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Physics Grav Fields
Physics Spring Y13
| Question | Answer |
|---|---|
| Type of force gravity is | Attractive so always negative. |
| What is G | Universal gravitational constant. |
| What is g | Force per unit mass (G for a specific value of R) |
| When can treat planet as point mass | When not below surface. Exponential curve downwards for g from surface. Straight line from origin to surface on the g vs r graph |
| Gravitational field shape | Radial but we treat it as uniform at the surface |
| Microgravity | g varies slightly around surface. Variation in radius and density can be measured with these g changes. The geoid is the shape the ocean surface would take due to gravity + earths rotation if winds + tides absent. |
| Ellipses | Have a minor axis and a major axis. The shortest/longest lines through centre. They have 2 foci. |
| Kepler's First Law | Planets orbit the sun in elliptical orbits with the sun at one focus. For A level *calculations* we assume circular but not theory. For planets, orbits are very close to circular. |
| Kepler's Second Law | A line joining a planet and the sun sweeps out equal areas during equal intervals of time Higher r but moves slower so same area/time. e.g. comets move very slowly because so far away then move very fast past sun occasionally. |
| Kepler's Third Law | The square of the *orbital period* of a planet is directly proportional to the cube of the *mean* radius of its orbit |
| e.g. Assuming circular orbit show Kepler's Third is true and determine constant | w = 2pi/T F = mrw^2 F = -GMm/r^2 = mr(2pi/T)^2 Cancel and rearrange for T^2 |
| What the Kepler's Third Law constant tells us | Orbital constant depends on the mass of the body being orbited but every orbiting mass has same constant around the same object. For any r, there is only one T. Also for any radius, v is constant. r depends on v. Closer = faster. |
| What the Kepler's Third Law constant tells us (condensed form) | Satellites at same altitude have same speed and orbital period |
| (manmade) Satellites | Purpose varies r. Spy satellites in polar orbit so if r is correct will eventually see whole planet as it rotates. Old SkyTV satellites geostationary with radio dishes but Starlink just a bunch of non-geostationary so less signal delay |
| Signal delay to geostationary | Geostationary satellites are very very far away |
| Speeding up a satellite | Increases its radius and time period as it leaves its orbit (but aren't things slower at higher orbits??) |
| Geostationary orbit | 24hr orbit above equator. 'Hovers' above point on the equator T must be 24hrs therefore all geostationary are same altitude Must be in same direction as earth. |
| Geosynchronous orbit | 24 hour orbit |
| For altitude | Remove planet radius |
| Reference Kepler in Qs | |
| e.g. question gives you r[b]/r[a] and you have to find T[b]/T[a] | rb/ra = 4 (rb/ra)^3 = 4^3 = 64 By Kepler's 3rd Law, (Tb/Ta)^2 = (rb/ra)^3 = 64 Tb/Ta = 8 |
| Technical point about orbiting bodies | Conservation of momentum, so orbits never circular as both bodies orbiting their joint CoM. |
| Joint CoM calculations | But for questions about calculating the gravitational force on one body, you use their separation and the mass of each other not the total, as the orbit is of each other But for the centripetal you still use the radius about the central point I think |
| Finding CoM of 2 bodies | M2/M1 = r1/r2 |
| GPE explanation | Energy an object has as a consequence of its position in a gravitational field Zero when infinitely far from mass. Attractive so always negative - bringing a mass away from another will increase GPE while still being -ve. |
| GPE definition | Work done bringing a mass from infinity to a position in a gravitational field. |
| Gravitational force graph | Force on y axis going down. r on x axis. Curve with reducing gradient. M1 at 0, M2 at R, where F = -GMm/r. The area from R to infinity above the curve is the work done. |
| Gravitational potential | Gravitational potential energy per unit mass at a point in a gravitational field. V(subscript g) = -GM/r GIVE IN JKG^-1 |
| Comments on electric fields | Analagous |
| mgh | Useful for CHANGES in GPE. For relatively small changes in height, assuming g constant. |
| Equipotentials | Plotted lines of constant grav potential around object. For uniform sphere will be spherical. Work done to move between equipotentials given by m*deltaV(subscriptg) Work done along is zero - hence circular motion of orbits |
| How to escape orbit | Need to give equal KE as the GPE so it converts into GPE. Can rearrange into v = sqrt(2GM/r) |
| How to calc mass of earth in exam | g = GM/r |
| Total energy of satellite | KE + GPE = 0.5GPE (negative answer) Negative because in 'bound state' needing extra positive energy to escape |
| How to do black hole calculations | Escape velocity = c |
| Explaining what GPE of -62.7 J means | Talk about how G force is attractive so work done is negative. Say that V(subscript g) is given value zero at infinity so it is negative nearer the earth. |
| Smaller distance effect on GPE easy reminder | Smaller radius means more negative energy, so more energy needed to escape |
| Important graph - Vector sum of g of earth and moon | g on y axis. Earth radius has -9.81 = g. Then curve with reducing gradient, which then curves up near to the moon into an upwards curve. |
| Important graph - Vector sum of GPE of earth and moon | Shallow curve from earth? Then steep curve from moon? What? Then the vector addition means that the point where the curves cross is the bottom of the sum curve. |
| If density constant | r proportional to g |
| Good explanation of GPE of a close satellite lowering in speed as it expands its radius | If thruster forwards, KE increases, causing unstable orbit, so r increases because centripetal too low. This causes GPE to increase. Energy from KE to GPE to allow GE to rise. KE and therefore speed, reduces |
| 'Expression for centripetal force' | Using circular motion formulas, not just repeating gravitation answer |
| K3L | Can only use if R2 is near to zero (one small mass around big) |
| Proving KE = 1/2 GPE | F = mv^2/r = GMm/r^2 v^2 = GM/r KE = GMm/2r |
| Why satellite needs to gain a lot of energy to get into orbit (much more than just the GPE) | KE = 1/2 GPE so will need to increase from zero to half of the total GPE (very high number). Only true if launching from poles, however |
| 'Prograde orbit' | In direction of spin: most KE gain. Retrograde needs much more energy to launch to reverse starting intertia |
| Issue with even prograde orbit | Compare energy from earth spin (small) to energy needed to gain (big when GPE + KE). So needs self-propulsion |
| Kepler's First Law | Orbit is elliptical with [body being orbited - be specific to question] at one focus |
| Why orbiting objects need so much kinetic energy added even if you start them on the equator pt 1 Can be thought about in terms of 'how fast do you have to throw a ball to have it orbit 1mm above the ground' | In order for the weight (as the centripetal force) to form a stable circular motion for the radius we're at, needs very high speed. Normally NCF pushes us up so only a very small amount of our weight is the centripetal, allowing this slow motion |
| Why orbiting objects need so much kinetic energy added even if you start them on the equator pt 2 What happens if the earth was suddenly shrunk to being a point mass at its core? | The stable orbit for the speed we have and the force acting (weight) has a very, very low radius, so we fall towards the core of the earth in order for circular motion to then happen (dont phrase the falling as part of cm) |
| Why orbiting objects need so much kinetic energy added even if you start them on the equator pt 3 Why do we need thrusters on rockets? | For their weight to act as the centripetal force of a stable orbit, their velocity must increase massively, especially more for a very low orbit, so they need lots more KE until KE = -1/2 GPE |
Created by:
Pyrogearos2