSE Physics 0625: Gravitational Field Strength and Elliptical Orbits

Two newly discovered exoplanets, Peris and Doven, orbit the same distant star, Halvor. Peris has a much greater mass than Doven. A comet named Ashkel also orbits Halvor, but its path is a long, narrow ellipse rather than a circle.

(a) State which of Peris or Doven produces the stronger gravitational field at a fixed distance from its centre, and explain your answer in terms of the property of a planet that determines the strength of its gravitational field. [2]

(b) The comet Ashkel's elliptical orbit is drawn on a diagram, with the star Halvor positioned inside the ellipse but noticeably off to one side, rather than in the middle. State the astronomical term for this off-centre point, and state the one special condition under which a star instead lies at the exact centre of an orbit. [2]

(c) State the difference between a minor planet, such as a dwarf planet or an asteroid, and a natural satellite (moon), giving an example of where in the Solar System each is typically found. [2]

Part (a): Comparing gravitational field strength by mass

The strength of a planet’s gravitational field, at any one fixed distance from its centre, depends on the mass of the planet producing the field. A more massive planet produces a stronger field.

Since Peris has the much greater mass, Peris produces the stronger gravitational field at a fixed distance from its centre.

Part (b): The focus of an elliptical orbit

Planets, minor planets and comets generally have elliptical orbits, and the star (or the Sun, in the Solar System) is not necessarily at the centre of that ellipse. The off-centre point where the star sits is called a focus of the ellipse.

A star lies at the exact centre of an orbit only in the special case where the orbit happens to be (approximately) circular. For a genuinely elliptical orbit like Ashkel’s, the star is offset toward one focus.

Part (c): Minor planets vs natural satellites

A minor planet, such as a dwarf planet (e.g. Pluto) or an asteroid, orbits the star directly, in the same way a full-sized planet does. Asteroids are typically found together in the asteroid belt.
A natural satellite (moon), by contrast, orbits a planet rather than orbiting the star directly. For example, the Moon orbits the Earth.

Final answers

(a) Peris has the stronger gravitational field, because field strength depends on the planet’s mass
(b) The off-centre point is a focus of the ellipse; the star is at the centre only for a circular orbit
(c) A minor planet orbits the star directly (e.g. an asteroid in the asteroid belt); a natural satellite orbits a planet (e.g. the Moon orbiting Earth)