Why calculation of Position and Momentum of subatomic particles is not possible simultaneously?

according to the uncertainty principle, which of the following statements is true?

a) It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy.

b) It is impossible to simultaneously determine both the energy and the momentum of a particle with arbitrary accuracy.

c) It is impossible to measure the position of a particle with arbitrary accuracy in a finite amount of time.

d) It is impossible to simultaneously measure both the energy and position of a particle with arbitrary accuracy.

e) It is impossible to determine a particle's energy with arbitrary accuracy in a finite amount of time.

Astronomy Parallax Lab

SCENARIO: Your lab group is planning an expedition to measure the distance to Mars by carefully measuring its position in the sky from two locations simultaneously when it is next at “opposition” (that is, when it is exactly opposite from the sun in the sky) on October 13, 2020. For the best, and most straightforward distance determination with the parallax method, Mars should be high in the sky (as near to your zenith as possible).  This can be done by observing Mars: (a) from locations whose LATITUDES are similar to the DECLINATION of Mars at the date of measurement and (b) at the time of night when Mars is highest in the sky.

1a). Determine the Sky Coordinates of Mars on the date of opposition.  The relevant coordinate is the Declination (RA/DE J2000 coordinates should be used) – this is the sky coordinate analogous to Latitude on the Earth’s surface.  (Note, it is ok to determine these coordinates for Mars from anywhere on Earth for this initial measurement)

Mars DECLINATION on October 13, 2020: ___________________________

Your lab team needs to send observers to two cities that:

(a) have latitudes that are similar to the declination of Mars on that date (within 20 degrees); and

(b) have nearly the same longitude (that is, are nearly due North-South from each other (hint, you will need to go close to the equator!).

1b). Choose two of the cities below and use google maps, google earth or another online resource to record their names and Latitudes.

1c). At what time should you measure the sky coordinates (right ascension and declination) to get the most accurate possible parallax distance?

The Hernquist density profile is convenient to represent the dark matter halo (See image attached).

a) calculate the cumulative mass M(r)

b) calculate the rotation curve v(r) and make a graph