A comet is going in a parabolic orbit lying in the plane of the Earth's orbit....
Suppose a comet travels on a parabolic orbit around the Sun. (i) Show that in this case the following holds: 1 k mji? + kro p2 0 T where k = GM,m and M. is the mass of the Sun. (ii) Starting from the result in part (i), show that the radial distance as a function of time from the moment of closest approach to the Sun is given by t(r) = 2 -(r + 2ro) Vr-TO 9GM,
Accidently uploaded the photo in a recent question and need help solving this one. 3. Earth's orbit. The Earth, with mass m and angular momentum L, moves around the Sun in arn elliptic orbit of eccentricity e. The equation of trajectory is given by, r=p1+ecoso 1+e where p is the distance of the closest approach to the Sun (perihelion) (a) Find the two components of the velocity as functions ofQie, v,(9) and vo(9). (8 marks) (b) Prove that the angle...
3) Suppose we have a hoop lying centered at (0, 0, 0) on the xx-plane, of radius "a, now remove the top half of the hoop (ask for a picture if necessary). It should have points at (a, 0, 0), (a, 0, 0), and (0,-a, 0). The object holds a charge of +Q distributed uniformly around it. Determine the electric field at a point P a distance z from its center at (0, 0, z). Write the resulting formulas for...
014 (part 1 of 2) 10.0 points Ever since it was learned that an aster- oid hit the earth 65 million years ago and destroyed most life-forms, including the di- nosaurs, observations of new comets are fol- lowed with great interest! Suppose a new comet is found orbiting the sun as it is pass- ing its point of closest approach at a distance Tmin 0.658 AU (1 AU-semimajor axis (average radius) of the Earth's orbit.) Careful studies determine that its...
1. This quasi-"walkthrough" problem is great practice in cross-products, vectors, and integration. Consider the current loop shown in Figure 2, with B _Bx, and the loop lying in the x - z plane of the page (y points into the page). We wish to find the net torque on this current loop. we'll do this by integrating in θ, the angle shown (a) We'll start with a little segment dl at point p as shown in the figure. What is...
need help Find the length of the curve defined by the parametric equations y3In(t/4)2-1) from t 5 tot- 7 Find the length of parametized curve given by a(t) -0t3 -3t2 + 6t, y(t)1t3 +3t2+ 0t, where t goes from zero to one. Hint: The speed is a quadratic polynomial with integer coefficients. A curve with polar equation 14 7sin θ + 50 cos θ represents a line. Write this line in the given Cartesian form Note: Your answer should be...
7Okn4. Tidal Forces: A comet of mass m and radius R approaches the Sun with a trajectory described by C ( L/Gm2 Mn)-4 x 10° km, and eccentricity e-0.967. Will the comet break apart by tidal forces, or retun another day? (m -2 x 10 kg, R 10 km, MN-2 x 10" kg) Points (20) m! eliptcal trajectory 34 Roche Limit 5). Binary Star System: Consider a planetary system as pictured (not to scale), with the stars in a circular...
Recall that the upper half plane H ((x, y)ly > 0) gives a "model" for hyperbolic space. In this model, distance decreases as one moves up (i.e. the distance between (0, 1) and (1, 1) is 1, the distance between (0,2) and (1,2) is 1/2, and the distance between (0, y) and (1, y) is 1/y. Draw a picture to see that this is strange.) The geodesics on H are given by (1) half circles with center somewhere on the...
An arm ABC lying in a horizontal plane and supported at A (see figure below) is made of two identical solid steel bars AB and BC of length L welded together at a right angle. The arm is subjected to its own weight only. Part 1- Determine the stress state at the top of the bar at the support A. then draw stress distributions for the section at A. (3 points for the drawings) Part 2- Draw Mohr's circle (2...
An arm ABC lying in a horizontal plane and supported at A (see figure below) is made of two identical solid steel bars AB and BC of length L welded together at a right angle. The arm is subjected to its own weight only. Part 1. Determine the stress state at the top of the bar at the support A. then draw stress distributions for the section at A. (3 points for the drawings) Part 2 Draw Mohr's circle (2...