Assume you are a scientist. Your group has found a new system of bodies. Th is system is made up of a star at the centre and five planets in a circular orbit around the star. Table 2 shows information on this system of bodies.
(a) Calculate the gravitational acceleration, escape velocity and orbital period of each planet.
(b) How do the values of gravitational acceleration, escape velocity and orbital period influence the suitability of a new planet to be inhabited by humans?
(c) Choose the most suitable planet to be inhabited by humans. Give a reason for your choice.
Answer:
(a)
Gravitational acceleration of a planet is calculated using the formula: $$ g=\frac{G M}{R^2} $$
Escape velocity of a planet is calculated using the formula: $$ v=\sqrt{\frac{2 G M}{R}} $$
Orbital period of a planet is calculated using the formula: $$
T=\sqrt{\frac{4 \pi^2 r^3}{G M}}
$$
(b)
– Value of g will determine the body weight of humans. A value of g that is too small or large will cause the blood circulatory system and fluids as well as internal organs in the human body to not function normally.
– A high enough escape velocity will ensure a planet has an atmosphere that is thick enough for human needs.
– Orbital period will determine changes in weather and season cycles. A period that is too short causes changes to happen too quickly and is not suitable for plants. On the other hand, too long a period causes each season to last for too long. For example, summers or winters that are too long.
(c)
Gravitational acceleration of Earth g = 9.81 m s-2
Escape velocity of Earth is 1.12 x 104 m s-1
Orbital period of Earth around the Sun is 1.00 year.
– Planet B has a gravitational acceleration closest to that of Earth.
– Humans can live comfortably with a few adjustments.
– Escape velocity of Planet B is not too small compared to the escape velocity of Earth.
– There is a high possibility that the layer of atmosphere of Planet B is thick and dense enough for human needs.
– Orbital period of Planet B is about the same as that of Earth.
– Planet B is chosen to be inhabited by humans.