Astronomy math tips

SCI 224 - Scientific Equations Study Guide

Scientific Equations Study Guide
Week 1

Gravitational Force
Calculate the gravitational force between a 1000 kg object and a 1300 kg object separated by a distance of 5 m.
Solution:

Circular Speed
Calculate the circular speed of an object that orbits the Sun at a distance of 6.7 AU.
Solution:
The astronomical unit 1 AU = 1.5 × 1011 m
The solar mass M = 1.989 × 1030 kg

SCI 224 - Scientific Equations Study Guide

Week 2
Wien’s Law
What is the temperature of a star whose brightness peaks at 480 nm?
Solution:
The Wien’s Law constant is 2.9 × 10-3 m K
= 480 nm = 4.8 × 10-7 m

The Average Speed of a Molecule
Calculate the average speed of a nitrogen molecule (mass is 4.7 × 10-26 kg) at temperature 320 K.
Solution:
The Boltzmann’s constant k = 1.38 × 10-23 kg m2/K s2

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SCI 224 - Scientific Equations Study Guide

Week 3

Density of a Gas
What is the density of a gas that has a temperature of 300K and its atmospheric pressure is
1.5 × 105 Pa?
Solution:
P=nkT

The Stefan-Boltzmann Law
What is the electromagnetic flux coming from the surface of a 4500K blackbody?
Solution:
The Stefan-Boltzmann constant
E=

= 5.67 × 10-8 W/ m2K4

T4

E = 5.67 × 10-8 × 45004 = 2.3 × 107 W/m2

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SCI 224 - Scientific Equations Study Guide

Week 4

Kepler’s Third Law
A small rock is orbiting the asteroid ABC1 at a distance of 11,500 meters and with an orbital period of 18,000 seconds. Calculate the mass of ABC1.
Solution:
P = 18000 s a = 11500 m

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SCI 224 - Scientific Equations Study Guide

Week 5
Parallax and Distance
What is the distance in parsecs of an object that has a parallax angle of 0.15 arcseconds?
Solution:

Luminosity and Absolute Magnitude
What is the apparent magnitude of a star with an absolute magnitude of 8.0 located at distance of
15.0 parsecs?

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SCI 224 - Scientific Equations Study Guide

Week 6
Resolution of a Telescope
What is the