Examples for


Astrophysics is a branch of astronomy that focuses on the inherent nature of celestial objects but often excludes the mechanics of their motions. It covers topics like studies of stellar spectra, stellar evolution and cosmology, among other topics.


The luminosity, a measure of power output, of a star can be derived from the mass, distance and apparent magnitude and vice versa. Other properties can also be inferred from the luminosity.

Compute the luminosity of a star of specified mass:

Compute luminosity from apparent magnitude and distance:

Black Holes

The properties of a black hole are determined primarily by its mass and type.

Compute properties of a black hole:

Compute properties of a rotating black hole:


Due to the expansion of the universe caused by the Big Bang, the properties of the universe have changed over time.

Compute cosmological properties of the universe:

Compute cosmological properties, given a redshift:

Asteroid Impacts

Asteroid impacts are dependent on many factors that can affect the properties of the resulting crater and many other effects.

Calculate the outcome of an asteroid impact:


Step-by-Step Solutions for Physics


  • Celestial Mechanics
  • Physics
  • Space & Astronomy
  • Cosmic Rays

    Cosmic ray exposure can be significant at higher elevations, especially for long periods of time.

    Find out how many cosmic rays reach Earth: