Homework Set 2

(Do after studying the lessons on The Gravity Field)

Explain in detail why the force of gravity is greater at the poles than at the equator.
Using values of a = 6,378,136.5 m GM = 3,986,005 ´ 10⁸ m³/sec², f = 1/298.256, and ω = 7,292,115 ´ 10⁻¹¹ rad/sec, what is the value of m in the generalized equation for the normal gravity field? Hint: b = a(1 − f)
Using the equation for the normal gravity field as adopted by the IAG in 1980, what is the normal gravity at a geodetic location of f = 42°16'44.0837" N; l = 75°58'12.3594" W, h = 379.124 m? If the observed gravity value at this location is 980.324 gals, what is the gravity anomaly at this point?
Using the g_e = 978,327.8 mgal and the positional data given in Problem 3 and a predicted model gravity value from NGS, what is the separation in the equipotential surfaces at the equator? If the gravity value at the pole g_p is 983,218.5 mgal, what is the separation of the equipotential surfaces at the pole?
Using the Geoid03 model, what is the geoid height for the point in Problem 3?
What the x and h for the point in Problem 3?
Compute the angular velocity, w, for the WGS84 ellipsoid?
The last ice-age occurred some 20,000 years ago. Discuss the effect of this ice age on the geoid, and how this affects surveying today. Search the Internet for this answer.
Given an observed astronomic azimuth of 83°16'52.01" that was measured at the point in Problem 3 on 2004.68, what is the azimuth corrected for deflection of the vertical? The observed zenith angle at the of the observation was 92°13'23.5".

(Bonus question)
1. Correct the azimuth in Problem 9 for the instantaneous spin axis. Assume the observation was made on August 28, 2006. (Remember the units are in seconds.)