Calculating mass of an orbiting body

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In summary, the conversation discusses calculating the distance and orbit of a star and its companion. The distance between the two was found to be 1.11x1010m and the radius of the orbit was calculated using the formula r = vt/2∏, resulting in 1.4x108m. The radius of the companion's orbit was also found to be 1.096x1010m. The conversation then mentions using a formula to find the mass of the companion, but the resulting answer of 5.47x1027kg seemed incorrect. It is noted that the observed magnitude of the oscillation in radial speed will be twice the actual orbital speed due to the difference in speed when heading away from and toward
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MegaDeth
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The Attempt at a Solution



I found out the distance between the star and companion which I calculated as 1.11x1010m (Ignoring the mass of the companion).Then I calculated the radius of the stars orbit, using r = vt/2∏ since vt = circumference. It turned out as1.4x108m. Then I simply found the radius of the companions orbit which was 1.096x1010m. I then used r2 = m1(m1) + m2 x d and then manipulated it to make m2 the subject. But my answer came out as 5.47x1027kg. Which I assume is wrong since it's supposed to be much less than the mass of the star.
 
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Remember that, assuming that we're observing the star\planet system edge on, the observed magnitude of the oscillation in radial speed is going to be twice that of the actual orbital speed of the star. Why? Because it's the difference between the observed speed when it's directly heading away from and when it's directly heading toward the observer.
 

1. How do you calculate the mass of an orbiting body?

To calculate the mass of an orbiting body, you will need to know the period of its orbit (the time it takes to complete one full revolution around the object it is orbiting) and the distance between the orbiting body and the object it is orbiting. You can then use the formula M = 4π²r³/GT², where M is the mass of the object being orbited, r is the distance between the two objects, G is the gravitational constant, and T is the period of the orbit.

2. What is the gravitational constant?

The gravitational constant, denoted by G, is a fundamental constant in physics that represents the strength of the force of gravity between two objects. It is approximately equal to 6.674 x 10^-11 Nm²/kg².

3. Can the mass of an orbiting body change?

Yes, the mass of an orbiting body can change over time. This can occur due to factors such as gaining or losing material, collisions with other objects, or interactions with other forces.

4. How accurate is the calculated mass of an orbiting body?

The accuracy of the calculated mass of an orbiting body depends on the accuracy of the values used in the calculation, such as the period of the orbit and the distance between the objects. Additionally, the accuracy may be affected by any external factors or uncertainties. However, with precise measurements and accurate calculations, the calculated mass can be very accurate.

5. Are there any other methods to determine the mass of an orbiting body?

Yes, there are other methods to determine the mass of an orbiting body, such as analyzing the gravitational interactions between multiple orbiting bodies or using observations from telescopes or other instruments to study the object's movements and properties. However, the method of calculating the mass using the orbital period and distance is a commonly used and reliable approach.

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