Suppose that a comet that was seen in 550 a. d. by chinese astronomers was spotted again in year 1941. assume the time between observations is the period of the comet and take its eccentricity as 0.997. what are (a) the semimajor axis of the comet's orbit and (b) its greatest distance from the sun?

To solve the problem it is necessary to apply the concepts related to Kepler's third law as well as the calculation of distances in orbits with eccentricities.

Kepler's third law tells us that

Where

T= Period

G= Gravitational constant

M = Mass of the sun

a= The semimajor axis of the comet's orbit

The period in years would be given by

PART A) Replacing the values to find a, we have

Therefore the semimajor axis is

PART B) If the semi-major axis a and the eccentricity e of an orbit are known, then the periapsis and apoapsis distances can be calculated by

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min