g = G M/R^2
here R = 525,000 meters
M = 2.59*10^20
G = 6.67 * 10^-11
for part 2 calculus helps
dg/dr = -2R G M /R^4
so
dg = -2 G M/R^3 dr
dg/g = -2 G M/R^3 (R^2/GM) dr
dg/g = -2 dR/R
here dR/R = 22/525
Vesta, a minor planet in the Asteriod Belt between Mars and Jupiter, has a mean radius of 525 km and mass of 2.59 X 10^20 kg. The Dawn Spacecraft (m = 1240 kg) orbited Vesta in 2011 & 2012.
Find the local acceleration due to gravity at the mean surface of Vesta. What is the fractional change if instead you are at the top of the highest point on the surface, an additional 22 km from the center of gravity. Assume all of Vesta's mass is concentrated at its center of gravity.
1 answer
1 answer