Astronomy Assignment 1 Student Version

8/3/2019 Astronomy Assignment 1 Student Version

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Astronomy – Assignment 1

Due week of 9/29 at the beginning of seminar

Question 1: Mission to Mars

Professor Helfand told a story aboutone of the Apollo missions in which

the time for radio signals to travel from the Moon to Earth and

back played a key role. The Moon is the nearest body in theSolar System; for radio (or any electromagnetic-based)communications from Earth to astronauts or robots on any

other member of the solar system the problem of

communication lag issignificantly worse.

Consider the case of Earthand Mars, the solar system

body that, after the Moon, has hosted the most visitsfrom (robotic) Earthly visitors.

A) Assume the orbits of both Earth and Mars to be

circular and their orbital separations (distance from

the Sun) to be 1.0 Astronomical Unit (AU) and 1.5 AU respectively. Calculate the

communication lag time (roundtrip) both when the two planets are closest and

farthest from one another. (Hints: It may help you to sketch a diagram of their

orbits. Pay attention to your units!)

B) Why might it be especially difficult to communicate with our robotic Martian

explorers when Earth and Mars are at their greatest distance from each other?

What strategy do your calculations in part A suggest for the successful operation of

robotic missions to Mars?

Useful Numbers:

Astronomical Unit (AU): 1 AU = 1.50 x 108

kmSpeed of light: c = 3.0 x 10

8m/s

Solar luminosity: Lsun = 3.8 x 1026

W



Communications are not the only challenge when venturing beyond our Earthly abode.All space missions must also take into consideration sources of power – it’s a long way to

the nearest filling station if the tank runs dry! Most often engineers solve this problemthrough a combination of rechargeable batteries and solar panels. But there’s no place

quite like home.

C) Using the numbers given in part A and above and the appropriate equation(s)

from lecture, determine how much less power (Joules/second or equivalently Watts)

a solar panel provides on Mars compared to Earth. Express your answer as a

percentage of the power the solar panel would provide on Earth. (You may assume

that the atmospheres of Earth and Mars allow roughly the same fraction of sunlight

through. N.B. This assumption is not actually accurate but is an acceptable

simplification for now.)

Launched in 1997 by NASA and ESA(European Space Agency), the Cassini

spacecraft arrived at Saturn in 2004 to begin afour-year mission to study the planet’s

extensive ring and moon system. Now on anextended mission to examine two of Saturn’s

most intriguing moons, Titan and Enceladus,the probe sends back several gigabytes of data

each day to scientists worldwide.

D) Cassini carries an onboard nuclear power supply rather than solar panels. Given

that Saturn is approximately 9.5 AU from the Sun, extend your reasoning from part

C to provide a quantitative explanation why.

Question 2: Climbing the Distance Ladder

Of all the stars in the Universe, we naturally know the most about our own: the Sun.Since we know the distance to the Sun and we can accurately measure its brightness, we

can thus determine its luminosity, or total power output. If we then identify another star like the Sun based on other observable properties (e.g. color, atomic composition, etc.),

we can deduce the luminosity of that star with some confidence – that is, we know it must be similar to the Sun’s.



Suppose we observe a Sun-like star (call it Pollack) in a star cluster (call it John Jay) that

also contains a star (Helfand) whose properties we don’t know. Since they are both inJohn Jay, we know that the stars Pollack and Helfand are in close proximity to one

another. We then observe some distant galaxy (Barnard) that contains many stars with

similar properties to Helfand.

A) Describe in a short paragraph but with as much detail as possible the logical

steps involved in deducing, from the information above, the distance to the galaxy

known as Barnard. (Hint: this process requires at least three steps.)

It is a general fact that we do not know much of anything with complete certainty, andthat also turns out to be true here. Suppose that for stars like the Sun, the true distribution

of luminosities is as shown in the histogram below. (Disclosure: these are not real data,we made them up.)

When we observe a particular Sun-like star (e.g., Pollack), we do not know where it lies

within the above histogram (for more on histograms, see Habits Chapter 3:35-37).Sometimes, as in part A, we must assume that it has the same luminosity as the Sun in

Luminosity (W)

R e l a t i v e n u m b e r o f s u n - l i k e s t a r s p e r b i n

3.5x1026 4.0x1026



order to proceed. However, this is not a perfectly accurate assumption, and it is importantto understand how reliable it is.

B) Use the histogram above to estimate the typical amount by which a Sun-like

star’s true luminosity differs from that of the Sun. This can be thought of as the

standard deviation (see Habits

Chapter 5:20-30) of the histogram and will be anumber in Watts (W). What percentage of the solar luminosity is this? (Hint: to

begin, it may help to draw a vertical line on the plot above marking the luminosity

of the Sun.)

C) The answer to part B gives an estimate of the error we make by assuming that

the star Pollack has exactly the same luminosity as the Sun. Given this, what canyou say about the accuracy of the distance estimate to the Barnard galaxy?

Optional: Express your answer quantitatively if you can.

D) Suppose that we only know of one system like John Jay (i.e., a star cluster

containing both a Sun-like star and a Helfand star) but we know of many galaxies

containing Helfand stars, and we use the Helfand stars to deduce the distances to all

of these galaxies. If the only source of error in these measurements is the one

considered in part B, have we made random errors or systematic errors in the

galaxies’ distances? (See Habits, Chapter 5:20-23.)

Astronomy Assignment 1 Student Version

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