BACKGROUND INFORMATION : The Dawn spacecraft's mission profile calls for it to study Ceres by orbiting it and taking photos at lower and lower elevations. Its first observational orbit around Ceres occurred in April, 2015. It entered an orbit at an altitude of 13,100 km ABOVE the surface (1.31 x 10^7m) and that circular orbit lasted for about 15 days (1.24 x 10^6 seconds)
Questions:
- What is the mass of Ceres?
- What is Ceres' volume? (hint - use the diameter data of Ceres above)
- What is the average density of Ceres?
- What is the acceleration due to gravity of the surface of Ceres?
- If Dawns final orbit will be 375 km above the surface of the planet what would the escape velocity be for Dawn if it were to leave Ceres' orbit? (Note- that this is not its mission.) Remember that you'll need to add the radius of the planet to the altitude to determine the radius of Dawns orbit.
Please provide ALL work possible
The following equations (formulas) may be needed: eccentricity, universal gravitation, acceleration due to gravity, escape velocity, Kepler's 3rd Law, Kepler's 3rd Law with Newtons update, and Universal Grav and Circ Motion.