Astronomy - USA (2020-06)

6 ASTRONOMY • JUNE 2020

ASTRO LETTERS

Desert memories

Thank you so much

for Stephen O’Meara’s

March article, “The

lunar blackdrop

ef fect.” In November,

we were in the Namib

Desert, watching

the daily show of

Jupiter passing

Venus in the west,

when our talented,

knowledgeable, and

obviously observant guide spotted the youngest Moon

either of us have ever seen. Although I was practically

shaking with excitement, I was still able to capture a

few handheld shots. Again, thank you for reigniting

my excitement for those moments! — Bob Goren,

Wynnewood, PA

Weighing black holes

The Ask Astro answer on page 68 of the March issue

states that Kepler’s laws of motion are used to measure

mass. In reviewing the three laws, I did not find

a reference to mass. I am guessing that other laws

are used in the calculation of mass? — Bruce Maier,

Shoreham, NY

From Senior Associate Editor Alison Klesman:

You are correct that Kepler’s laws don’t mention mass.

The step our answer left out is that one can apply

Newton’s work to Kepler’s third law to calculate mass.

Kepler’s third law of motion states that P^2 α a^3 , which

means that the period (P) of an orbiting object is

proportional to the distance at which it orbits (a is the

semi-major axis, or distance between the center and

farthest point, of an ellipse). Newton’s work shows that,

thanks to gravity, mass also comes into play. So, Kepler’s

third law can also be written this way:

P^2 =[4π^2 /(G(m 1 +m 2 ))]a^3

G is the gravitational constant, while m 1 and m 2 are the

masses of the two objects in question (e.g., a neutron

star and a black hole). Using this form of Kepler’s third

law, astronomers can make observations of the system’s

properties and determine the masses of the objects.

The Namib Desert, southern Africa

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name, city, state, and

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and clarity.

SER

GI^ F

ERR

ETE

/UN

SPL

ASH

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