(a)Orbital speed = circumference ÷ period, v = 2πr / T.

(a)Distance = speed × time, with time converted to seconds (4.24 years × 365.25 × 24 × 3600 s/year).

(a)Orbital period increases as orbital radius increases (Kepler's Third Law).

(b)Gravitational force from the Sun provides the centripetal force needed for orbit, and this force weakens with distance (F ∝ 1/r²). A weaker centripetal force is enough to keep a more distant planet on a larger, slower orbit, so it needs a lower orbital speed than a planet closer in.

(a)Redshift is the stretching of light to longer (redder) wavelengths, observed when a light source is moving away from the observer. Nearly all distant galaxies show redshift, and more distant galaxies show greater redshift — this tells astronomers that galaxies are moving away from us, and that the universe is expanding.

(a)v = 2πr/T.

(a)distance = speed × time.

(a)Planets closer to the Sun orbit faster than planets further away.

(a)The theory that the universe began from an extremely hot, dense point and has been expanding (and cooling) ever since.

(a)Nearly all distant galaxies show redshift, and more distant galaxies show greater redshift. This is exactly what would be expected if space itself is expanding and carrying galaxies apart — consistent with the universe having expanded from a single point in the past, as the Big Bang theory describes.

(a)At a lower orbit, gravity is stronger, providing a larger centripetal force. To stay in a stable circular orbit against this stronger force, the satellite must move faster.