Question

1. Suppose we discover a new stealth planet that orbits the Sun in the same plane and the same direction as the known planets. The planet has a circular orbit, orbits twice as far from the Sun as Earth. The equator of this planet is perfectly aligned with its orbital plane. Answer the following questions about the new planets. Show your work for full credit.

   1. How long is a year on the new planet?

   2. Does the new planet have seasons?

   3. How quickly does it orbit (km/s)

2. In 1 billion years, predict how the following quantities would be different from their current values. Answers should be qualitative (e.g. shorter, longer, no change) but you must explain your reasoning for full credit. [15 points]

   1. Earth-moon separation

   2. Length of the day

   3. Length of the month

   4. The height of ocean tides.

   5. Frequency of eclipses

Answer 1

PART A)

By kepler's third law

where T is the time period and is the semi-major axis

it is given that the orbit of the new planet is twice as that of earth that is if we are taking R as the radius of orbit( semi-major axis) of earth then 2R is the semi-major axisof the new planet

let be the time period of earth and be the time period of the planet

and

so time period of new planet will be 8 times the time period of earth

time period of earth is approximated as 365 days

1 yearin the new planet is

PART B)

There will be no seasons in the new palnet. thereason for the seaons in earth is because of the tilt of the Earth.

Earth is tilted by an amount of 23.5 degrees. The varying amount of sunlight around Earth during an year makesthe seasons. The earth is always pointing to one sideas it goes around the sun. So sometimes the sun is in the direction of earth is pointing but not at other times. If north pole lean towards the sun then it will be summer in northern hemisphere and winter in southern hemisphere. If north pole tiltes away from the sun it will be winter in northern hemispher and summer in southern hemisphere

In the case of new planet it is not tilted so the effect of sun will be the same all time as it revolve around the sun. The light will be incident at same rate at all time.

PART C)

we have the orbital velocity

where g is the universal gravitational constant

M is the mass of the star

R is the radius of orbit