Question

Modern Physics

Problem 9. Satellites can exist in orbits as shown in the diagram. The satellite of mass m is at what is referred to as the L1 point or the first Lagrange point. At this extremely specific location,the satellite will orbit the Sun with the exact same period as the Earth. Given that the satellite is closer to the Sun than the Earth is, you would normally expect the satellite to have a shorter period. However, the satellite is influenced by gravitational forces from the Sun and the Earth.The combination of those forces leads to the same orbital period as the Earth when the satellite is at just the right distance from the Sun. (a) Write out Newton's 2nd Law for the satellite. Your expression must be written in terms of G, M sun, M Earth, R, d and T where T is the Earth's orbital period. This expression could be solved for the distance d. Do not attempt to do that since you would obtain a fifth order polynomial for d. (b) Is this satellite in a stable or unstable orbit? In other words, if it is slightly perturbed (for example, imagine that it is pushed slightly closer to the Sun), would it continue to orbit with the same period as the Earth? Explain.

Note that the Solar & Heliospheric Observatory (SOHO) is at the L1 point.

Verified

### Question 52422

Modern Physics

1A cruiser moves away from the planet Hoth at a speed of 0.5c. A frigate follows, catching up at a speed of 0.25c as viewed from the cruiser. With what speed does the frigate appear to be moving according to observers on the planet? You should use the relativistic velocity transformation, clearly defining all the parameters used.
u^{\prime}=\frac{u-v}{1-\frac{u v}{c^{2}}}

### Question 44658

Modern Physics

Question 5: A spaceman goes out on a trip. First, he travels at 1/3 the speed of light in one direction. Then he comes back home at 2/3 of the speed of light. On Earth 9 years have passed,by how much has the spaceman aged? (Make sure you draw a space-time diagram).

### Question 44657

Modern Physics

Question 4: The typical pole for pole vaulting is 17 feet long. How fast would a pole vaulter have to run (in the direction of the pole) in order for a spectator sitting in the stands to see it 15feet long?

### Question 44656

Modern Physics

Question 3: If you weigh 150 lb in Chicago, how much do you weigh on top of mount Everest?(mount Everest is 8,848 m high).

### Question 44655

Modern Physics

Question 2: As a result of an explosion a stationary object breaks into three pieces. One piece flies east, one west and one north.
Explain why this is impossible.
Now, there are only two pieces; one flies east the other west. One piece weighs three times as much as the other. What is the ratio of the kinetic energies of the two pieces?

### Question 44654

Modern Physics

Question 1: The international Space Station (ISS) orbits the Earth once every 90 mins at an-altitude of 409 km. How high would it have to be in order to be to be in geosynchronous orbit?(make sure you show how you worked it out).

### Question 44179

Modern Physics

Question 6: A "star" made of ideal gas radiates away 10% of its energy while remaining in hydrostatic balance. Assuming that there are no nuclear reactions
Does the radius of the "star" increases or decreases? By how much?
Does the (average) temperature of the "star" increases or decreases? By how much?

### Question 44178

Modern Physics

5: There are two stars, one has twice the luminosity of the other and half the radius.
What is the ratio of their temperatures?
What is the ratio of their (apparent) brightness if the more luminous one is 100 times more distant than the other.

### Question 44177

Modern Physics

Question 4: According to general relativity people who live in hi-rise buildings age at differentrates depending on their floor.
Is that true?
Which floor ages fastest?

### Question 44176

Modern Physics

Question 3: Consider two time-like events P and Q. P is at the space-time origin P=(0,0); Q is at the space origin but one second later Q=(0,1).
Show that the order of events is preserved by all observers travelling at less than the speed of light.
Now events P and Q are space-like. P is still at the origin, but Q is simultaneous with P but one meter to the right 0=(1.0)
.Show that the order of events is not preserved by observers travelling at less than the speed of light.