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EQUATION SHEET - FIRST MID-TERM
Astronomy 103, Fall 2007
Prof. Alex Lazarian, TA Katie Devine
The following equations come from your homework, with a few extras thrown in for good measure. When in doubt about how to use an equation or what it means, consult your book for more information!
ALWAYS CHECK UNITS TO MAKE SURE YOUR ANSWERS MAKE SENSE!
- Circumference of a Circle:
C = 2πR
C is Circumference R is the Radius of the circle
- Angular size vs. Real Size
360 Aoo^ =^ CL
or
L = d ∗ 57 A. 3 o
A is the number of degrees (the Angle) an object covers on the sky L is the real size of the object C is the circumference of the circle on the celestial sphere at distance d d is the distance to the object
- Kepler’s Third Law
P 2 = A^3
P is orbital period in Years
A is orbital distance (semimajor axis) in AU
Modified Kepler’s Third Law:
MA + MB = PA 32 ((AUY R^ ))
MA and MB are the masses of two bodies orbiting each other P is orbital period in Years A is orbital distance between the two bodies in AU
- Force and Acceleration
F = Ma
F is force M is the mass of the object acted on by the force a is the acceleration the mass gets from the force
a = V T^11 −−VT^22 a is the acceleration
V 1 is the initial velocity V 2 is the final velocity T 1 is the initial time T 2 is the final time so, V 1 − V 2 is the change in velocity and T 1 − T 2 is the change in time
- Force from gravity (Universal Law of Gravity)
Fgravity = mM G d 2
Fgravity is Force of gravity between two objects m is the mass of one of the objects M is the mass of the other object
V =
√GM
R V is orbital velocity G is gravitational constant M is mass of object being orbited R is the radius of the orbit
- Escape Velocity
Vesc =
2 GM R V is escape velocity G is gravitational constant M is mass of object being escaped R is the radius of the planet/object being escaped
- Energy
EK = 12 mV 2
EK is the Kinetic Energy of an object m is mass of the object V is the velocity of the object
EP = −GmM d
EP is the Potential Energy of an object m is the mass of the object with gravitational potential energy M is mass of the object giving gravitation potential energy G is gravitational constant d is distance between center of mass m and mass M
- Angular Momentum
L = mvr
L is the angular momentum of an object in a circular orbit m is the mass of the object r is the radius of the orbit
