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How to Calculate the Beta Angle

Beta angles provide information about the absorption of solar energy by satellites, space shuttles and anything else in orbit. According to the NASA, the beta angle is "the angle measured between the sun vector and the orbital plane of any Earth-orbiting object." You can use the beta angle equation if you have certain information regarding right ascension, declination and velocity vector or use an online beta angle calculator to make the calculation easier.

Instructions

Online Beta Angle Calculator
- 1
  Visit Johns Hopkins University's FUSE website -- a slit position angle and beta angle calculator is available.
- 2
  Enter the following information into the input fields: right ascension, declination, start date, time, time step and number of steps. Right ascension must be in HH:MM:SS.SS format and declination in DD:MM:SS.S format.
- 3
  Press the "Calculate Beta and Roll Angles" button.
Beta Angle Equation
- 4
  Calculate the geocentric unit position vector of the sun, respectively. To find this, you'll need the sine and cosine of the right ascension, as well as the sine and cosine of the declination of the sun.
- 5
  Calculate the unit angular momentum vector of the object's orbit. This is the cross product of the velocity vector and the unit position.
- 6
  Multiply the geocentric unit position vector of the sun by the unit angular momentum vector of the object's orbit. Take the inverse sine -- sin-1 -- of this product to calculate the beta angle.

Astronomy