## What is a in vis viva equation?

a is the length of the semi-major axis (a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas, and a < 0 for hyperbolas) G is the gravitational constant. M is the mass of the central body.

## How do you calculate orbital trajectory?

The orbit formula, r = (h2/μ)/(1 + e cos θ), gives the position of body m2 in its orbit around m1 as a function of the true anomaly. For many practical reasons we need to be able to determine the position of m2 as a function of time.

**Who came up with Vis Viva?**

Gottfried Wilhelm Leibniz

The vis viva controversy started as a dispute between Gottfried Wilhelm Leibniz (1646–1716) and followers of René Descartes (1596–1650). It continued throughout the 18th century, becoming the topic of several prize competitions.

**How are Hoffman transfers calculated?**

Calculating a Hohmann Transfer

- Introduction: Calculating a Hohmann Transfer.
- Step 1: Gather Supplies.
- Step 2: Find the Planets’ Distances From the Sun.
- Step 4: Convert the Planets Orbital Periods to Seconds.
- Step 5: Compute the Semi-major Axis of the Transfer Orbit.
- Step 6: Find the Period of the Transfer Orbit.

### What is the meaning of vis viva?

: the force of a moving body calculated as the product of its mass and the square of its velocity : twice the kinetic energy.

### What is gravity assist?

The first question is easy—a gravity assist (also called a gravity slingshot) is a space maneuver in which a spacecraft gets a speed boost by moving past a planet. You could also use the gravity assist to slow down or even to change directions. However, in this case let’s just consider boosting the speed.

**Where does the vis viva equation come from?**

In the specific cases of an elliptical or circular orbit, the vis-viva equation may be readily derived from conservation of energy and momentum. Specific total energy is constant throughout the orbit. Thus, using the subscripts a and p to denote apoapsis (apogee) and periapsis (perigee), respectively, where a is the length of the semimajor axis.

**What is the vis viva equation for Keplerian orbit?**

For any Keplerian orbit (elliptic, parabolic, hyperbolic, or radial), the vis-viva equation is as follows: = where: v is the relative speed of the two bodies; r is the distance between the two bodies

#### Can you calculate R and V at any other point?

Given the total mass and the scalars r and v at a single point of the orbit, one can compute r and v at any other point in the orbit. ε {\\displaystyle \\varepsilon \\,\\!}