Date | May 2021 | Marks available | 2 | Reference code | 21M.2.HL.TZ2.10 |
Level | Higher level | Paper | Paper 2 | Time zone | 2 |
Command term | Calculate | Question number | 10 | Adapted from | N/A |
Question
The table gives data for Jupiter and three of its moons, including the radius r of each object.
A spacecraft is to be sent from IoIo to infinity.
Calculate, for the surface of IoIo, the gravitational field strength gIo due to the mass of IoIo. State an appropriate unit for your answer.
Show that the gravitational potential due to Jupiter at the orbit of Io gravitational potential due to Io at the surface of Iogravitational potential due to Jupiter at the orbit of Io gravitational potential due to Io at the surface of Io is about 80.
Outline, using (b)(i), why it is not correct to use the equation √2G×mass of Ioradius of Io√2G×mass of Ioradius of Io to calculate the speed required for the spacecraft to reach infinity from the surface of IoIo.
An engineer needs to move a space probe of mass 3600 kg from Ganymede to Callisto. Calculate the energy required to move the probe from the orbital radius of Ganymede to the orbital radius of Callisto. Ignore the mass of the moons in your calculation.
Markscheme
«GMr2=6.67×10-11×8.9×1022(1.8×106)2=»1.8 ✓
N kg−1 OR m s−2 ✓
1.9×10274.9×108 AND 8.9×10221.8×106 seen ✓
«1.9×1027×1.8×1064.9×108×8.9×1022=»78 ✓
For MP1, potentials can be seen individually or as a ratio.
«this is the escape speed for Io alone but» gravitational potential / field of Jupiter must be taken into account ✓
OWTTE
-GMJupiter(11.88×109-11.06×109)=«5.21×107 J kg-1» ✓
« multiplies by 3600 kg to get » 1.9 × 1011 «J» ✓
Award [2] marks if factor of ½ used, taking into account orbital kinetic energies, leading to a final answer of 9.4 x 1010 «J».
Allow ECF from MP1
Award [2] marks for a bald correct answer.