What are the four equations on page 1 of the Earth Science Reference Tables?

Page 1 of the ESRT gives four equations the Regents tests every administration: eccentricity equals the distance between the foci divided by the length of the major axis; gradient equals the change in field value divided by the distance; rate of change equals the change in value divided by the time; and density equals mass divided by volume. Learn the layout of each, always substitute with units, and remember that eccentricity is unitless. Show the equation, the substitution and the final answer with units to earn full points on constructed-response questions.

Is eccentricity unitless on the Earth Science Regents?

Yes. Eccentricity is the distance between the foci divided by the length of the major axis, and because both are lengths in the same unit, the units cancel and the answer has no unit. It is a number between 0 (a perfect circle) and just under 1 (a very flattened ellipse). Round to the nearest thousandth unless told otherwise, and never write a unit such as cm on an eccentricity answer.

How fast does Earth rotate according to the Reference Tables?

Earth rotates 360 degrees in 24 hours, which is 15 degrees per hour. This constant appears constantly on the Regents: the Sun's apparent motion across the sky is about 15 degrees per hour, and one hour of time difference corresponds to 15 degrees of longitude. Many questions ask you to use this rate to find a rate of change of the Sun's altitude or a difference in longitude.

How do you use the Luminosity and Temperature of Stars diagram?

The Luminosity and Temperature of Stars diagram (a Hertzsprung-Russell diagram) plots stars by surface temperature (hottest on the left) and luminosity (brightest at the top). Most stars, including the Sun, lie on the diagonal main sequence. Giants and supergiants are cool but very luminous (upper right, so very large); white dwarfs are hot but dim (lower left, so very small). Use a star's position to read its type, temperature, color and relative size, and remember the temperature axis increases to the left.

Why is learning the Reference Tables worth so much on the Regents?

A large share of Part B-1, Part B-2 and Part C questions are written so that correct use of the Reference Tables is essential. The tables hold the equations, the planetary and star data, the New York landscape and bedrock maps, the rock identification schemes, the earthquake travel-time graph, the particle-size graph, the dewpoint and humidity tables and the geologic time scale. Knowing where each is and how to read it can be the difference of many marks, so practice with the tables open until finding and using each page is automatic.

New YorkEarth and Environmental Science

Reading the Earth Science Reference Tables (ESRT): astronomy, the four equations, and the graphs every NY Regents student must master

A deep-dive guide to the Earth Science Reference Tables (ESRT) for the NY Regents: where everything is, the four page-1 equations (eccentricity, gradient, rate of change, density) with worked layouts, the astronomy data (planets, stars, Earth's rotation), and how to read the key graphs so you earn the Reference Tables marks every administration.

Generated by Claude Opus 4.818 min readESCI-ESRTUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

Why the Reference Tables decide your grade
The four equations on page 1
The astronomy data pages
The graphs and maps to rehearse
A worked astronomy calculation set
Check your knowledge

Why the Reference Tables decide your grade

The Earth Science Reference Tables (ESRT) are the most important pages you will hold during the Regents. NYSED writes a large share of Part B-1, Part B-2 and Part C so that correct use of the tables is essential. If you know where each page is and how to read it, you collect marks that students who never opened the booklet simply leave behind. This guide walks through the astronomy data and, above all, the four equations on page 1, with layouts you can copy under pressure.

It ties together the astronomy dot-point pages, each with its own practice questions: Earth's motions and the celestial sphere, eccentricity and the shape of orbits, insolation and the seasons, the solar system and Kepler's laws and stars, the Sun and the origin of the universe.

The four equations on page 1

Every administration tests these. Master the layout of each, and always show the equation, the substitution with units, and the final answer with units.

Eccentricity

\text{eccentricity} = \frac{\text{distance between foci}}{\text{length of major axis}}

The answer is unitless (the lengths cancel) and lies between 0 (a circle) and just under 1 (very flattened). Round to the nearest thousandth. For example, foci 4.0 cm apart on a major axis of 20.0 cm give $\dfrac{4.0}{20.0} = 0.200$ .

Gradient

\text{gradient} = \frac{\text{change in field value}}{\text{distance}}

Used on topographic and field maps. Units are things like m/km or degrees Celsius per km. For example, a 60 m drop over 4.0 km is a gradient of $\dfrac{60\ \text{m}}{4.0\ \text{km}} = 15\ \text{m/km}$ .

Rate of change

\text{rate of change} = \frac{\text{change in value}}{\text{time}}

Used for any quantity changing over time: temperature in degrees Celsius per hour, sea-floor spreading in cm per year, the Sun's altitude in degrees per hour. For example, a 12 degree Celsius rise over 8 hours is $\dfrac{12}{8} = 1.5$ degrees Celsius per hour.

Density

\text{density} = \frac{\text{mass}}{\text{volume}}

Common units are g/cm cubed. A key Regents idea: the density of a given substance is constant (at the same temperature and pressure), so cutting a rock in half leaves each piece with the same density. For example, 80.0 g in 20.0 cm cubed is $\dfrac{80.0}{20.0} = 4.0$ g/cm cubed.

The astronomy data pages

Earth's rotation rate

Earth rotates 360 degrees in 24 hours = 15 degrees per hour. The Sun appears to move across the sky at this rate, and one hour of time difference equals 15 degrees of longitude. So if two places differ by 45 degrees of longitude, their solar time differs by $\dfrac{45}{15} = 3$ hours.

Selected Properties of the Planets

Read across the table to compare planets. The pattern to remember (Kepler's third law): as distance from the Sun increases, the period of revolution increases and the orbital velocity decreases. Mercury is closest, fastest and shortest-period; Neptune is farthest, slowest and longest-period.

Luminosity and Temperature of Stars

This Hertzsprung-Russell diagram plots temperature (hottest on the left) against luminosity (brightest at the top). Most stars, including the Sun, lie on the diagonal main sequence. Giants and supergiants (upper right) are cool but very luminous, so very large; white dwarfs (lower left) are hot but dim, so very small. Color shows temperature: blue hottest, red coolest.

The graphs and maps to rehearse

Beyond astronomy, the Regents leans on several other Reference Tables pages. Know how to read each:

Earthquake P-wave and S-wave travel time: find the S-minus-P time difference to read epicenter distance, then use the P-wave travel time to find the origin time.
Relationship of transported particle size to water velocity: larger particles need faster water to stay moving; as a stream slows, the largest particles are deposited first.
Generalized Landscape Regions and Generalized Bedrock Geology of New York State: match a location to its landscape region, and read bedrock type and age.
Dewpoint and relative humidity tables: use the dry-bulb temperature and the wet-bulb depression to read dewpoint and relative humidity.
Geologic Time Scale and the radioactive decay data: count half-lives (Carbon-14 is 5700 years) and read major events and index fossils.

A worked astronomy calculation set

Three page-1 calculations

Work each using the page-1 equations, showing the layout.

step 1 Eccentricity

An orbit has foci 2.4 cm apart and a major axis of 12.0 cm. $\text{eccentricity} = \dfrac{2.4\ \text{cm}}{12.0\ \text{cm}} = 0.200$ (unitless, to the nearest thousandth).

step 2 Rate of change of the Sun's altitude

The Sun rises from 20 degrees at 8 a.m. to 50 degrees at 10 a.m. $\text{rate} = \dfrac{50^\circ - 20^\circ}{2\ \text{h}} = \dfrac{30^\circ}{2\ \text{h}} = 15^\circ \text{ per hour}$ , matching Earth's rotation.

step 3 Density of a mineral

A mineral has mass 75 g and volume 25 cm cubed. $\text{density} = \dfrac{75\ \text{g}}{25\ \text{cm}^3} = 3.0\ \text{g/cm}^3$ . Cutting it in half leaves each piece at 3.0 g/cm cubed (density is constant).

Check your knowledge

Attempt these with the Reference Tables open, then check against the solutions.

State the four equations on page 1 of the Reference Tables. (4 marks)
An ellipse has foci 5.0 cm apart and a major axis of 20.0 cm. Calculate the eccentricity. (2 marks)
Two points on a map differ by 90 m in elevation over 3.0 km. Calculate the gradient. (2 marks)
The Sun's altitude rises 45 degrees in 3 hours. Calculate the rate of change and state what it matches. (2 marks)
A rock has a mass of 60 g and a volume of 30 cm cubed. Calculate the density, and state the density of a piece half its size. (2 marks)
State Earth's rate of rotation and use it to find the solar time difference for 60 degrees of longitude. (2 marks)
On the star diagram, where do white dwarfs lie and what does that tell you about their size? (2 marks)

Solutions

Q1: Eccentricity = distance between foci over length of major axis; gradient = change in field value over distance; rate of change = change in value over time; density = mass over volume.
Q2: $\dfrac{5.0}{20.0} = 0.250$ (unitless).
Q3: $\dfrac{90\ \text{m}}{3.0\ \text{km}} = 30\ \text{m/km}$ .
Q4: $\dfrac{45^\circ}{3\ \text{h}} = 15^\circ$ per hour, which matches Earth's rotation rate.
Q5: $\dfrac{60\ \text{g}}{30\ \text{cm}^3} = 2.0\ \text{g/cm}^3$ ; a half-size piece has the same density, 2.0 g/cm cubed.
Q6: Earth rotates 15 degrees per hour, so $\dfrac{60^\circ}{15^\circ \text{ per hour}} = 4$ hours.
Q7: White dwarfs lie in the lower left (hot but dim), which means they must be very small to give off so little light despite a high temperature.

Sources & how we know this

Reference Tables for Physical Setting/Earth Science (2011 edition) — New York State Education Department (2011)
Regents Examination in Physical Setting/Earth Science — New York State Education Department (2026)